A Search for · would allow to increase up to a factor 100 the statistics presently available....

Scuola di Dottorato “Vito Volterra”

Dottorato di Ricerca in Fisica

A Search for

the Rare Decays B → K∗ννwith the BABAR Detector

Thesis submitted to obtain the degree of

“Dottore di Ricerca” – Philosophiæ DoctorPhD in Physics – XXI cycle – October 2008

by

Francesco Renga

Program Coordinator Thesis Advisors

Prof. Enzo Marinari Dr. Riccardo Faccini

Dr. Gianluca Cavoto

“Philosophe, physicien,Rimeur, bretteur, musicien,Et voyageur aerien,Grand risposteur du tac au tac,Amant aussi – pas pour son bien ! – ”

Edmond Rostand,Cyrano De Bergerac,Acte V, Scene IV

Contents

Introduction VII

1 B → K∗νν in the Standard Model and beyond 11.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 A few notes on renormalization . . . . . . . . . . . . . . . . . . . . . 41.2 Effective lagrangian formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 B → K(∗)νν in the Standard Model and beyond . . . . . . . . . . . . . . . . 9

1.3.1 B → K(∗)νν with non-standard Z couplings . . . . . . . . . . . . . . 111.4 B → K(∗) + invisible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4.1 Light Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.2 Unparticle physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 The BABAR detector and data set 172.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 The PEP-II B-Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3 Tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.1 The silicon vertex tracker . . . . . . . . . . . . . . . . . . . . . . . . 202.3.2 The drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4 Cerenkov light detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5 Electromagnetic calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.6 Instrumented Flux Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.7 Data and Monte Carlo samples . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 The Semileptonic Recoil technique 393.1 Reconstruction of B → D`ν(X) . . . . . . . . . . . . . . . . . . . . . . . . . 393.2 Continuum background rejection . . . . . . . . . . . . . . . . . . . . . . . . 403.3 Tagging performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Reconstruction and selection of B → K∗νν 434.1 K∗ Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Best candidate selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3 Selection of signal events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3.1 Background characterization . . . . . . . . . . . . . . . . . . . . . . . 52

V

4.3.2 Event shape selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.3.3 Signal side selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.3.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.4 Efficiency and background studies . . . . . . . . . . . . . . . . . . . . . . . . 75

5 Control samples 895.1 The Double Tag Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.2 Data-MC Comparison in the Double Tag Sample . . . . . . . . . . . . . . . 905.3 Data-MC comparison in the mD sidebands . . . . . . . . . . . . . . . . . . . 905.4 Data-MC comparison in the mK∗ sidebands . . . . . . . . . . . . . . . . . . 91

6 Results 956.1 Bayesian approach for the BR measurement . . . . . . . . . . . . . . . . . . 956.2 Maximum likelihood fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.2.1 Signal and background shapes . . . . . . . . . . . . . . . . . . . . . . 996.2.2 Fit validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046.2.3 Fit results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.3 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.3.1 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126.3.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126.3.3 Signal yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.4 Final results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7 The b→ s νν and b→ s `+`− decays at a Super B-Factory 1257.1 The SuperB project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1257.2 Recoil analyses: impact of detector improvements . . . . . . . . . . . . . . . 1277.3 Prospects for b→ s νν at SuperB . . . . . . . . . . . . . . . . . . . . . . . . 1297.4 Prospects for b→ s `+`− at SuperB . . . . . . . . . . . . . . . . . . . . . . . 131

8 Phenomenological constraints 1358.1 General approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1358.2 Constraints on NP in Z- and magnetic-penguins from exclusive b→ s decays 137

8.2.1 B → K(∗)νν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1378.2.2 B → K∗`+`− . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1438.2.3 B → K∗γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1478.2.4 Combined constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 1478.2.5 Prospects at SuperB . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

8.3 Constraints on new sources of missing energy . . . . . . . . . . . . . . . . . . 1498.3.1 Light Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Conclusions 153

Acknowledgments 159

VI

Introduction

The Standard Model (SM) of particle physics is currently used to describe properties andinteractions of the elementary particles. In the last decades several experimental studieshave been performed in order to test the validity of the model. The tests confirmed theability of the SM to explain the particle phenomenology, while signals of New Physics (NP)have never been observed. In particular, the precision electroweak measurements at the Zpole [1], along with several other flavour physics measurements [2], show no significant andunambiguous deviation from the SM expectations.

On the other hand, the model looks unsatisfactory from the theoretical point of view.At first, the introduction of a scalar Higgs boson, used to generate the electroweak scale,

destabilizes the scale itself, due to radiative corrections tending to push the Higgs mass at themaximum scale the validity of the SM can be extended to, unless a fine tuned cancellationof the divergences occurs [3].

Moreover, the SM provides poor explanations for the flavour dependence of the particleproperties (masses, number of families, etc.) and the presence of accidental symmetries likethe conservation of the lepton and barion numbers.

Finally, particle physics should hopefully be suitable for the explanation of the cosmo-logical and astrophysical observations, while at present dark matter, dark energy, matter-antimatter asymmetry and other topics cannot be addressed in the SM framework [4].

Thereby, the search for NP effects is the main topic for particle physics in the presentyears. The Large Hadron Collider is just starting operations and looking for new particlesat the TeV scale. In the same time, precision measurements at a lower energy can providealternative handles to explore the same or a higher scale, comparing precise SM expectationsand experimental measurements in order to spot the effect of new virtual states entering atloop level.

Among the low energy phenomena, a particular attention has to be devoted to the pro-cesses mediated by the so-called flavour-changing neutral currents (FCNC). These processes,where the flavour of a quark changes, leaving the electric charge unchanged, are not possiblein the SM at tree level and are allowed at loop level only due to the mass difference betweenthe different quarks that can enter the loops. Hence, they are suppressed in the SM and NPcontributions, even though small, can be competitive. On the other hand, the suppressionmakes these processes particularly rare.

This thesis is devoted to the search for the rare FCNC B0+ → K∗0+νν decays 1, basedon the data collected by the BABAR experiment at the asymmetric e+e− collider PEP-II,

1Charge conjugation is understood here and elsewhere, unless explicitly stated.

VII

operated by the Stanford Linear Accelerator Center (SLAC). We also evaluate the expectedreach (for this and other similar B decay modes) of a new generation of e+e− machines thatwould allow to increase up to a factor 100 the statistics presently available. Finally, we alsostudy the phenomenological implications of these experimental results.

In the first Chapter we give a short introduction to the SM and its interpretation as a lowenergy effective theory which can be extended in order to include effects from a NP emergingmanifestly only at higher scales. We also present the SM predictions for the B → K∗νν decayin the SM and in a few NP scenarios. Notice that, being the two neutrinos undetectablefor this kind of experiments, the experimental signature we look for is B → K∗ + invisible,where the invisible part appears as a missing energy. Hence, exotic scenarios with sourcesof missing energy other than neutrinos can be investigated. We stress here that, for the firsttime, this search has been performed in a model independent way, so that our results canbe actually interpreted in a wide range of NP scenarios.

In Chapter 2 we present the BABAR experiment, giving some details on the differentsubdetectors it is made of.

In Chapter 3 we describe the recoil technique that has been used in this analysis. Since thee+e− collisions at PEP-II take place at the center-of-mass energy of 10.58 GeV, correspondingto the mass of the Υ (4S) resonance, mainly decaying into two B mesons, a large amountof BB pairs are available at BABAR. The recoil technique consists in reconstructing one ofthese two B mesons in a frequent decay mode and looking for the signal signature in therest of the event (the recoil). This method makes it possible to obtain a data sample with asmall amount of non–BB events and only few particles contaminating the signal side. In thiswork we use, in particular, the semileptonic recoil technique, by looking for the B → K∗ννdecays in the recoil of a semileptonic B → D(∗)`ν decay.

In Chapter 4 we explain in detail the techniques used in order to select the signal events.The performances of the analysis, evaluated from simulated events, are also presented andthe simulations are compared with the real data. Control samples used for cross-checks aredescribed in Chapter 5.

The methods adopted in order to measure the B → K∗νν branching ratio from the realdata sample are described in Chapter 6.

Chapter 7 presents the experimental reach, for the B → K (∗)νν, B → K(∗)`+`− and theinclusive B → Xs`

+`− decay modes, of a recently proposed e+e− collider (SuperB), whichwould be able to collect a BB statistics up to 100 times larger than the present one.

Finally, Chapter 8 is devoted to the study of some phenomenological implications thancan be drawn from a few measurements concerning the B → K (∗)νν, B → K(∗)`+`− andB → K∗γ decay modes.

The original work on the basis of this thesis mainly concerns: the refinement of the recoiltechnique previously used for other measurements (Chapters 3); the study of the signalselection, the analysis performances and all the corresponding cross-checks (Chapters 4 and5); the development of the strategies adopted in the extraction of the results from the realdata, along with the corresponding uncertainties (Chapter 6); the estimate of the SuperB

VIII

reach in B → K(∗)νν, B → K(∗)`+`− and B → Xs`+`− (Chapter 7); the evaluation of

the phenomenological impact of some exclusive b→ s decay measurements in some specificscenarios (Chapter 8).

IX

Chapter 1

B → K∗νν in the Standard Model andbeyond

We already pointed out in the introduction that the SM explains quite well the presentexperimental observations but looks unsatisfactory from a theoretical point of view. Inthis chapter, we will give a short introduction to the model (Sec. 1.1) and present a modelindependent formalism allowing to treat the SM as an effective version of a more generaltheory operating at higher scale (Sec. 1.2). This treatment will allow to study the B → K∗ννdecays in the SM and will provide a way to constraint the possible extensions in a modelindependent way.

1.1 The Standard Model

According to the Standard Model of particle physics, matter is constituted by fractional spinparticles called fermions, interacting through the exchange of integer spin particles namedgauge bosons.

Two kind of interactions, strong and electroweak, are described by the SM. Stronglyinteracting fermions are called quarks, while fermions experiencing only the electroweakinteractions are called leptons. The electroweak interaction manifests itself at low energy astwo distinct forces, weak and electromagnetic.

Until now, 6 leptons and 6 quarks have been discovered, while the strong, weak andelectromagnetic interactions have, respectively, 8 gauge bosons (gluons), 3 gauge bosons(W± and Z) and 1 gauge boson (photon). Properties of all known elementary particles arelisted in Tab. 1.1.

Fermions are organized as multiplets of the three groups SU(3), SU(2) and U(1), in sucha way that the interactions can be described in terms of a lagrangian density L, satisfyingthe SU(3)× SU(2)× U(1) symmetry. Quantum cromodynamics (QCD) for strong interac-tions emerges from the SU(3) symmetry, while the SU(2) × U(1) symmetry generates theelectroweak interactions.

For a multiplet Ψ of fermions fields, the transformation under a group G (gauge trans-

1

2 CHAPTER 1. B → K∗νν IN THE STANDARD MODEL AND BEYOND

Table 1.1: Known elementary particles and their properties: approximate mass in MeV,charge in units of the elementary charge, spin. For each fermion, an antifermion exists withopposite charge.

Particle Symbol Mass charge spin Particle Symbol charge spin

LEPTONS QUARKSelectron e 0.511 -1 1/2 down d -1/3 1/2neutrino e νe ∼ 0 0 1/2 up u 2/3 1/2muon µ 106 -1 1/2 strange s -1/3 1/2neutrino µ νµ ∼ 0 0 1/2 charm c 2/3 1/2tau τ 1777 -1 1/2 bottom b -1/3 1/2neutrino τ ντ ∼ 0 0 1/2 top t 2/3 1/2

GAUGE BOSONSW W± 80× 103 ±1 1Z Z 91× 103 0 1photon γ 0 0 1gluons g 0 0 1

formation) is defined by:

Ψ 7→ GΨ , (1.1)

where G ∈ G is usually written in the form G = ei2αi(x)Oi

, being Oi a set of operators calledgenerators of G.

The simplest transformation we can define is ψ 7→ eiαψ, where ψ is a fermion field and αis a constant (this is a transformation belonging to the global U(1) group). The lagrangiandensity 1:

L = ψiγµ∂µψ (1.2)

is invariant under this transformation. When switching to a local U(1) symmetry, i.e. whenintroducing an x dependence of the parameter α, the lagrangian can be kept invariant byreplacing the derivative ∂µ by a covariant derivative Dµ defined by:

Dµ ≡ ∂µ − igAµ(x) . (1.3)

where g is a constant (coupling constant) and Aµ is a new field (gauge field), with a suitablegauge transformation, corresponding to a gauge boson. The formalism can be extended tomore complicated groups like SU(2) and SU(3), by introducing the corresponding generatorsin the transformations and organizing the fermions in multiplets of the gauge groups.

We are mostly interested on the electroweak sector. In order to reproduce the observedparity violation of weak interactions, the SU(2)×U(1) lagrangian is built by classifying thefermions in left handed doublets and right handed singlets of SU(2). Each doublet defines

1In this chapter we adopt the units where h = c = 1.

1.1. THE STANDARD MODEL 3

a flavour family :

ΨL ∈{(

νe

e−

)

L

,

(

νµ

µ−

)

L

,

(

ντ

τ−

)

L

,

(

u′

d′

)

L

,

(

c′

s′

)

L

,

(

t′

b′

)

L

}

, (1.4)

ΨR ∈ {eR, µR, τR, qR} q ∈ {u′, d′, c′, s′, t′, b′} . (1.5)

Here, we indicate the quarks with a primed symbol since the electroweak eigenstates donot necessarily coincide with the mass eigenstates of Tab. 1.1.

Unfortunately, when introducing a mass term in the lagrangian, the SU(2)× U(1) sym-metry is broken. Since the gauge symmetry ensures the physical predictions of the model tobe finite [5], the SM does not contemplate an explicit symmetry breaking but introduces aspontaneous symmetry breaking : a new doublet of scalar fields (Higgs doublet) is introducedand the corresponding invariant lagrangian is written, by introducing a potential that issymmetric under SU(2) × U(1), but whose minimum (corresponding to the vacuum state)has to be chosen among infinite equivalent non-symmetric states. As a result, at low energy,the Higgs field can be replaced in the lagrangian with its vacuum expectation value (v.e.v)plus perturbations around it: the v.e.v. breaks the symmetry and produces mass terms forthe gauge bosons, while perturbations (identified with a Higgs boson) can produce additionalinteractions.

The 3 gauge bosons arising from the SU(2) and the gauge boson arising from U(1) arereplaced by the mass eigenstates W±, Z (massive) and photon (massless), where Z andthe photon are a mix of the U(1) boson and one SU(2) boson. The fermion-fermion-bosoninteractions can be written as:

Lint =g√2

[

u′iγµ 1− γ5

2d′i + νiγ

µ 1− γ5

2ei

]

W+µ + h.c. +

− eJemµ Aµ − g

2 cos θW

JZµ Z

µ, (1.6)

where we defined the neutral currents:

Jemµ =

∑

f

qffγµf , (1.7)

JZµ =

∑

f

fγµ(gfV − gf

Aγ5)f , (1.8)

(1.9)

with:

gfV = I3

f − 2qf sin2 θW , (1.10)

gfA = I3

f . (1.11)

In these equations, u′i ∈ {u′, c′, t′} (up sector), d′i ∈ {d′, s′, b′} (down sector), ei ∈ {e, µ, τ},νi ∈ {νe, νµ, ντ}; f is a generic fermion with electric charge qf and I3

f is the third component


of the weak isospin (+1/2 for ui and νi, −1/2 for di and ei); θW is the Weinberg angle definingthe mixing that produces the Z and the photon. Notice that right handed neutrinos wouldnot interact with anything in this model, so are not introduced in Eq. (1.5).

Yukawa couplings between the Higgs and the fermion doublets are also introduced inorder to produce fermion mass terms from the Higgs vacuum. These coupling can mix theflavour families, so that, as already mentioned, the flavour and mass eigenstates can bedifferent. The diagonalization of the mass matrices requires unitary transformations thatcan be written as:

u′

c′

t′

= UU

uct

,

d′

s′

b′

= UD

dsb

(1.12)

When introducing these transformations in the couplings with the charged W , we get termslike:

(

u′ c′ t′)

γµ(1− γ5)

d′

s′

b′

=(

u c t)

γµ(1− γ5)U †UUD

dsb

. (1.13)

The unitary matrix V = U †UUD in general is not diagonal and is known as the Cabibbo-

Kobayashi-Maskawa (CKM) matrix [6]:

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4) . (1.14)

This matrix introduces couplings among quarks of different families. Notice that the sameoperation for the neutral current interactions gives, for the up sector:

(

u′ c′ t′)

γµ(1− γ5)

u′

c′

t′

=(

u c t)

γµ(1− γ5)U †UUU

uct

. (1.15)

and, given the unitarity of UU , it follows U †UUU = 1 and there is no mixing. The same holds

obviously for the down sector. Flavour-changing neutral currents are then forbidden at treelevel in the SM. They are allowed at loop level thanks to the different quark masses thatavoid exact cancellations of the contributions involving different quarks in the loops.

1.1.1 A few notes on renormalization

It is well known that, when performing calculations with loops, divergent integrals appears.In order to remove these divergences from the theory, they are absorbed in the definitionof the lagrangian fields and parameters (masses and couplings), with a technique calledrenormalization. In other words, the lagrangian depends on the unobservables bare param-eters, while the final results depend only on the renormalized parameters, the only that can

1.2. EFFECTIVE LAGRANGIAN FORMALISM 5

be actually measured (for a mass, for instance, we can write the redefinition in the formm0 = Zmm, being m0 the bare mass and m the renormalized one). Since the divergencesare absorbed in the definition of the renormalized parameters, they do not appear in thefinal result. This procedure introduces in the masses and in the couplings a dependence(called running) on the mass scale µ of the process taken into account. In particular, inthe case of QCD, the coupling αs becomes greater than 1 below a scale ΛQCD ∼ O(1GeV ),precluding the possibility of performing perturbative calculations in this region. Anotherfeature of QCD renormalization is the appearance of terms of the form αn

s (µ0)(log(µ0/µ))m

(m = n, n − 1, . . .), when running the couplings and the masses from a high scale µ0 toa lower scale µ. The large logarithms log(µ0/µ) compensate the smallness of αn

s (µ0) andmake important the impact of higher order terms in any perturbation expansion. In orderto obtain reliable results, the largest logarithms (up to m = n, up to m = n− 1 and so on,according to the required precision of the calculation) need to be summed for all n. It canbe done by means of the renormalization group (RG) equations. Thanks to these equations,the quantities measured at the scale µ0 can be runned down to the scale µ in such a way thatlarge logarithms are automatically summed for all orders. For a mass m(µ) the equation canbe written in the form:

dm(µ)

d logµ= −γm(g(µ))m(µ) , (1.16)

where g(µ) is the coupling and γm(g(µ)) is called anomalous dimension:

γm(g(µ)) =1

Zm

dZm

d logµ. (1.17)

Similar large logarithms log(MW/µ) arise when calculating QCD corrections to the elec-troweak processes, and also in this case RG equations can be written and allow to sum themfor all orders.

1.2 Effective lagrangian formalism

Problems involving multiple energy scales can be often simplified by the introduction of aneffective field theory (EFT). For instance, when treating interactions mediated by a massivegauge boson much heavier than the scale at which the interaction is happening, it is possibleto remove from the theory the degrees of freedom associated to the massive boson.

The general idea is that, at a scale lower than a cut-off Λ, only the low frequency com-ponents of a field can appear in the initial and final state, hence we do not need explicitlythe presence of the high frequency fields in the lagrangian. Formally, one says that thecorresponding degrees of freedom can be “integrated out” of the action integral [7].

The result is that an effective lagrangian can be introduced, depending only on thelow frequency modes, and expanded in terms of all the possible operators satisfying thesymmetries of the original lagrangian:

LeffΛ =

∑

i

ciQi . (1.18)


f

f

f f f

f ff

W

Figure 1.1: Feynman diagrams for the four-fermion weak interaction in the full theory (left)and in the Fermi theory (right).

where the coefficients ci are called Wilson coefficients and are related to the couplings of thefull theory. The operators Qi can be classified according to their dimension. Consideringthat the dimension of the lagrangian has to be 4, we can write:

LeffΛ =

∑

i

Ci

Λdi−4Qi . (1.19)

where Ci is a dimensionless coefficient and di is the dimension of Qi. From “naturalness”arguments, we can say that Ci ∼ O(1), unless some symmetry forces it to be much smaller orlarger. Hence, just few operators with the lower dimensions are important in the lagrangianexpansion.

In this context, assuming that there is some NP at some high scale, the SM itself canbe treated as an EFT, with additional operators and corrections to the Wilson coefficientsintroduced by the NP. Hence, it is interesting to write the SM in the formalism of the EFTs.In doing that, considering that flavour physics is mainly interested on weak interactions atthe GeV scale, we can also integrate out the degrees of freedom associated to the gaugeboson field, by setting a cut-off Λ = MW . This is the spirit of the Fermi theory of weakinteractions, expressed in the modern language of the EFTs. The typical result is that theboson exchange diagram in the left of Fig. 1.1 is replaced by the effective local four-fermioninteraction in the right of the same figure.

Notice that the operators involved in this case are at least of order 6, due to the fourfermions in the final state. So, we expect an M−2

W scaling law for the Wilson coefficients atthe leading order. Hence, it is useful to write the effective lagrangian as:

Leffweak = −GF√

2

∑

CiQi , (1.20)

where GF/√

2 ≡ g2/8M2W and the coefficients Ci are dimensionless for operators with di-

mension 6.At tree level the effective lagrangian for the four-fermion process reads:

Leff4f = −GF√

2J−

µ J+µ , (1.21)

1.2. EFFECTIVE LAGRANGIAN FORMALISM 7

where:

J+µ =

∑

ij

Vij uiγµ(1− γ5)dj +∑

i

νiγµ(1− γ5)ei , J−µ = (J+

µ )† . (1.22)

The Wilson coefficients are computed by means of a matching procedure: the amplitudefor simple processes are calculated in both the full and effective theories and the resultsare compared. Since the Wilson coefficient are process independent, the ones obtainedby matching a specific process can then be used in the calculations for the others. Thisprocedure can be performed including QCD corrections up to the desired order O(αn). Inthis case, new operators arise and their color structure becomes important. Moreover, aQCD renormalization scale µ has to be introduced, of the same order of magnitude of themomenta involved in the process under study. The scale enters the matrix elements of Qi andsuch a dependence is compensated by an analogous dependence in the Wilson coefficients.

Now, an effective hamiltonian can be built. In the SM, the operators to be used can beclassified in 6 categories. In the notation of [8]:

Current-Current Operators:

Q1 = (sicj)V−A (cjbi)V−A Q2 = (sici)V−A (cjbj)V−A (1.23)

QCD-Penguins Operators:

Q3 = (sibi)V−A

∑

q

(qjqj)V−A Q4 = (sibj)V−A

∑

q

(qjqi)V−A (1.24)

Q5 = (sibi)V−A

∑

q

(qjqj)V+A Q6 = (sibj)V−A

∑

q

(qjqi)V+A (1.25)

Electroweak-Penguins Operators:

Q7 =3

2(sibi)V−A

∑

q

eq (qjqj)V+A Q8 =3

2(sibj)V−A

∑

q

eq (qjqi)V+A (1.26)

Q9 =3

2(sibi)V−A

∑

q

eq (qjqj)V−A Q10 =3

2(sibj)V−A

∑

q

eq (qjqi)V−A(1.27)

Magnetic- and Chromomagnetic Penguins Operators:

Q7γ =α

2πmbsiσ

µν(1 + γ5)biFµν Q8G =αs

2πmbsiσ

µν(1 + γ5)TaijbjG

aµν (1.28)

∆S = 2 and ∆B = 2 Operators:

Q(∆S = 2) = (sidi)V −A(sjdj)V −A Q(∆B = 2) = (bidi)V −A(bjdj)V −A(1.29)

Semi-Leptonic Operators:

Q7V = (sidi)V −A(ee)V Q7A = (sidi)V −A(ee)A (1.30)

Q9V = (bisi)V −A(ee)V Q10A = (bisi)V −A(ee)A (1.31)

QνL = (sibi)V −A(νν)V −A Qµ

L = (sibi)V −A(µµ)V −A (1.32)


The examples provided above illustrate only the structure of the operators, while thequark content can change according to the process under study. Here, (ff)V ±A = fγµ(1±γ5)f (indices for quarks indicate the color), mb is the b quark mass, Fµν and Gµν the elec-tromagnetic and the gluon field strength tensors and T a the Gell-Mann matrices.

The effective hamiltonian arising from this set of operators is usually written by makingexplicit the impact of the quark mixing, through the CKM matrix elements:

Heff =GF√

2

∑

i

V iCKMCi(µ)Qi , (1.33)

where the sum runs over all the operators and V iCKM is the suitable CKM factor (V ∗

tsVtb forb→ s transitions). The amplitude for a process will be given by [8]:

A(M → F ) = 〈F |Heff |M〉 =GF√

2

∑

i

V iCKMCi(µ) 〈F |Qi(µ)|M〉 = (1.34)

=∑

i

BiηiQCDV

iCKMFi (1.35)

The last step comes from a rearrangement of the operators, where the master functionsFi’s [9] are linear combinations of the Wilson coefficients at an high scale µ0 ∼ O(Mw, mt),the Bi’s parameterize the corresponding rearrangement of the matrix elements (and ofteninclude non-perturbative effects) and the ηi

QCD’s contain factors summarizing the evolutionof the coefficients from the high to the low scale. Each of the Fi’s (also known as Inami-Limfunctions) represents a precise kind of box or penguin diagrams [10], making the expressionsfor the decay amplitudes more intuitive. For instance, we will have Inami-Lim functionsassociated to the Z0-penguin diagrams (i.e. electroweak and semileptonic penguin diagramsmediated by a Z0 boson), the γ-penguin diagrams (as before, but mediated by a photon),magnetic penguin diagrams and so on.

The Inami-Lim functions can depend in general on a set υ of several parameters, but inthe SM the dominant contributions depend only on xt = m2

t /M2W

2. Hence, we will writeFi(υ) when talking about the general form of these functions, and just Fi(xt) when referringto their SM expressions.

From a practical point of view, the effective hamiltonian can be calculated as follows. Atfirst, one defines the Inami-Lim functions at the high scale µ0 and, with a matching proce-dure, translates them into the Wilson coefficients at the same scale. Since µ0 ∼ O(MW ) �ΛQCD, QCD perturbation theory can be used. At this point, it is possible to write the RGequations for the Wilson coefficients (which assume a form similar to Eq. (1.16)), and usethem to evolve the coefficients from µ0 to µ, with large logarithms automatically summed.Finally, non-perturbative methods have to be used to evaluate the matrix elements at thelow scale. Notice these three features of this method:

1. the possibility of working in a well perturbative regime at MW ;

2. the possibility of resumming large logarithms in the running.

2Here, mt is intended as the renormalized top mass at the µ0 scale.

1.3. B → K(∗)νν IN THE STANDARD MODEL AND BEYOND 9

3. the difficulty of including the scale dependence in the non-perturbative calculations,so that the µ dependence of the Wilson coefficients is not completely compensated andthe final results can show an unphysical µ dependence.

As already anticipated, this formalism make easier the inclusion of NP effects in thetheory. They can appear as:

• Corrections to the master functions;

• New operators not present in the SM;

• New complex phases in the master functions;

• New sources of mixing not controlled by the CKM matrix;

hence, the comparison between experiments and SM predictions can be done by setting someconstraint on:

• Corrections to the master functions or the Wilson coefficients;

• Wilson coefficients of new operators;

• CP violation and mixing effects not expected in the SM.

The failure of the recent NP searches in CP violation and mixing processes forced thetheoreticians to concentrate on models where no new operators, no new phases and no newsources of mixing are present. This scenario, where all NP effects can be parameterizedthrough corrections to the master functions (or equivalently to the SM Wilson coefficients),is called Minimal Flavour Violation (MFV) [11].

1.3 B → K(∗)νν in the Standard Model and beyond

In the SM, the effective hamiltonian for b→ s`+`−(νν) transitions can be written as:

Heff = −GF√2V ∗

tsVtb ×

×[

6∑

i=1

CiQi + C7γQ7γ + C8GQ8G + C9VQ9V + C10AQ10A

+ CνLQ

νL + Cµ

LQµL

]

+ h.c. , (1.36)

with the notations and the quark content of Eqq. 1.23–1.32.


`

ν ν

t, c

WW

b s

W

Zν

ν

t, c

sb

Figure 1.2: SM diagrams for b→ sνν transitions.

The only operator contributing to b→ sνν is QνL. The corresponding Wilson coefficient

has the advantage of being scale independent, and can be directly expressed in terms of theInami-Lim functions as:

CνL|SM =

4B(xt)− C(xt)

sin2 θW

, (1.37)

where the functions B0(xt) and C0(xt) are related, respectively, to the box and Z-penguindiagrams of Fig. 1.2 (left and right, respectively). At the leading order:

B(xt) = B0(xt) =1

4

[

xt

1− xt+

xt ln xt

(xt − 1)2

]

, (1.38)

C(xt) = C0(xt) =xt

8

[

xt − 6

xt − 1+

3xt + 2

(xt − 1)2ln x

]

, (1.39)

Hence CνL|SM ∼ −6.6. The O(αs) expressions can be found in [12]. The gauge independent

combination X(xt) ≡ C(xt)− 4B(xt) is often used [13].Beyond the SM, the b → s`+`−(νν) hamiltonian can be extended including the helicity

flipped counter parts of the SM operators, like for instance:

QνR = (sibi)V +A(νν)V −A (1.40)

Model independent searches for new physics in B → K (∗)νν can be performed by settinglimits on Cν

R (expected to be 0 in the SM) and on the difference between CνL and its SM value

(only this latter deviation can be considered in a MFV scenario). These limits can be set bymeasuring the branching ratios (BR) of the B → K (∗)νν decays. Given the reduced invariantmass of the two neutrinos s ≡ m2

νν/m2B, the differential rates can be written as [14]:

dΓ(B → Kνν)

ds=

G2Fα

2m5B

256π5|V ∗

tsVtb|2 λ3/2K (s)f 2

+(s)|CνL + Cν

R|2 , (1.41)

dΓ(B → K∗νν)

ds=

G2Fα

2m5B

1024π5|V ∗

tsVtb|2 λ1/2K∗ (s)

{

8sλK∗(s)V 2(s)

(1 +√rK∗)2

|CνL + Cν

R|2

+1

rK∗

[

(1 +√rK∗)2 (λK∗(s) + 12rK∗s)A2

1(s) +λ2

K∗(s)A22(s)

(1 +√rK∗)2

− 2λK∗(s)(1− rK∗ − s)A1(s)A2(s)

]

|CνL − Cν

R|2}

.(1.42)

1.3. B → K(∗)νν IN THE STANDARD MODEL AND BEYOND 11

where λH(s) = 1+r2H +s2−2s−2rH−2rHs (H = K, K∗), rH = m2

H/m2B and we introduced

the B → K(∗) form factors defined by:

〈K(pk)|sγµb|B(p)〉 = f+(q2)(p+ pk)µ + f−(q2)qµ , (1.43)

〈K∗(pK, ε)|sγµγ5b|B(p)〉 = 2mK∗A0(q2)ε∗ · qq2

qµ + (mB +mK∗)A1(q2)

[

ε∗µ −ε∗ · qq2

qµ

]

− A2(q2)

ε∗ · qmB +mK∗

[

(p+ pK)µ −m2

B −m2K∗

q2qµ

]

, (1.44)

〈K∗(pK, ε)|sγµb|B(p)〉 = i2V (q2)

mB +mK∗

εµνρσε∗νpρpσ

K . (1.45)

Different estimates and parameterizations of the form factors can be found in the litera-ture [18, 19].

According to [14], the SM estimates for the BRs, obtained by integrating the differentialrates over s, are given by:

B(B → Kνν) = (3.8+1.2−0.6)× 10−6 , (1.46)

B(B → K∗νν) = (1.3+0.4−0.3)× 10−5 . (1.47)

Before the analysis described in this thesis, the experimental knowledge on these decays,provided by the BABAR and Belle collaborations [15, 16], was given by:

BR(B0 → K0νν) < 14× 10−5 , (1.48)

BR(B+ → K+νν) < 16× 10−5 , (1.49)

BR(B0 → K∗0νν) < 34× 10−5 , (1.50)

BR(B± → K∗±νν) < 14× 10−5 , (1.51)

(1.52)

consistent with the SM expectations.Notice that these theoretical estimates are much cleaner than the ones that can be

obtained for B → K(∗)`+`−, where the possibility of producing the `+`− pair from aphoton introduces large non-perturbative contributions from the four-fermions operatorsQ1 . . . Q6 [17].

1.3.1 B → K(∗)νν with non-standard Z couplings

An important example of NP effects that can affect the B → K (∗)νν decays is represented bynon-standard Z couplings, i.e. non-standard contributions to the SM operator bLγ

µsLZµ andcontributions from the new operator bRγ

µsRZµ. The peculiarity of these contributions is thatthe operators have dimension 4, hence they are not suppressed by any inverse power of thecut-off in the effective lagrangian. When writing the effective hamiltonian, they introduce,for instance, a correction to the Wilson coefficients Cν

L,R [14].A typical example of a non-standard Z coupling is represented, in a generic scenario with

Supersymmetry (SUSY), by the chargino-up-squark diagram of Fig. 1.3, and can enhancethe B → K(∗)νν BRs up to a factor 10.


uu

is

Z

χb

Figure 1.3: chargino-up-squark contribution to bL,RγµsL,RZµ.

1.4 B → K(∗) + invisible

From the experimental point of view, it is not possible to detect the two neutrinos in thefinal state of a B → K(∗)νν decay, hence the quantity that is actually measured is theBR of the B → K(∗) + invisible process, where the invisible part appears as a missingenergy. Since in the SM the only particles that cannot be detected by a collider experimentare the neutrinos, the two processes coincide. Anyway, many extensions of the SM predictundetectable particles or other exotic sources of missing energy. Here we give the examplesof light dark matter candidates and Unparticle physics.

1.4.1 Light Dark Matter

It is well established that known particles provide just a 4.2 to 5.6 per cent of the totalenergy density of the Universe and constitute just a 17.5 to 23.3 per cent of the total matterdensity [2], indicating that the most of the matter is of unknown nature. The ideal candidatefor such a kind of matter is a weakly interacting massive particle (WIMP) with a mass in theregion between the GeV and the TeV [22]. The B → K (∗) + invisible process is a uniqueplace to look for WIMPs with a mass up to a few GeV.

The enhancement of the B → K(∗) + invisible BRs due to the presence of one scalarWIMP S with mass mS < 2.6 GeV has been calculated in [20]. It is due to the b → sSSdecay, which proceeds through the diagram in Fig. 1.4 and is mediated by the SM Higgs h.The corresponding lagrangian contribution is written as:

LhSS = −λυS2h , (1.53)

being υ the Higgs v.e.v. (246 GeV).The contributions to the B → K(∗) + invisible differential rates, in terms of s = m2

SS,can be written as [21]:

dΓB→KSS

ds=

x2tC

2DMf0(s)

2

512π3

IK(s, mS)m2b(m

2B −m2

K)2

m3B(mb −ms)2

, (1.54)

dΓB→K∗SS

ds=

x2tC

2DMA0(s)

2

512π3

IK∗(s, mS)h(s)

mB(1.55)

1.4. B → K(∗) + INV ISIBLE 13

W

S

Sh

t, c

b s

Figure 1.4: Feynman diagram for b→ sSS.

where:

CDM =λ

m2h

3g2WV

∗tsVtb

32π2xt , (1.56)

IH(s, mS) = [s2 − 2s(m2B +m2

K) + (m2B −m2

K)2]12 [1− 4m2

S/s]12 , (1.57)

h(s) =

(

1 +m2

K∗

m2B

− s

m2B

)2

− 4m2

K∗

m2B

, (1.58)

f0(s) = f+(s/m2B) + f−(sm2

B)s2

m2B −m2

K

. (1.59)

Numerically:

B(B → KSS) ∼ 2.8× 10−4κ2FK(mS) , (1.60)

B(B → K∗SS) ∼ 4.3× 10−4κ2FK∗(mS) , (1.61)

(1.62)

being:

FK(mS) =∫ smax

smin

f0(s)2IK(s, mS) ds

[

∫ smax

smin

f0(s)2IK(s, 0) ds

]−1

, (1.63)

FK∗(mS) =∫ smax

smin

A0(s)2h(s)IK∗(s, mS) ds

[

∫ smax

smin

A0(s)2h(s)IK∗(s, 0) ds

]−1

, (1.64)

κ2 = λ2(

100 GeV

mh

)4

. (1.65)

It is also interesting to notice here that, in the presence of such a light dark matter can-didate, the H → SS decay would saturate the Higgs decay width, precluding the possibilityof observing the Higgs at hadronic machines like LHC.

1.4.2 Unparticle physics

It has been recently proposed [23] the possibility of observing at low energy the effects ofan interaction, mediated by a very massive particle, between standard fields and the fields


of a nontrivial scale invariant theory (Banks-Zaks fields) emerging above a scale ΛU . Thesefields cannot correspond to particles with a definite non-zero mass, since the mass termwould break the scale invariance. In the same time, there is the possibility that they do notcorrespond to massless particles either. In this case, we call them Unparticles. Let:

1

MkU

OSMOBZ (1.66)

be the effective coupling at a scale below MU , the mass of the mediating particle. Below thecut-off ΛU the coupling matches into an effective coupling:

CUΛdBZ−dUU

MkU

OSMOU (1.67)

where dBZ and dU are the dimensions of OBZ and OU , and dU can be non-integer. It hasbeen shown [23] that the effect of this coupling at low energy can look like the productionof a non-integer number of invisible particles.

The impact of Unparticles in the B → K (∗) + invisible process has been studied in [24]. Itdepends on the scalar or vector nature of the unparticle operator OU . For scalar unparticles:

dΓSU

dEK

=1

8π2mB

AdU

Λ2dUU

|CS|2√

E2K −m2

K

(

m2B +m2

K − 2mBEK

)dU−2

×[

f+(m2B −m2

K) + f−(m2B + 2m2

K − 2mBEK)]2

, (1.68)

dΓSU

dEK∗

=mB

2π2

AdU

Λ2dUU

|CP |2A20

(

E2K∗ −m2

K∗

)3/2 (

m2B +m2

K∗ − 2mBEK∗

)dU−2. (1.69)

where CS and CP are the Wilson coefficients of the effective couplings and:

AdU =16π5/2

(2π)2dU

Γ(dU + 1/2)

Γ(dU − 1)Γ(2dU). (1.70)

For vector unparticles:

dΓV U

dEK=

1

8π2mB

AdU

Λ2dU−2U

|CV |2|f+|2(

m2B +m2

K − 2mBEK

)dU−2√

E2K −m2

K ×

×{

− (m2B +m2

K + 2mBEK) +(m2

B −mK)2

(m2B +m2

K − 2mBEK)

}

, (1.71)

dΓV U

dEK∗

=1

8π2mB

(q2)dU−2√

E2K∗ −m2

K∗

AdU(

ΛdU−1U

)2 ×

×{

8|CV |2m2B

(

E2K∗ −m2

K∗

) V 2

(mB +mK∗)2+

+ |CA|21

m2K∗(mB +mK∗)2q2

×

1.5. FINAL REMARKS 15

×[

(mB +mK∗)4(3m4K∗ + 2m2

Bm2K∗ − 6mBm

2K∗EK∗ +m2

BE2K∗)A2

1

+ 4m4B(E2

K∗ −m2K∗)2A2

2

+ 4(mB +mK∗)2(mBEK∗ −m2K∗)(m2

K∗ − E2K∗)m2

BA1A2

]

}

. (1.72)

where again CA and CV are the Wilson coefficients.

1.5 Final remarks

The formulas for the differential rates quoted in the previous sections show that there canbe a significant model dependence of the νν mass (or in general missing mass) spectrum.

From the phenomenological point of view, it means that it is possible to extract importantinformations about the underlying physics if the mass spectrum is measured.

On the other hand, from the experimental point of view, it means that the measurementof the BR can be affected by a significant model dependence if the analysis strategy relieson some kinematical variables like the missing energy or the K (∗) momentum.

Experimental searches are usually performed by applying selection requirements on thesevariables and assuming the SM differential rate when calculating the efficiency. For the firsttime concerning this kind of analysis, we perform a model independent search, by using onlythe observables that do not show any significant correlation with the νν reduced invariantmass s. A systematic uncertainty is also associated to the residual model dependence of oursignal efficiency. This feature allows to easily interpret our results in any NP scenario.

Chapter 2

The BABAR detector and data set

The analysis described in this work has been performed on the data collected by the BABAR

detector [25], operating at PEP-II the asymmetric B-Factory of the Stanford Linear Ac-celerator Center (SLAC). In this chapter we briefly describe PEP-II and the subsystemscomposing the BABAR detector. We also describe the data samples and Monte Carlo simu-lations used in the analysis.

2.1 Introduction

The PEP-II B-Factory is an e+e− asymmetric collider running at a center of mass energy of10.58 GeV corresponding to the mass of the Υ (4S) resonance. The electron beam in the HighEnergy Ring (HER) has 9.0 GeV and the positron beam in the Low Energy Ring (LER) has3.1 GeV. The Υ (4S) is therefore produced with a Lorentz boost of βγ = 0.56, allowing fora precise measurement of the time difference between the two B decays, as needed by thetime-dependent CP violation measurements that are the primary goal of BABAR.

A longitudinal section of the BABAR detector is shown in Fig.2.1. The detector is com-posed by several subsystems. The tracking system, used to reconstruct the charged particlesand the decay vertex, includes two different detectors: a Silicon Vertex Detector (SVT) anda Drift Chamber (DCH), both operating in a 1.5 T magnetic field provided by a super-conducting solenoid. A detector of internal reflected Cherenkov light (DIRC) allows forparticle identification (PID) and an Electromagnetic Calorimeter (EMC) is employed forphotons reconstruction and energy measurements. Finally, muon candidates are identifiedin the instrumented flux return (IFR) of the solenoid.

The detector is characterized by a hexagonal section and is divided in an central part(barrel) and two end-caps. The covered polar angle ranges from 350 mrad, in the forward,to 400 mrad in the backward directions (defined with respect to the high energy beamdirection). The BABAR coordinate system has the z axis along the boost direction (or thebeam direction): the y axis is vertical and the x axis is horizontal and goes toward theexternal part of the ring. In order to maximize the geometrical acceptance for Υ (4S) decaysthe whole detector is offset, with respect to the beam-beam interaction point (IP), by 0.37m in the direction of the lower energy beam.

17

18 CHAPTER 2. THE BABAR DETECTOR AND DATA SET

��

� �

��

��

��

��

��

��

��

�

��

��

�

�

�

��

Scale

BABAR Coordinate System

0 4m

Cryogenic Chimney

Magnetic Shield for DIRC

Bucking Coil

Cherenkov Detector (DIRC)

Support Tube

e– e+

Q4Q2

Q1

B1

Floor

yx

z1149 1149

Instrumented Flux Return (IFR))

BarrelSuperconducting

Coil

Electromagnetic Calorimeter (EMC)

Drift Chamber (DCH)

Silicon Vertex Tracker (SVT)

IFR Endcap

Forward End Plug

1225

810

1375

3045

3500

3-2001 8583A50

1015 1749

4050

370

I.P.

Detector CL

Figure 2.1: BABAR detector longitudinal section.

2.2. THE PEP-II B-FACTORY 19

2.2 The PEP-II B-Factory

PEP-II is a system consisting of two accumulating asymmetric rings designed in order tooperate at a center of mass energy of the Υ (4S) resonance mass, 10.58 GeV. Tab. 2.1 showsthe design parameters and typical parameters in the 2007 run.

Table 2.1: PEP-II beam parameters. Design and typical values are quoted and are referredto the last year of machine running at the Υ (4S) resonance (2007).

Parameters Design TypicalEnergy HER/LER (GeV) 9.0/3.1 9.0/3.1Current HER/LER (A) 0.75/2.15 1.96/3.03

# of bunch 1658 1732bunch time separation (ns) 4.2 4.2

σLx (µm) 110 157σLy (µm) 3.3 4.7σLz (µm) 9000 10000

Luminosity (1033 cm−2s−1) 3 12Daily average integrated luminosity (pb−1/d) 135 700

Data are mostly collected at Υ (4S) peak energy. Tab.2.2 shows the active processes crosssections breakdown at peak energy. From now on the production of light quark pairs (u, d, s)and charm quark pairs will be referred to as continuum production. In order to study thisnon-resonant production ∼ 10% of data is collected with a center of mass energy 40 MeVbelow the Υ (4S) mass value (off-peak data).

Table 2.2: Various processes cross sections at√s = MΥ (4S). Bhabha cross section is an

effective cross section, within the experimental acceptance.

e+e− → Cross section (nb)bb 1.05cc 1.30ss 0.35uu 1.39dd 0.35τ+τ− 0.94µ+µ− 1.16e+e− ∼ 40

Recently, the machine has been run at different center of mass energies, correspondingto the Υ (2S) ans Υ (3S) masses, in order to study rare bottomonium decays and look forunobserved bottomonium states [26]. An energy scan between 10.54 and 11.2 GeV has been


also performed in order to look for exotic bottomonium states and assess the parameters ofthe Υ (5S) and Υ (6S) resonances [27].

The interaction region design, with the two beams crossing in a single interaction pointwith particles trajectories modified in order to have head on collisions, is realized with amagnetic field, produced by a dipole magnetic system, acting near the interaction point.The collision axis is off-set from the z-axis of the BABAR detector by about 20 mrad inthe horizontal plane to minimize the perturbation of the beams by the solenoidal field. Inthis configuration the particles and the beams are kept far apart in the horizontal planeoutside the interaction region and parassite collisions are minimized. Magnetic quadrupolesincluded inside the detector’s magnetic field, and hence realized in Samarium-Cobalt, arestrongly focusing the beams inside the interaction region.

2.3 Tracking system

The charged particle tracking system is composed by a silicon vertex tracker (SVT) and adrift chamber (DCH): the main purpose of this tracking system is the efficient detection ofcharged particles and the measurement of their momentum and angles with high precision.

2.3.1 The silicon vertex tracker

The vertex detector has a radius of 20 cm from the primary interaction region: it is placedinside the support tube of the beam magnets and consists of five layers of double-sided siliconstrip sensors detectors to provide five measurements of the positions of all charged particleswith polar angles in the region 20.1◦ < θ < 150◦. Because of the presence of a 1.5T magneticfield, the charged particle tracks with transverse momenta lower than ∼ 100 MeV/c cannotreach the drift chamber active volume. So the SVT has to provide stand-alone tracking forparticles with transverse momentum less than 120 MeV/c. For high momentum tracks, italso provide the measurement of track angles that is required to achieve design resolutionfor the Cerenkov angle in the DIRC.

In order to reach the required performances, the SVT is very close to the productionvertex. It allows a very precise measure of points on the charged particles trajectories onboth longitudinal (z) and transverse directions. The longitudinal coordinate information isnecessary to measure the decay vertex distance, while the transverse information allows abetter separation between secondary vertices coming from decay cascades.

More precisely, the design of the SVT was carried out according to some importantguidelines:

• The number of impact points of a single charged particle has to be greater than 3to make a stand-alone tracking possible, and to provide an independent momentummeasure.

• The first three layers are placed as close as possible to the impact point to achieve thebest resolution on the z position of the B meson decay vertices.

2.3. TRACKING SYSTEM 21

580 mm

350 mrad520 mrad

ee +-

Beam Pipe

Space Frame

Fwd. support cone

Bkwd. support cone

Front end electronics

Figure 2.2: SVT schematic view: longitudinal section

• The two outer layers are close to each other, but comparatively far from the innerlayers, to allow a good measurement of the track angles.

• The SVT must withstand 2 MRad of ionizing radiation: the expected radiation dose is1 Rad/day in the horizontal plane immediately outside the beam pipe and 0.1 Rad/dayon average.

• Since the vertex detector is inaccessible during normal detector operations, it has tobe reliable and robust.

These guidelines have led to the choice of a SVT made of five layers of double-sidedsilicon strip sensors: the spatial resolution, for perpendicular tracks must be 10 − 15µmin the three inner layers and about 40µm in the two outer layers. The three inner layersperform the impact parameter measurement, while the outer layers are necessary for patternrecognition and low pt tracking. The silicon detectors are double-sided (contain active stripson both sides) because this technology reduces the thickness of the materials the particleshave to cross, thus reducing the energy loss and multiple scattering probability compared tosingle-sided detectors. The sensors are organized in modules (see Fig. 2.2). The SVT fivelayers contain 340 silicon strip detectors with AC-coupled silicon strips.

Each detector is 300µm-thick but sides range from 41mm to 71mm and there are 6different detector types. Each of the three inner layers has a hexagonal transverse cross-section and it is made up of 6 detector modules, arrayed azimuthally around the beam pipe,while the outer two layers consist of 16 and 18 detector modules, respectively. The innerdetector modules are barrel-style structures, while the outer detector modules employ thenovel arch structure in which the detectors are electrically connected across an angle. Thisarch design was chosen to minimize the amount of silicon required to cover the solid anglewhile increasing the solid angle for particles near the edges of acceptance: having incidenceangles on the detector closer to 90 degrees at small dip angles insures a better resolutionon impact points. The readout electronics is enterely mounted outside the active detector


Beam Pipe 27.8mm radius

Layer 5a

Layer 5b

Layer 4b

Layer 4a

Layer 3

Layer 2

Layer 1

Figure 2.3: Cross-sectional view of the SVT in a plane perpendicular to the beam axis.

volume. The redout is organized in such a way that each module can be divided in a forwardand a backward half-module, electrically separated.

The strips on the two sides of the rectangular detectors in the barrel regions are orientedparallel (φ strips) or perpendicular (z strips) to the beam line: in other words, the inner sidesof the detectors have strips oriented perpendicular to the beam direction to measure the zcoordinate (z-size), whereas the outer sides, with longitudinal strips, allow the φ-coordinatemeasurement (φ-side). In the forward and backward regions of the two outer layers, theangle between the strips on the two sides of the trapezoidal detectors is approximately 90◦

and the φ strips are tapered.

The inner modules are tilted in φ by 5◦, allowing an overlap region between adjacentmodules: this provide full azimuthal coverage and is convenient for alignment. The outermodules are not tilted, but are divided into sub-layers and placed at slightly different radii(see Fig. 2.3).

The total silicon area in the SVT is 0.94m2 and the number of readout channels is about150 000. The geometrical acceptance of SVT is 90% of the solid angle in the center of masssystem and typically 80% are used in charged particle tracking.

The SVT efficiency can be calculated for each half-module by comparing the number ofassociated hits to the number of tracks crossing the active area of the half-module. Thecombined hardware and software efficiency is 97%.

The spatial resolution of SVT hits is calculated by measuring the distance (in the planeof the sensor) between the track trajectory and the hit, using high-momentum tracks in twoprong events: the uncertainty due to the track trajectory is subtracted from the width ofthe residual distribution to obtain the hit resolution. The track hit residuals are defined asthe distance between track and hit, projected onto the wafer plane and along either the φ or


SVT Hit Resolution vs. Incident Track Angle

Monte Carlo - SP2

Layer 1 - Z View

(deg)

(µm

)

Data - Run 7925

B A B A R

Monte Carlo - SP2

Layer 1 - φ View

(deg)

(µm

)

Data - Run 7925

B A B A R

0

20

40

60

-50 0 50

0

20

40

60

-50 0 50

Figure 2.4: SVT hit resolution in the z and φ coordinate in microns, plotted as functions ofthe track incident angle in degrees.

z direction. The width of this residual distribution is then the SVT hit resolution. Fig. 2.4shows the SVT hit resolution for z and φ side hits as a function of the track incident angle:the measured resolutions are in very good agreement with the MonteCarlo expected ones.Over the whole SVT, resolutions are raging from 10 − 15µm (inner layers) to 30 − 40µm(outer layers) for normal tracks.

The double-sided sensors also provide up to ten measurements of dE/dx per track: withsignals from at least four sensors, a 60% truncated mean dE/dx is calculated. For MIPs, theresolution on the truncated mean dE/dx is approximately 14%: a 2σ separation betweenkaons and pions can be achieved up to momentum of 500 MeV/c and between kaons andprotons beyond 1 GeV/c.

2.3.2 The drift chamber

The principal purpose of the DCH is the efficient detection of charged particles and themeasurement of their momenta and angles with high precision. The DCH complements themeasurements of the impact parameter and the directions of charged tracks provided bythe SVT near the impact point (IP). At lower momenta, the DCH measurements dominatethe errors on the extrapolation of charged tracks to the DIRC, EMC and IFR. The recon-struction of decay and interaction vertices outside of the SVT volume, for instance the K0

S

decays, relies only on the DCH. For these reasons, the chamber should provide maximalsolid angle coverage, good measurement of the transverse momenta and positions but alsoof the longitudinal positions of tracks with a resolution of ∼ 1mm, efficient reconstruction


IP1618

469236

324 681015 1749

551 97317.19ÿ20235

Sense

Field Guard 1-2001

8583A16

Figure 2.5: Side view of the BABAR drift chamber (the dimensions are in mm) and isochrones(i.e. contours of equal drift time of ions) in cells of layer 3 and 4 of an axial super-layer.The isochrones are spaced by 100ns.

of tracks at momenta as low as 100 MeV/c and it has to minimally degrade the performanceof the calorimeter and particle identification devices (the most external detectors). For lowmomentum particles, the DCH is required to provide particle identification by measuring theionization loss (dE/dx). A resolution of about 7% allows π/K separation up to 700 MeV/c.This particle identification (PID) measurement is complementary to that of the DIRC inthe barrel region, while in the extreme backward and forward region, the DCH is the onlydevice providing some discrimination of particles of different mass. The DCH should alsobe able to operate in presence of large beam-generated backgrounds having expected ratesof about 5 kHz/cell in the innermost layers.

To meet the above requirements, the DCH is a 280 cm-long cylinder (see left plot inFig. 2.5), with an inner radius of 23.6 cm and an outer radius of 80.9 cm: it is boundedby the support tube at its inner radius and the particle identification device at its outerradius. The flat end-plates are made of aluminum: since the BABAR events will be boostedin the forward direction, the design of the detector is optimized to reduce the material in theforward end. The forward end-plate is made thinner (12mm) in the acceptance region ofthe detector compared to the rear end-plate (24mm), and all the electronics is mounted onthe rear end-plate. The device is asymmetrically located with respect to the IP: the forwardlength of 174.9 cm is chosen so that particles emitted at polar angles of 17.2◦ traverse atleast half of the layers of the chamber before exiting through the front end-plate. In thebackward direction, the length of 101.5 cm means that particles with polar angles down to152.6◦ traverse at least half of the layers.

The inner cylinder is made of 1mm beryllium and the outer cylinder consists of two layersof carbon fiber glued on a Nomex core: the inner cylindrical wall is kept thin to facilitatethe matching of SVT and DCH tracks, to improve the track resolution for high momentumtracks and to minimize the background from photon conversions and interactions. Material


in the outer wall and in the forward direction is also minimized in order not to degrade theperformance of the DIRC and the EMC.

The region between the two cylinders is filled up by a gas mixture consisting of Helium-isobutane (80% : 20%): the chosen mixture has a radiation length that is five times largerthan commonly used argon-based gases. 40 layers of wires fill the DCH volume and form7104 hexagonal cells with typical dimensions of 1.2× 1.9 cm2 along the radial and azimuthaldirections, respectively (see right plot in Fig. 2.5). The hexagonal cell configuration hasbeen chosen because approximate circular symmetry can be achieved over a large portion ofthe cell. Each cell consist of one sense wire surrounded by six field wires: the sense wiresare 20µm gold-plated tungsten-rhenium, the field wires are 120µm and 80µm gold-platedaluminum. By using the low-mass aluminum field wires and the helium-based gas mixture,the multiple scattering inside the DCH is reduced to a minimum, representing less than0.2%X0 of material. The total thickness of the DCH at normal incidence is 1.08%X0.

The drift cells are arranged in 10 super-layers of 4 cylindrical layers each: the super-layers contain wires oriented in the same direction: to measure the z coordinate, axial wiresuper-layers and super-layers with slightly rotated wires (stereo) are alternated. In thestereo super-layers a single wire corresponds to different φ angles and the z coordinate isdetermined by comparing the φ measurements from axial wires and the measurements fromrotated wires. The stereo angles vary between ±45 mrad and ±76 mrad.

While the field wires are at ground potential, a positive high voltage is applied to thesense wires: an avalanche gain of approximately 5 × 104 is obtained at a typical operatingvoltage of 1960V and a 80:20 helium:isobutane gas mixture.

In each cell, the track reconstruction is obtained by the electron time of flight: the preciserelation between the measured drift time and drift distance is determined from sample ofe+e− and µ+µ− events. For each signal, the drift distance is estimated by computing thedistance of closest approach between the track and the wire. To avoid bias, the fit doesnot include the hit of the wire under consideration. The estimated drift distances and themeasured drift times are averaged over all wires in a layer.

The DCH expected position resolution is lower than 100µm in the transverse plane,while it is about 1mm in the z direction. The minimum reconstruction and momentummeasure threshold is about 100 MeV/c and it is limited by the DCH inner radius. The designresolution on the single hit is about 140µm while the achieved weighted average resolutionis about 125µm. Left plot in Fig. 2.6 shows the position resolution as a function of the driftdistance, separately for the left and the right side of the sense wire. The resolution is takenfrom Gaussian fits to the distributions of residuals obtained from unbiased track fits: theresults are based on multi-hadron events for data averaged over all cells in layer 18.

The specific energy loss (dE/dx) for charged particles through the DCH is derived fromthe measurement of the total charge collected in each drift cell: the specific energy lossper track is computed as a truncated mean from the lowest 80% of the individual dE/dxmeasurements. Various corrections are applied to remove sources of bias: these correctionsinclude changes in gas pressure and temperature (±9% in dE/dx), differences in cell geometryand charge collection (±8%), signal saturation due to space charge buildup (±11%), non-linearities in the most probable energy loss at large dip angles (±2.5%) and variation of cell


0

0.1

0.2

0.3

0.4

–10 –5 0 5 101-2001 8583A19 Distance from Wire (mm)

Res

olut

ion

(m

m)

104��

103��

10–1 101

eµ

π

K

p d

dE/d

xMomentum (GeV/c)1-2001

8583A20

Figure 2.6: Left plot: DCH position resolution as a function of the drift chamber in layer18, for tracks on the left and right side of the sense wire. The data are averaged over allcells in the layer. Right plot: measurement of dE/dx in the DCH as a function of the trackmomenta. The data include large samples of beam background triggers as evident from thehigh rate of protons. The curves show the Bethe-Bloch predictions derived from selectedcontrol samples of particles of different masses.

charge collection as a function of the entrance angle (±2.5%).Right plot in Fig. 2.6 shows the distribution of the corrected dE/dx measurements as a

function of track momenta: the superimposed Bethe-Bloch predictions have been determinedfrom selected control samples of particles of different masses. The achieved dE/dx rmsresolution for Bhabha events is typically 7.5%, limited by the number of samples and Landaufluctuations, and it is close to the expected resolution of 7%.

2.4 Cerenkov light detector

The Detector of Internally Reflected Cerenkov light (DIRC) is designed to provide a goodK/π separation (∼ 4σ) in particular above 700 MeV/c.

The particle identification in the DIRC is based on the Cerenkov radiation produced bycharged particles crossing a material with a speed higher than light speed in that material.The angular opening of the Cerenkov radiation cone depends on the particle speed:

cosθc =1

nβ(2.1)

where θc is the Cerenkov cone opening angle, n is the refractive index of the material and βis the particle velocity over c. The principle of the detection is based on the fact that themagnitudes of angles are maintained upon reflection from a flat surface.

2.4. CERENKOV LIGHT DETECTOR 27

~2 m

~5 m

Quartz Bar Sector

Plane Mirror (12)

Hinged Cover (12)

PMT Module

Standoff Cone

��

��

��

��

��

Window Frame

Quartz Window

Assembly Flange

Sector Cover

Quartz Bar

Figure 2.7: Mechanical elements of the DIRC and schematic view of bars assembled into amechanical and optical sector.

Since particles are produced mainly forward in the detector because of the boost, theDIRC photon detector is placed at the backward end: the principal components of the DIRCare shown in Fig. 2.7. The DIRC is placed in the barrel region and consists of 144 long,straight bars arranged in a 12-sided polygonal barrel. The bars are 1.7 cm-thick, 3.5 cm-wide and 4.90m-long: they are placed into 12 hermetically sealed containers, called barboxes, made of very thin aluminum-hexcel panels. Within a single bar box, 12 bars areoptically isolated by a ∼ 150µm air gap enforced by custom shims made from aluminumfoil.

The radiator material used for the bars is synthetic fused silica: the bars serve both asradiators and as light pipes for the portion of the light trapped in the radiator by total inter-nal reflection. Synthetic silica has been chosen because of its resistance to ionizing radiation,its long attenuation length, its large index of refraction, its low chromatic dispersion withinits wavelength acceptance.

The Cerenkov radiation is produced within these bars and is brought, through succes-sive total internal reflections, in the backward direction outside the tracking and magneticvolumes: only the backward end of the bars is instrumented. A mirror placed at the otherend on each bar reflects forward-going photons to the instrumented end. The Cerenkov an-gle at which a photon was produced is preserved in the propagation, modulo some discreteambiguities (the forward-backward ambiguity can be resolved by the photon arrival-timemeasurement, for example). The DIRC efficiency grows together with the particle incidenceangle because more light is produced and a larger fraction of this light is totally reflected. Tomaximize the total reflection, the material must have a refractive index (fused silica index isn = 1.473) higher than the surrounding environment (the DIRC is surrounded by air withindex n = 1.0002).

Once photons arrive at the instrumented end, most of them emerge into a water-filledexpansion region (see Fig. 2.8), called the Standoff Box: the purified water, whose refractiveindex matches reasonably well that of the bars (nH2O = 1.346), is used to minimize the total


Mirror

4.9 m

4 x 1.225m Bars glued end-to-end

Purified Water

Wedge

Track Trajectory

17.25 mm Thickness (35.00 mm Width)

Bar Box

PMT + Base 10,752 PMT's

Light Catcher

PMT Surface

Window

Standoff Box

Bar

{ {1.17 m

8-2000 8524A6

Figure 2.8: Schematics of the DIRC fused silica radiator bar and imaging region. Not shownis a 6 mrad angle on the bottom surface of the wedge.

internal reflection at the bar-water interface.The standoff box is made of stainless steel and consists of a cone, cylinder and 12 sectors

of PMTs: it contains about 6000 liters of purify water. Each of the 12 PMTs sectors contains896 PMTs in a close-packed array inside the water volume: the PMTs are linear focused2.9 cm diameter photo-multiplier tubes, lying on an approximately toroidal surface.

The DIRC occupies only 8 cm of radial space, that allows for a relatively large radiusfor the drift chamber while keeping the volume of the CsI Calorimeter reasonably low: itcorresponds to about 17%X0 at normal incidence. The angular coverage is the 94% of theφ azimuthal angle and the 83% of cos θCM .

Cerenkov photons are detected in the visible and near-UV range by the PMT array. Asmall piece of fused silica with a trapezoidal profile glued at the back end of each bar allowsfor significant reduction in the area requiring instrumentation because it folds one half ofthe image onto the other half. The PMTs are operated directly in water and are equippedwith light concentrators: the photo-multiplier tubes are about 1.2m away from the end ofthe bars. This distance from the bar end to the PMTs, together with the size of the barsand PMTs, gives a geometric contribution to the single photon Cerenkov angle resolutionof about 7 mrad. This is a bit larger than the resolution contribution from Cerenkov lightproduction (mostly a 5.4 mrad chromatic term) and transmission dispersions. The overallsingle photon resolution expected is about 9 mrad.

The image from the Cerenkov photons on the sensitive part of the detector is a conecross-section whose opening angle is the Cerenkov angle modulo the refraction effects on thefused silica-water surface. In the most general case, the image consists of two cone cross-sections out of phase one from the other by a value related to an angle that is twice the

2.4. CERENKOV LIGHT DETECTOR 29

0

20000

40000

-50 0 50∆ θC,γ (mrad)

entri

es p

er m

rad

B AB A R

0

5000

10000

15000

-10 0 10θC, track (measured) - θC (µ) (mrad)

Trac

ks

B AB A R

Figure 2.9: From di-muon data events, left plot: single photon Cerenkov angle resolution.The distribution is fitted with a double-Gaussian and the width of the narrow Gaussian is9.6 mrad. Right plot: reconstructed Cerenkov angle for single muons. The difference betweenthe measured and expected Cerenkov angle is plotted and the curve represents a Gaussiandistribution fit to the data with a width of 2.4 mrad.

particle incidence angle. In order to associate the photon signals with a track traversing abar, the vector pointing from the center of the bar end to the center of each PMT is takenas a measure of the photon propagation angles αx, αy and αz. Since the track position andangles are known from the tracking system, the three α angles can be used to determinethe two Cerenkov angles θC and φC . In addition, the arrival time of the signal providesan independent measurement of the propagation of the photon and can be related to thepropagation angles α. This over-constraint on the angles and the signal timing are useful indealing with ambiguities in the signal association and high background rates.

The expected number of photo-electrons (Npe) is ∼ 28 for a β = 1 particle enteringnormal to the surface at the center of a bar and increases by over a factor of of two in theforward and backward directions.

The time distribution of real Cerenkov photons from a single event is of the order of 50nswide and during normal data taking they are accompanied by hundreds of random photonsin a flat background distribution within the trigger acceptance window. The Cerenkov anglehas to be determined in an ambiguity that can be up to 16-fold: the goal of the reconstructionprogram is to associate the correct track with the candidate PMT signal with the requirementthat the transit time of the photon from its creation in the bar to its detection at the PMTbe consistent with the measurement error of about 1.5ns.

The resolution (σC,track) on the track Cerenkov angle is expected to scale as

σC,track =

σC,γ√

Npe

where σC,γ is the single photon angle resolution. This angular resolution (obtained fromdi-muon events) can be estimated to be about 10.2 mrad, in good agreement with the ex-


11271375920

1555 2295

2359

1801

558

1979

22.7˚

26.8˚

15.8˚

Interaction Point 1-2001 8572A03

38.2˚

External Support

CsI(Tl) Crystal

Diode Carrier Plate

Silicon Photo-diodes

Preamplifier BoardFiber Optical Cable

to Light Pulser

Aluminum Frame

TYVEK (Reflector)

Mylar (Electrical Insulation)

Aluminum Foil

(R.F. Shield)

CFC Compartments (Mechanical

Support)

Output Cable

11-2000 8572A02

Figure 2.10: The electromagnetic calorimeter layout in a longitudinal cross section and aschematic view of the wrapped CsI(Tl) crystal with the front-end readout package mountedon the rear face (not to scale).

pected value (see left plot in fig. 2.9). The measured time resolution is 1.7ns close to theintrinsic 1.5ns time spread of the PMTs.

2.5 Electromagnetic calorimeter

The electromagnetic calorimeter is designed to measure electromagnetic showers with ex-cellent efficiency and energy and angular resolution over the energy range from 20 MeV to9 GeV. This capability should allow the detection of photons from π0 and η decays as wellas from electromagnetic and radiative processes. The upper bound of the energy range isgiven by the need to measure QED processes like e+e− → e+e−(γ) and e+e− → γγ forcalibration and luminosity determination. The lower bound is set by the need for highlyefficient reconstruction of B-meson decays containing multiple π0s and η0s. The measure-ment of very rare decays containing π0s in the final state (for example, B0 → π0π0) putsthe most stringent requirements on energy resolution, expected to be of the order of 1− 2%.Below 2 GeV energy, the π0 mass resolution is dominated by the energy resolution, whileat higher energies, the angular resolution becomes dominant and it is required to be of theorder of few mrad. The EMC is also used for electron identification and for completing theIFR output on µ and K0

L identification. It also has to operate in a 1.5T magnetic field.

The EMC has been chosen to be composed of a finely segmented array of thallium-dopedcesium iodide (CsI(Tl)) crystals. The crystals are read out with silicon photo-diodes whichare matched to the spectrum of scintillation light. The energy resolution of a homogeneouscrystal calorimeter can be described empirically in terms of a sum of two terms added inquadrature:

2.5. ELECTROMAGNETIC CALORIMETER 31

σE

E=

a

4√

E( GeV)⊕ b

where E and σE refer to the energy of a photon and its rms error, measured in GeV. Theenergy dependent term a(∼ 2%) arises basically from the fluctuations in photon statistics,but also from the electronic noise of the photon detector and electronics and from the beam-generated background which leads to large numbers of additional photons. This first termdominates at low energy, while the constant term b(∼ 1.8%) is dominant at higher energies(> 1 GeV). It derives from non-uniformity in light collection, leakage or absorption in thematerial in front of the crystals and uncertainties in the calibration.

The angular resolution is determined by the transverse crystal size and the distance fromthe interaction point: it can be empirically parameterized as a sum of an energy dependentand a constant term

σθ = σφ =c

√

E( GeV)+ d

where E is measured in GeV and with c ∼ 4 mrad and d ∼ 0 mrad.In CsI(Tl), the intrinsic efficiency for the detection of photons is close to 100% down to a

few MeV, but the minimum measurable energy in colliding beam data is about 20 MeV forthe EMC: this limit is determined by beam and event-related background and the amountof material in front of the calorimeter. Because of the sensitivity of the π0 efficiency to theminimum detectable photon energy, it is extremely important to keep the amount of materialin front of the EMC to the lowest possible level.

Thallium-doped CsI has high light yield and small Moliere radius in order to allow forexcellent energy and angular resolution. It is also characterized by a short radiation lengthfor shower containment at BABAR energies. The transverse size of the crystals is chosen to becomparable to the Moliere radius achieving the required angular resolution at low energieswhile limiting the total number of crystals and readout channels.

The BABAR EMC (left plot in Fig. 2.10) consists of a cylindrical barrel and a conicalforward end-cap: it has a full angle coverage in azimuth while in polar angle it extends from15.8◦ to 141.8◦ corresponding to a solid angle coverage of 90% in the CM frame. Radially thebarrel is located outside the particle ID system and within the magnet cryostat: the barrelhas an inner radius of 92 cm and an outer radius of 137.5 cm and it’s located asymmetricallyabout the interaction point, extending 112.7 cm in the backward direction and 180.1 cmin the forward direction. The barrel contains 5760 crystals arranged in 48 rings with 120identical crystals each: the end-cap holds 820 crystals arranged in eight rings, adding up to atotal of 6580 crystals. They are truncated-pyramid CsI(Tl) crystals (right plot in Fig. 2.10):they are tapered along their length with trapezoidal cross-sections with typical transversedimensions of 4.7× 4.7 cm2 at the front face, flaring out toward the back to about 6.1.0 cm2.All crystals in the backward half of the barrel have a length of 29.6 cm: toward the forwardend of the barrel, crystal lengths increase up to 32.4 cm in order to limit the effects ofshower leakage from increasingly higher energy particles. All end-cap crystals are of 32.4 cm


length. The barrel and end-cap have total crystal volumes of 5.2m3 and 0.7m3, respectively.The CsI(Tl) scintillation light spectrum has a peak emission at 560nm: two independentphotodiodes collect this scintillation light from each crystal. The readout package consists oftwo silicon PIN diodes, closely coupled to the crystal and to two low-noise, charge-sensitivepreamplifiers, all enclosed in a metallic housing.

A typical electromagnetic shower spreads over many adjacent crystals, forming a clusterof energy deposit: pattern recognition algorithms have been developed to identify theseclusters and to discriminate single clusters with one energy maximum from merged clusterswith more than one local energy maximum, referred to as bumps. The algorithms alsodetermine whether a bump is generated by a charged or a neutral particle. Clusters arerequired to contain at least one seed crystal with an energy above 10 MeV: surroundingcrystals are considered as part of the cluster if their energy exceeds a threshold of 1 MeV orif they are contiguous neighbors of a crystal with at least 3 MeV signal. The level of thesethresholds depends on the current level of electronic noise and beam-generated background.

A bump is associated with a charged particle by projecting a track to the inner faceof the calorimeter: the distance between the track impact point and the bump centroid iscalculated and if it is consistent with the angle and momentum of the track, the bump isassociated with this charged particle. Otherwise it is assumed to originate from a neutralparticle.

On average, 15.8 clusters are detected per hadronic event: 10.2 are not associated to anycharged particle. Currently, the beam-induced background contributes on average with 1.4neutral clusters with energy above 20 MeV.

Cluster shape informations are also used in the PID process. In particular, the secondand the lateral momentum of the cluster energy distribution are used:

Second Momentum:∑

Ei · r2i

Ei

(2.2)

Lateral Momentum (LAT):

∑

i=2,nEi · r2i

(

∑

i=2,nEi · r2i

)

+ 25(E0 + E1)(2.3)

being Ei the energy deposit on a crystal and ri its distance from the center of the cluster.The sum is extended to the crystals of the cluster. In the analysis describe in this thesis,photons are taken as EMC clusters, not associated to tracks, with ECM > 0.030 GeV andLAT < 0.8.

At low energy, the energy resolution of the EMC is measured directly with a 6.13 MeVradioactive photon source (a neutron-activated fluorocarbon fluid) yielding σE/E = 5.0 ±0.8%. At high energy, the resolution is derived from Bhabha scattering where the energy ofthe detected shower can be predicted from the polar angle of the electrons and positrons. Themeasured resolution is σE/E = 1.9±0.1% at 7.5 GeV. Fig. 2.11 shows the energy resolutionon data compared with expectations from MonteCarlo. From a fit to the experimental

2.6. INSTRUMENTED FLUX RETURN 33

/ GeVγE10-2

10-1

1

(E

) / E

σ

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

2σ ⊕ 1/4/E1σ(E)/E = σ

0.3)%± 0.03 ± = (2.32 1σ

0.1)%± 0.07 ± = (1.85 2σ

γγ → 0πγγ → η

Bhabhasγ ψ J/→ cχ

radioakt. SourceMonteCarlo

Figure 2.11: EMC resolution as a function of the energy.

results to Eq. (2.5), a = 2.32±0.30% and b = 1.85±0.12% are obtained. The constant termcomes out to be greater than expected: this is mainly caused by a cross talk effect, still notcorrected, in the front-end electronics.

The measurement of the angular resolution is based on Bhabha events and ranges between12 mrad and 3 mrad going from low to high energies. A fit to Eq. (2.5) results in c =(3.87± 0.07) mrad and d = (0.00± 0.04) mrad.

2.6 Instrumented Flux Return

The Instrumented Flux Return (IFR) detector is dedicated to muon identification and neutralhadrons detection (mainly K0

L) in a wide range of momentum and angles.

The IFR, as all the other BABAR subsystems, has an asymmetric structure with a polarangle coverage that is 17◦ ≤ θlab ≤ 150◦. The IFR (Fig. 2.12) was originally made of 19layers of Resistive Plate Chambers (RPC) in the barrel region and 18 layers in forward andbackward regions, placed inside the iron layers used for the solenoidal magnetic field returnjoke. Recently, part of the RPCs have been replaced by Limited Streamer Tubes (LST).

The iron structure is subdivided in three main parts: the barrel one surrounding thesolenoid, made of 6 sextants covering the radial distance between 1.820 m and 3.045 m witha length of 3.750 m (along the z axis); the forward end-cap and backward end-cap coveringthe forward (positive z axis) and backward regions. The endcaps are instrumented with


Figure 2.12: IFR view

RPCs, the barrel is completely instrumented with LSTs since 2006.The RPC section is shown in Fig. 2.13.

Figure 2.13: RPC section with HV connection scheme.

Signals produced by particles crossing the gas gap inside the RPCs are collected on bothsides of the chamber by using thin strips (thickness ∼ 40µm) with witdh of the order ofa centimeter. Strips are applied in two orthogonal directions on insulating planes 200 µmthick, in order to have a bi-dimensional view.

The used gas mixture is made of 56.7% Argon, 38.8% Freon-134a and 4.5% Isobutane.Working voltage for RPCs is ∼ 7.5 kV . Iron layers keeping apart RPC planes are chilled by

2.7. DATA AND MONTE CARLO SAMPLES 35

a water system that keeps the temperature ∼ 20oC. RPC efficiencies have been measuredby using cosmics taken on a weekly base.

The gaps in the IFR barrel are filled with LSTs. Each tube is composed by 7 or 8 cells.Each cell has a 18 × 18mm section with a silver plated wire at the center and a resistivegraphite coating. The wire provides the high voltage while the signal is read by strips likein RPCs. The operating voltage is typically 5500 V. A gas admixture of 2.5% Argon, 9.5%Isobutane and 88% CO2 is used.

Muons are identified by measuring the number of traversed interaction lengths in theentire detector and comparing it with the number of expected interaction lengths for a muonof a given momentum. Moreover, the projected intersections of a track with the RPC planesare computed and, for each readout plane, all strips clusters detected within a predefineddistance from the predicted intersection are associated with the track: the average numberand the r.m.s. of the distribution of RPC and LST strips per layer gives additional µ/πdiscriminating power. We expect in fact the average number of strips per layer to be largerfor pions producing an hadronic interaction than for muons. Other variables exploitingclusters distribution shapes are constructed. Selection criteria based on all these variablesare applied to select muons.

2.7 Data and Monte Carlo samples

The data used in the analysis we are going to describe have been collected by the BABAR

experiments between 2000 and 2007, in six different run periods (Run1–6), correspondingto an integrated luminosity of about 413 fb−1 at the Υ (4S) resonace and about 41 fb−1 off-peak. The measured number of BB pairs produced at the Υ (4S) resonance is (454± 5) ×106, extracted by measuring the number of events passing a multi-hadron selection andsubtracting the expected continuum events (estimated from off-peak data).

Monte Carlo (MC) simulations are also used in order to test the analysis strategy andevaluate its performances. The MC samples include:

• Signal MC: B0 → K∗0νν, B± → K∗±νν;

• B0B0 Generic MC;

• B+B− Generic MC;

• cc Generic MC;

• τ+τ− Generic MC;

• uu, dd, ss (uds) Generic MC.

In the generic samples, the particles produced in the e+e− interaction can decay in anyallowed final state, according to their known BRs. In the signal MC, BB pairs are producedand one of the two Bs decays into the signal channel, the other decays generically. TheB0 → K∗0νν includes only the K∗0 → K+π− final state (Notice that BR(K∗0 → K+π−) =


Table 2.3: Data samples with total number of events.

Run period EventsRun1 280407361Run2 917764240Run3 485066397Run4 1482896628Run5 1964332114Run6 1032649880

66.57%). The kinematics of the signal decay is described by a phase space model, despite ofthe expected SM spectrum of Eq. (1.42).

The number of events in the on-peak data samples corresponding to the six differentrun periods are listed in Tab. 2.3. All the MC samples, with the corresponding numbersof generated events, are quoted in Tab. 2.4. Also the generic MC samples are divided insub-samples corresponding to the different run periods. The signal scale factors have beenevaluated according to the SM expected BR (1.3× 10−5).

2.7. DATA AND MONTE CARLO SAMPLES 37

Table 2.4: MC samples with total number of generated events and scale factor (data lumi-nosity / equivalent MC luminosity). The signal scale factors have been evaluated accordingto the SM expected BR (1.3× 10−5). The scale factor for B0 → K∗0νν includes the BR ofK∗0 → K+π−.

Sample Run Period Events Scale FactorB0 → K∗0νν Signal MC Run1–6 5270000 0.00074587B± → K∗±νν Signal MC Run1–6 7767000 0.00076023

B0B0 Generic MC Run1 37200000 0.3010778Run2 103356000 0.3260300Run3 48466000 0.3669505Run4 167332000 0.3300319Run5 235964000 0.2889020Run6 102348000 0.3499633

B+B− Generic MC Run1 36968000 0.3029666Run2 103124000 0.3267634Run3 49766000 0.3573650Run4 167994000 0.3287314Run5 244322000 0.3003362Run6 100818000 0.3552742

cc Generic MC Run1 58900000 0.4708575Run2 168844000 0.4941874Run3 83974000 0.5244256Run4 252830000 0.5408669Run5 366758000 0.4954213Run6 157200000 0.5642003

uds Generic MC Run1 47180000 0.9450391Run2 130858000 1.0251323Run3 66892000 1.0584187Run4 213380000 1.0713617Run5 317846000 0.9190528Run6 127926000 1.1146280

τ+τ− Generic MC Run1 20378000 0.9840739Run2 55606000 1.0850259Run3 27988000 1.1377357Run4 90032000 1.0982636Run5 132234000 0.9935635Run6 56436000 1.1363552

Chapter 3

The Semileptonic Recoil technique

Searches for rare B decays with undetected neutrinos are affected by large backgrounds, dueto the impossibility of fully constraining the kinematics of the final state. On the other hand,a satisfactory background suppression can be obtained in the framework of recoil analyses.In these searches, one of the two B mesons produced by the Υ (4S) decay is reconstructedin some set of clean and frequent channels (we will denote this procedure as the taggingand the reconstructed B will be the tagging B, Btag, in opposition to the signal B, Bsig).Then, a signal is searched in the rest of the event (ROE), not considering the particles usedto reconstruct the tagging B. This method provides a reasonably pure sample (i.e. with asmall amount of non–BB events) and a clean environment to look for the signature of a raredecay.

The BABAR collaboration developed two different recoil strategies, based on the recon-struction of a semileptonic or a hadronic Btag decay respectively. The search described inthis thesis has been performed exploiting the semileptonic recoil technique. In this chapter,we describe the reconstruction of the tagging B (Sec. 3.1) and the discriminating variablesthat allow to reject background events and wrongly reconstructed Btag’s (Sec. 3.2). Finally,we briefly comment on the tagging performances (Sec. 3.3).

3.1 Reconstruction of B → D`ν(X)

The analysis starts from the reconstruction of semileptonic B → D`ν(X) decays, where ldenotes an electron or a muon, while X can be a photon or a soft pion coming from thedecay of higher mass charm states.

Charged and neutral D mesons are reconstructed in the following modes:

• D0 → K−π+, D0 → K−π+π0(γγ), D0 → K−π+π+π−, D0 → K0Sπ+π−;

• D+ → K−π+π+, D+ → K0Sπ+;

Charged kaons and pions are selected among tracks with a distance of closest approach tothe interaction point lower than 1.5 cm in the transversal plane and 10 cm along the z axis.Charged kaons are also required to satisfy a particle ID requirement, based on a likelihood

39

40 CHAPTER 3. THE SEMILEPTONIC RECOIL TECHNIQUE

ratio built from the energy loss dE/dx in the SVT and DCH, the Cerenkov angle and thenumber of photons in the DIRC. The kaon ID efficiencies ranges between 95% and 99%depending on the momentum. The probability of identifying a pion as a kaon is between10% and 20%.

Pairs of photons are used to reconstruct neutral pions in the π0 → γγ mode. The π0

mass is required to lie between 0.115 and 0.150 GeV/c2 and the π0 energy to be greater than0.200 GeV in the laboratory frame. A single EMC clusters with a suitable second momentumand energy can be identified as a π0, decayed into a pair of photons with a relative angle toosmall to produce two distinct clusters (merged π0).

The K0S

candidates are reconstructed in the K0S→ π+π− mode, from pairs of tracks with

invariant mass in the range 0.47267 < mK0S< 0.52267 GeV/c2. A kinematical fit is applied

to reconstruct the K0S

decay vertex. The χ2 probability of the fit is required to be greaterthan 0.1% and the distance of the vertex from the interaction point is required to be greaterthan 3 times the uncertainty on the distance itself, due to the flight length of the K0

S.

Electrons and muons are finally associated with the D(∗) candidates. Electrons are se-lected among tracks satisfying a particle ID requirement, based on a likelihood ratio builtfrom 9 variables, related to the EMC cluster shape, the energy loss and the DIRC measure-ments. If a photon can be found, separated from the electron by a small angle, it can beassociated with the electron in order to correct the electron 4-momentum for bremsstrahlungemission. Muons are selected among tracks satisfying a particle ID requirement, based ona neural network output built form 8 variables, mainly related to EMC and IFR measure-ments. The electron and muon ID efficiencies are ∼ 92% and ∼ 90% respectively in themomentum range of interest, while the probability of identifying kaons or pions as leptonsis at the permil level for the electron hypothesis and ∼ 1% for the muon hypothesis.

We also implemented algorithms allowing to reconstruct a D∗ from the D candidate.A neutral or charged pion can be associated to the D in order to build a D∗+ → D0π+

or D∗+ → D+π0 decay, if the difference ∆m between the D∗ mass and the D0 mass iswithin 0.130 GeV/c2 and 0.170 GeV (the nominal value, from the PDG [2], is ∆mPDG =0.14217± 0.00007 MeV/c2). A photon with energy greater than 0.050 GeV can be combinedwith the D to build a D∗ → Dγ decay if the resulting ∆m is between 0.100 GeV/c2 and0.150 GeV.

Considering the expected particle multiplicities of the final states we are looking for, weuse only events with less than 12 tracks and 15 photons (counting only photons with energyE > 0.05 GeV).

3.2 Continuum background rejection

Two classes of contaminations affect the tagging B reconstruction: contamination from non-BB events and form wrongly reconstructed BB pairs, the latter giving the main contribution.

Several possibilities of BB mis-reconstruction exist: for instance, a Btag candidate canbe built using particles coming from two different B’s or missing one of the particles it hasdecayed to. These events can contribute to the background, since the absence of a particle orthe presence of unwanted particles in the ROE can fake the signal signature. A wide variety

3.2. CONTINUUM BACKGROUND REJECTION 41

of B decay modes can produce these effect and it makes hard a systematic classification ofthe BB background in terms of a few specific decay channels.

Anyway, it is possible to identify a set of variables that can be used in order to reducethe amount of continuum events and misreconstructed B mesons:

• mD: the reconstructed D mass. It is expected to peak around the nominal value forwell reconstructed Btag’s, while flatter distributions are expected for continuum andmiserconstructed B’s.

• ∆m: the difference between the reconstructed D and D∗ masses. The expected valueis 0.14212± 0.00007 GeV/c2. This quantity is used instead of mD when a D∗ is recon-structed. The difference is used in place of the D∗ mass in order to reduce the impactof the resolution of the D 4-momentum.

• cos θB,Dl: the angle between the Btag and the Dl pair. This quantity can be evaluated,assuming that the only particle missed in the Btag reconstruction is a massless neutrino,using the formula:

cos θB,Dl =2EBED(∗)l −m2

B −m2D(∗)l

2|~pB||~pD∗l|. (3.1)

Due to the finite resolution in the reconstructed quantities used to calculate it, cos θB,Dl

can fall outside the physical range [−1, 1] also for correctly reconstructed Btag’s.

• |~p ∗l |: the momentum of the lepton in the CM frame. In the continuum sample its

distribution peaks at lower values with respect to the BB sample.

Table 3.1: Pre-selection applied to the Btag candidates (mPDGD is the nominal D mass).

Variable Modes Range

cos θB,Dl All [-5.0,1.5]

mD −mPDGD B+ → D0(K−π+π0)`+ν [-0.070,0.070]

( GeV/c2) other B → D`ν modes [-0.040,0.040]

∆m D∗0 → D0γ [0.100,0.150]

( GeV/c2) D∗+ → D+π0 [0.140,0.150]

D∗+ → D0π+ [0.137,0.175]

|~p ∗l | All [0.100,0.150]

( GeV/c)

The variables listed above are used for a preliminary selection, which will be refined ina subsequent stage of the analysis (see Sec. 4.3). The D mass is required to differ fromits nominal value by no more than 0.070 GeV/c2 in the D0 → K−π+π0 mode, 0.040 GeV/c2

elsewhere, corresponding to a 6σ range. The D∗0 → D0γ reconstruction algorithm allows

42 CHAPTER 3. THE SEMILEPTONIC RECOIL TECHNIQUE

only 0.100 < ∆m < 0.150 GeV. We require 0.135 < ∆m < 0.175 GeV for D∗+ → D0π+ and0.140 < ∆m < 0.150 GeV for D∗+ → D+π0. The value of cos θB,Dl is allowed to lie between−5 and 1.5. The momentum of the lepton |~p ∗

l | is required to be greater than 0.8 GeV/c.These requirements are summarized in Tab. 3.1. In the case of D∗ → Dγ, the value ofcos θB,Dl calculated using the D∗` pair is required to be higher than the value calculatedusing the D` pair, otherwise the D meson is used instead of the D∗.

3.3 Tagging performances

After the loose preliminary selection described in this section, ∼ 6.5% of BB events areselected. The data sample is expected to be composed by ∼ 65% of BB, while the remainingfraction is given at 70% by cc and 30% by uds. The contribution from τ+τ− events is expectedto be negligible.

The purity of the sample is improved by refining the selection described above. Thestrategy adopted in order to optimize this selection is interconnected with the reconstructionand selection of the signal B and is the main topic of the next chapter.

Chapter 4

Reconstruction and selection ofB → K∗νν

Once a Btag candidate has been reconstructed, charged tracks and neutral EMC clusters usedfor the Btag reconstruction are removed from the event. The remaining particle candidatesare used to search for a K∗, the only particle we can detect in the Bsig → K∗νν decay.

In Sec. 4.1, we describe the reconstruction of the K∗. When more than one BtagBsig

pair candidates can be reconstructed in the same event, we need to select one of them. Wedeveloped a best candidate selection algorithm that is described in Sec. 4.2. In Sec. 4.3 wedefine the discriminating variables that can be used to reject background events, and inSec. 4.3.4 we illustrate the optimization of the selection requirements. Finally, the efficiencyof the reconstruction and selection procedure are studied in detail (Sec. 4.4).

4.1 K∗ Reconstruction

In this analysis, the Bsig is reconstructed looking for a K∗ decaying in one of the followingmodes:

• K∗0 → K+π−;

• K∗+ → K0Sπ+ (with K0

S→ π0π0 and K0

S→ π+π−), K∗+ → K+π0.

The K0S→ π0π0 channel is reconstructed by taking a neutral pions with energy greater

than 0.200 GeV and another one with energy greater than 0.500 GeV in the laboratory frame.A preliminary selection 0.446 < mKS < 0.540 GeV/c2 is imposed. Requirements on the K0

S

energy (> 0.800 GeV) and transversal momentum (> 0.050 GeV/c) in the laboratory frameare also applied.

The K0S→ π0π0 channel, the charged kaons and the pions are selected with the same

strategies adopted for the tag side (see Sec. 3.1), but applying different PID and recon-struction requirements, chosen among several options in order to optimize the signal versusbackground discrimination. Independently on the strategy used to extract the BR, it canbe done looking for the set of selection criteria that maximizes a suitable function of the

43

44 CHAPTER 4. RECONSTRUCTION AND SELECTION OF B → K∗νν

expected signal and background yields, called figure of merit (FOM). We chose, in particularthe so-called Punzi FOM [28] 1.

FOMPunzi ≡ε

nσ

2+√Nb

(4.1)

where ε is the expected signal efficiency, nσ is the number of sigmas corresponding to aone-sided Gaussian test with a given significance (nσ = 1.285 for a 90% confidence level),and Nb is the expected background yield. The efficiency can be estimated using the signalMC sample, while the expected background yield is extracted from the generic MC samples,taking into account the luminosity scale factors.

As a result, with respect to the requirements applied on the tag side, we tighten the PIDcriteria on the charged kaons. We use only photons with energy greater than 0.050 MeVwhen reconstructing π0’s. We do not apply any selection on the K0

Sflight length.

The number of tracks in the ROE is required to match the number of expected tracksfor the reconstructed channel. In other words, we require that all reconstructed tracks areassociated with one and only one of the two B mesons. The corresponding criteria aresummarized in Tab. 4.1

Table 4.1: Requirements applied on the number of tracks in the ROE.

Decay Mode RequirementK∗0 → K+π− # Tracks = 2K∗+ → K0

Sπ+ (K0

S→ π+ π−) # Tracks = 3

K∗+ → K0Sπ+ (K0

S→ π0 π0) # Tracks = 1

K∗+ → K+π0 # Tracks = 1

The signal K∗ candidate is also rejected if its flavour does not match the Bsig flavour,extrapolated from the Btag flavour. Signal events fail this selection if B0B0 mixing occurred;it implies the rejection of ∼ 19% of signal events (corresponding to the time integrated B0B0

mixing probability, (18.8± 0.3)% [2]), but allows to reduce the background by a factor of 2.In practice, we look for the following combinations:

D(∗)−l+ν ← B0B0 → K∗0νν

D(∗)+l−ν ← B0B0 → K∗0νν

D(∗)0l+ν ← B+B− → K∗−νν

1The expression for the Punzi FOM is extracted by evaluating the ability of a counting experiment fordiscovering, with a significance α, a process with cross section σ, given an efficiency ε, a luminosity L and anexpected background Nb. In particular, an experiment is said to be sensitive to the cross section σ if thereis a probability > 1− β of observing it. By choosing β = α and by approximating the Poisson distributionswith gaussian distributions, it is possible to show that the maximization of the Punzi FOM minimizes thelower cross section the experiment is sensitive to. We preferred the Punzi FOM with respect to other classicalFOMs like Ns/

√Nb or Ns/

√Ns + Nb since it is independent on the cross section and works well both at low

and high values of Nb.

4.2. BEST CANDIDATE SELECTION 45

D(∗)0l−ν ← B−B+ → K∗+νν

(4.2)

There is no other requirement on the number of neutral candidates, apart from theprimordial one (see Sec. 3.1). Instead, photons in the ROE, with energies Ei > 0.050 GeV,are used to define the extra energy:

Eextra ≡∑

i ∈ ROEEi (4.3)

A kinematical fit is also applied to determine the K∗ decay vertex and refine the 4-momentum of the reconstructed candidates.

At the same time of the signal reconstruction, we also look for a second B → D`ν(X)candidate on the signal side. If we can find one or more, any other B → K∗νν candidate isrejected and the event is classified as a double tagged event and stored for systematic studies(see Sec.6.3).

4.2 Best candidate selection

At this stage of the analysis, various Btag candidates can be reconstructed, and, for eachof them, we can have various Bsig candidates. It happens for about 20% of signal events.Hence, we need to select a single BB pair, to be submitted to the selection procedure. Inthis section we describe the algorithm we developed in order to chose the best pair BB pairs.

In this algorithm, we try to assign to each pair the probability that the two B mesons arecorrectly reconstructed. Then, we select the pair with the highest probability. In the MC,correctly reconstructed Btag can be identified by comparing the reconstructed candidatesand the generated particles (MC truth information). We will say that a Btag is correctlyreconstructed (or truth matched) if:

1. The lepton matches the MC truth;

2. The D0,± matches the MC truth.

We will say that the Bsig is correctly reconstructed if:

1. The two daughters of the K∗ match the MC truth and have the same true mother.

Table 4.2: Priors and pch factors.

Channel pch P (TT ) P (TF ) P (FT ) P (FF )K∗0 → K+π− 0.3678 0.690792 0.0283082 0.256895 0.0240044K∗+ → K0

Sπ+ (K0

S→ π+π−) 0.3093 0.424766 0.111244 0.209443 0.254547

K∗+ → K0Sπ+ (K0

S→ π0π0) 0.0489 0.284879 0.149649 0.169135 0.396337

K∗+ → K+π0 0.2740 0.413285 0.159454 0.224364 0.202896


So, we can define this complete set of classes:

• The two B are both correctly reconstructed (we will identify this class as TT);

• Only the Btag is correctly reconstructed (TF);

• Only the Bsig is correctly reconstructed (FT);

• None of the two B is correctly reconstructed (FF).

Now, given a set of observable x, the probability of the class TT can be written, usingthe Bayes Theorem, as:

P (TT |x) =P (x|TT )P (TT )∑

i P (x|i)P (i)i = TT, TF, FT, FF (4.4)

The likelihoods P (x|i) can be derived from the MC distribution of truth matched and notmatched event, as well as the a priori probabilities P (i), calculated as the ratio between thenumber of events in the class i and the total number of reconstructed events.

When different pairs have been reconstructed using different K∗ modes, we have also totake into account that these channels can have different branching ratios and can pass thereconstruction and the primordial selection with different efficiencies. In other word, theycan have different priors. To account for this effect, we can simply multiply each P (TT |x)by a factor pch = Bch ·εreco, where Bch is the branching ratio of the specific K∗ decay channeland εreco is the corresponding efficiency of the reconstruction and the primordial selection,evaluated just before the best pair selection algorithm is applied.

The choice of the observables x to be used in the application of this method is driven by acouple of considerations: at first, we need a reasonable discrimination between true and falsecandidates; however, we would avoid variables we plan to use in the final selection. In fact,the best candidate selection can modify their distribution and reduce their discriminatingpower. Finally, the observables we choose are the χ2 probabilities of the Btag and Bsig

vertex fits. Their distributions in TT, TF, FT and FF events in the signal MC are shownin Figg. 4.1–4.4. These distributions are described using a Gaussian function summed to afirst order polynomial function. The corresponding parameters are extracted from a χ2 fit.The values of the priors P (i) and the factors pch are quoted in Tab.4.2.

Alternative best candidate selection strategies have been tested. In particular, using thesame set of variables x, for each candidate we have such a set xi. So, we tried to definethe probability P (i|x1 . . .xn) of the i-th candidate to be the true one, among n candidates.Considering that only one candidate can be the true one, this probability can be written as:

P (i|x1 . . .xn) =P (x1 . . .xn|i)P (i)

∑

j P (x1 . . .xn|j)P (j)(4.5)

where P (x1 . . .xn|i) = P (x1|F ) . . . P (xi|T ) . . . P (xn|F ), being P (xi|T ) = P (xi|TT ) andP (xi|F ) = P (xi|TF ) + P (xi|FT ) + P (xi|FF ), according to the definitions given above; i.e.


P (x1 . . .xn|i) is the probability that the i-th candidate is true while the others are false 2. Theprior probabilities p(i) can be taken identical since a priori there is no privileged candidate.The candidate with the higher P (x|i) is selected.

In order to compare the two methods, we compare the Punzi FOM obtained by adoptingthe two methods and calculated after a non-optimized selection based on discriminatingvariables which we will describe later. By using the first method, i.e. the probability definedin Eq. (4.4), we obtained the best FOM.

2we are neglecting here the possibility of correlations among the xi, but is not completely correct sincedifferent candidates can share the same Btag or the same K∗. It is expected to worsen the performances ofthe method, but no bias is expected as far as the effect is the same in data and MC


Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Figure 4.1: Btag (left) and Bsig (right) Vertex Probability distributions in the K∗0 → K+π−

signal sample. From the top to the bottom: TT, TF, FT and FF.


Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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0100200300400500600700800900

Figure 4.2: Btag (left) and Bsig (right) Vertex Probability distributions in the K∗+ → K0Sπ+

(K0S→ π+π−) signal sample. From the top to the bottom: TT, TF, FT and FF.


Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

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020406080

100120140160180200220240

Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

000

050

100150200250300350

Figure 4.3: Btag (left) and Bsig (right) Vertex Probability distributions in the K∗+ → K0Sπ+

(K0S→ π0π0) signal sample. From the top to the bottom: TT, TF, FT and FF.


Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

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Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

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Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

000

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50

100

150

200

250

Figure 4.4: Btag (left) and Bsig (right) Vertex Probability distributions in the K∗+ → K+π0

signal sample. From the top to the bottom: TT, TF, FT and FF.


4.3 Selection of signal events

After the selection of the best BB candidates, we refine the Btag selection and apply furthercriteria related to the event shape and the signal side reconstruction. The variables used inthe selection are required to lie within given ranges (rectangular cuts), whose optimizationin terms of the Punzi FOM will be described in Sec. 4.3.4.

In order to avoid the possible model dependence discussed in Sec. 1.5, we need a suit-able choice of the selection criteria. In particular, only these variables that do not show asignificant correlation with s = m2

νν/m2B can be used. In the next sections we will define the

discriminating variables we have chosen and we will prove, on the MC, their independenceon s.

4.3.1 Background characterization

As already mentioned, a wide variety of processes can fake the signal signature, mainly dueto the interplay between the signal and tag side, i.e. the possibility of using signal sideparticles in order to reconstruct the Btag or loosing particles in the tag side reconstruction.Moreover, particle mis-identification effects can be significant. As a consequence, a system-atic classification of the background in terms of a few specific decay channels is not possible.On the other hand, it can be interesting to classify the background in terms of the effectsthat allowed it to fake the signal signature. Taking as an example the K∗0 → K+π− channeland concentrating on the dominant B0B0 background, in the MC we can distinguish thefollowing categories:

1. no true particle associated with the reconstructed K or π;

2. π → K mis-identification;

3. K → π mis-identification;

4. µ→ K mis-identification;

5. µ→ π mis-identification;

6. e→ K mis-identification;

7. e→ π mis-identification;

8. Generic mis-identification (Cat. 2 to 7 plus other mis-identifications);

9. K and π from two different B’s;

10. K and π from the same B but different mothers;

11. X → Kπ but X is not a K∗;

12. true K∗.

4.3. SELECTION OF SIGNAL EVENTS 53

Table 4.3: Breakdown of the B0B0 background affecting the K∗0 → K+π− channel. See thetext for a definition of the categories. Since these categories are not exclusive one with theother, the sum of the percent fractions is not 100%.

Category Fraction of events (%)Cat. 1 0.1Cat. 2 2.1Cat. 3 6.8Cat. 4 0.9Cat. 5 9.3Cat. 6 1.3Cat. 7 8.5Cat. 8 29.4Cat. 9 13.9Cat. 10 42.7Cat. 11 18.6Cat. 12 24.8

A breakdown of the K∗0 → K+π− background, after the preliminary Btag selection, thesignal reconstruction and the best candidate choice, can be found in Tab. 4.3. Notice thelarge contribution due to the particle mis-identification.

A specific attention is needed for the background coming from the rare B → τν decay.It will be discussed when treating the systematic uncertainties (Sec. 6.3).

4.3.2 Event shape selection

Selection criteria related to the event shape allow to reject a large fraction of non–BB events,providing a clean sample of BB pairs. In particular, we decided to use:

• cos θDl,T : it is the cosine of the angle between the D(∗)l pair an the thrust axis [29] ofthe ROE. Given the jet-like shape of the continuum background, the distribution ofcos θDl,T is peaked at ±1, while a flatter distribution is expected in the BB sample;

• R2: it is the ratio of the second and zeroth Fox-Wolfram moments [30]. This quantity,ranging between 0 and 1, assumes lower values in more spherical events. Also in thiscase, the jet-like shape of the continuum, produces higher values of R, hence removingthe events with the highest R2 values helps to reduce the continuum contribution tothe background;

• E∗miss + c|~p ∗

miss|: Let us consider E∗miss, |~p ∗

miss| and M2miss, which are respectively the

time component, the module of the space component and the invariant norm of themissing 4-momentum p∗miss, evaluated in the CM frame as the difference betweenthe Υ (4S) 4-momentum and the sum of the 4-momenta of all the tracks and neutral


clusters in the event. In a perfectly reconstructed signal event, it represents the sum ofthe 4-momenta of the three neutrinos. As expected, we notice a significant correlationbetween these variables and s (see Figg. 4.14–4.16) and it precludes the possibilityof using these variables singularly. Anyway, the correlation disappears considering thesum E∗

miss+c|~p ∗miss|. Since this quantity peak at higher values in the signal with respect

to the background, allowing for a strong discrimination, we adopt this combination inour selection.

• cos(θmiss): The polar angle of the missing 3-momentum.

At this level, we also apply a further tightening of the PID requirements on the D mesondecay products. In particular, charged pions do not have to pass the PID requirements ofelectrons, muons and kaons. Charged kaons do not have to pass the PID requirements ofelectrons and muons.

Figg. 4.5–4.12 show the distributions of the event shape variables before the applicationof the selection. Tag side discriminating variables are also shown. The distributions aretaken from the full signal sample and generic samples (scaled to the data luminosity), alongwith the on-peak and off-peak data. Each row shows the plots for a different channel. Fromthe top, K∗0 → K+π−, K∗+ → K0

Sπ+ with K0

S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0,

K∗+ → K+π0.The overall data-MC agreement is good, apart from a 5% discrepancy in the normalization

of K∗+ → K0Sπ+ (K0

S→ π+π−).

Some relevant correlation plots are shown in Figg. 4.13–4.18. The plots show that thevariables chosen for the selection do not have significant correlations with s.


)T,Dlθcos(-1 -0.5 0 0.5 1

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0.360.380.4

0.420.440.460.48

0.5

Figure 4.5: cos θDl,T distribution in the generic MC samples (filled histograms in the leftplot) in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


R20 0.2 0.4 0.6 0.8 1

N.e

v./(0

.066

667

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R20 0.2 0.4 0.6 0.8 1

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0

0.2

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1

1.2

Figure 4.6: R2 distribution in the generic MC samples (filled histograms in the left plot)in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


cosBY-3 -2 -1 0 1

N.e

v./(0

.300

000

)

0200400600800

100012001400160018002000

-3 -2 -1 0 10200400600800

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cosBY-3 -2 -1 0 1

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12000

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cosBY-3 -2 -1 0 1

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cosBY-3 -2 -1 0 1

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00.10.20.30.40.50.60.70.8

Figure 4.7: cos θB,Dl distribution in the generic MC samples (filled histograms in the leftplot) in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


)2 (GeV/cDm1.8 1.85 1.9

)2N

.ev.

/(0.0

0800

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eV/c

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)2N

.ev.

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eV/c

01000200030004000500060007000

1.8 1.85 1.901000200030004000500060007000


)2 (GeV/cDm1.8 1.85 1.9

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)2 (GeV/cDm1.8 1.85 1.9

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1.8 1.85 1.90200400600800

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)2 (GeV/cDm1.8 1.85 1.9

)2N

.ev.

/(0.0

0800

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eV/c

00.20.40.60.8

11.21.41.6

Figure 4.8: mD distribution in the generic MC samples (filled histograms in the left plot)in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


)2 M (GeV/c∆0.13 0.14 0.15 0.16 0.17 0.18

)2N

.ev.

/(0.0

0333

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eV/c

0

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800

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)2N

.ev.

/(0.0

0333

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eV/c

0.060.08

0.10.120.140.160.180.2

0.22

Figure 4.9: ∆m distribution in the generic MC samples (filled histograms in the left plot)in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


| (GeV/c)l

*p|1 1.5 2 2.5

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/c)

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*p|1 1.5 2 2.5

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Figure 4.10: |~p ∗l | distribution in the generic MC samples (filled histograms in the left plot)

in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


| (GeV)miss

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Figure 4.11: E∗miss + c|~p ∗

miss| distribution in the generic MC samples (filled histograms in theleft plot) in the data sample (dots in the left plot) and in the signal MC sample (right). AllMC samples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+

with K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


)missθcos(-1 -0.5 0 0.5 1

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)

0.150.2

0.250.3

0.350.4

0.450.5

0.55

Figure 4.12: cos(θmiss) distribution in the generic MC samples (filled histograms in the leftplot) in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

R2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

R2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

R2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

R2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 4.13: R2 vs. s distribution in the signal MC sample. K∗0 → K+π− (top left),K∗+ → K0

Sπ+ with K0

S→ π+π− (top right), K∗+ → K0

Sπ+ with K0

S→ π0π0 (bottom left),

K∗+ → K+π0 (bottom right).


s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

2m

0

5

10

15

20

25

30

35

40

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

2m

0

5

10

15

20

25

30

35

40

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

2m

0

5

10

15

20

25

30

35

40

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

2m

0

5

10

15

20

25

30

35

40

Figure 4.14: M 2miss vs. s distribution in the signal MC sample. K∗0 → K+π− (top left),

K∗+ → K0Sπ+ with K0


Sπ+ with K0




s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

E

-1

0

1

2

3

4

5

6

7

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

E

-1

0

1

2

3

4

5

6

7

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

E

-1

0

1

2

3

4

5

6

7

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

E

-1

0

1

2

3

4

5

6

7

Figure 4.15: E∗miss vs. s distribution in the signal MC sample. K∗0 → K+π− (top left),



Sπ+ with K0




s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

p

0

1

2

3

4

5

6

7

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

p

0

1

2

3

4

5

6

7

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

p

0

1

2

3

4

5

6

7

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

p

0

1

2

3

4

5

6

7

Figure 4.16: c|~p ∗miss| vs. s distribution in the signal MC sample. K∗0 → K+π− (top left),



Sπ+ with K0




s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

+ p

miss

E

0

1

2

3

4

5

6

7

8

9

10

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

+ p

miss

E

0

1

2

3

4

5

6

7

8

9

10

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

+ p

miss

E

0

1

2

3

4

5

6

7

8

9

10

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

miss

+ p

miss

E

0

1

2

3

4

5

6

7

8

9

10

Figure 4.17: E∗miss + c|~p ∗

miss| vs. s distribution in the signal MC sample. K∗0 → K+π− (topleft), K∗+ → K0

Sπ+ with K0


Sπ+ with K0

S→ π0π0 (bottom

left), K∗+ → K+π0 (bottom right).


s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)m

issθ

cos(

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)m

issθ

cos(

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)m

issθ

cos(

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)m

issθ

cos(

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1

Figure 4.18: cos(θmiss) vs. s distribution in the signal MC sample. K∗0 → K+π− (top left),K∗+ → K0

Sπ+ with K0


Sπ+ with K0




4.3.3 Signal side selection

The tag side algorithm, along with optimized selection criteria on the variables describedin the previous section 3, provides a clean sample of BB events with a small continuumcontamination (mainly cc).

Removing from the event the tracks and the neutral clusters associated with the Btag

provides, at this point, a clean environment to look for rare decays with missing energy, suchas B → K∗νν. Anyway, a large residual background is still present, due to combinatoriccombinations of products of other decays. This effect is mainly driven by:

1. particle mis-identification;

2. loss of particles in the event reconstruction;

3. a wrong tag side reconstruction, performed including signal side particles or not in-cluding real tag side particles.

In these cases, the remaining particles in the signal side can casually match the requirementsimposed by the B → K∗νν reconstruction. Notice also that these effects are not exclusiveone with the other and are often mixed.

In order to reduce the amount of the background contributions, some selection criteriaare applied on the variables related to the signal B. On the other hand, also in this case,we want to avoid to use selection variables correlated to s. In particular, we cannot use thekinematical properties of the K∗ and its daughters, in spite of their strong discriminatingpower between signal and background. We chose to use just few discriminating variables:the K∗ mass, the K0

Smass and the already defined extra energy Eextra. The latter is the

most discriminating variable in this kind of analysis. In the signal events, Eextra mainlycomes from a random activity in the EMC, so it is expected to peak around zero for signalevent. Conversely, in the background, Eextra receives contributions from real particles and asmooth distribution is expected.

Figg. 4.19–4.21 show the distributions of the signal side variables used in the selection,taken from the full signal sample and generic MC samples. The correlations with s, whichare negligible, are shown in Figg. 4.22–4.24.

3Concerning the optimization, see Sec. 4.3.4 and Tab. 4.4


)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

0200400600800

10001200140016001800

0.8 0.85 0.9 0.95 10200400600800

10001200140016001800


)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

00.20.40.60.8

11.21.4

)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

010002000300040005000600070008000

0.8 0.85 0.9 0.95 1010002000300040005000600070008000


)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

0

0.2

0.4

0.6

0.8

1

)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

0100200300400500600700

0.8 0.85 0.9 0.95 10100200300400500600700


)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

00.020.040.060.08

0.10.120.14

)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

0200400600800

10001200140016001800

0.8 0.85 0.9 0.95 10200400600800

10001200140016001800


)2 (GeV/cK*m0.8 0.85 0.9 0.95 1

)2N

.ev.

/(0.0

1333

3 G

eV/c

00.10.20.30.40.50.60.70.80.9

Figure 4.19: K∗ mass distribution in the generic MC samples (filled histograms in the leftplot) in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


)2 (GeV/cKm0.46 0.48 0.5 0.52 0.54

)2N

.ev.

/(0.0

0533

3 G

eV/c

02000400060008000

10000120001400016000

0.46 0.48 0.5 0.52 0.5402000400060008000

10000120001400016000


)2 (GeV/cKm0.46 0.48 0.5 0.52 0.54

)2N

.ev.

/(0.0

0533

3 G

eV/c

0

0.5

1

1.5

2

2.5

)2 (GeV/cKm0.46 0.48 0.5 0.52 0.54

)2N

.ev.

/(0.0

0533

3 G

eV/c

0

100

200

300

400

500

600

0.46 0.48 0.5 0.52 0.540

100

200

300

400

500

600


)2 (GeV/cKm0.46 0.48 0.5 0.52 0.54

)2N

.ev.

/(0.0

0533

3 G

eV/c

00.020.040.060.08

0.10.120.14

Figure 4.20: K0S

mass distribution in the generic MC samples (filled histograms in the leftplot) in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗+ → K0

Sπ+ with K0

S→ π+π−,


S→ π0π0.


(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

050

100150200250300350

0 0.5 1050

100150200250300350


(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

00.5

1

1.52

2.5

3

(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

0200400600800

100012001400160018002000

0 0.5 10200400600800

100012001400160018002000


(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

00.20.40.60.8

11.21.41.61.8

2

(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

0

50

100

150

200

250

0 0.5 10

50

100

150

200

250


(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

00.05

0.10.15

0.20.25

0.30.35

(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

0

100

200

300

400

500

0 0.5 10

100

200

300

400


(GeV)extraE0 0.5 1

N.e

v./(0

.080

000

GeV

)

00.20.40.60.8

11.21.41.61.8

2

Figure 4.21: Eextra distribution in the generic MC samples (filled histograms in the left plot)in the data sample (dots in the left plot) and in the signal MC sample (right). All MCsamples are scaled to the data luminosity. From the top: K∗0 → K+π−,K∗+ → K0

Sπ+ with

K0S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.


s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

K*

m

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

K*

m

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

K*

m

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

K*

m

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Figure 4.22: K∗ mass vs. s distribution in the signal MC sample. K∗0 → K+π− (top left),K∗+ → K0

Sπ+ with K0


Sπ+ with K0



s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)K

m

0.46

0.47

0.48

0.49

0.5

0.51

0.52

0.53

0.54

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)K

m

0.46

0.47

0.48

0.49

0.5

0.51

0.52

0.53

0.54

Figure 4.23: K0S

mass vs. s distribution in the signal MC sample. K∗+ → K0Sπ+ with

K0S→ π+π− (left), K∗+ → K0

Sπ+ with K0

S→ π0π0 (right).


s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eext

ra

0

0.5

1

1.5

2

2.5

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eext

ra

0

0.5

1

1.5

2

2.5

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eext

ra

0

0.5

1

1.5

2

2.5

s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eext

ra

0

0.5

1

1.5

2

2.5

Figure 4.24: Eextra vs. s distribution in the signal MC sample. K∗0 → K+π− (top left),K∗+ → K0

Sπ+ with K0


Sπ+ with K0



4.4. EFFICIENCY AND BACKGROUND STUDIES 75

4.3.4 Optimization

Most of the selection requirements are optimized in order to get the best sensitivity to theB → K∗νν branching ratio. Independently on the strategy used to extract the BR, theoptimization can be done looking for the set of selection criteria that maximizes a suitablefunction of the expected signal and background yields, called figure of merit (FOM). Wechose, in particular, the already defined Punzi FOM. Signal efficiency and background yieldsare estimated applying the selection on the available MC samples.

We developed a set of automatic tools to perform the selection optimization, based onthe SIMPLEX minimization algorithm provided by MINUIT [31]. Each selection range isdefined by two parameters: the lower bound and the upper bound. The signal efficiency andthe background yield in the MC (and hence the FOM) are functions of these parameters.So, we can provide to MINUIT this set of parameters and a method to evaluate the FOM,and ask it to move the parameters (i.e. the definition of the selection ranges) to minimizethe inverse of the FOM, by using the SIMPLEX algorithm.

Since this automatic procedure can produce a sort of over-training and get a selectiontoo finely tuned on the specific MC sample we use, we adopted the following procedure:

1. A MINUIT SCAN of the parameters is performed in the full sample to get a firstminimum;

2. The sample is divided in 5 subsamples, and, starting from the first minimum, theminimization is performed independently in each of them;

3. The average of each parameter over the 5 samples is taken as the nominal one.

We optimized the ranges of the following variables: cos θDl,T , R2, |~p ∗l |, mK∗, E∗

miss +c|~p ∗

miss| and cos(θmiss). We do not optimize the selection requirement on Eextra, because wewant to use the full Eextra distribution in a maximum likelihood fit to extract the signal yield(see Sec. 6.2). Instead, the optimization has been performed using events in a signal regiondefined by Eextra < 0.6 GeV. Tab. 4.4 show the final selection criteria.

4.4 Efficiency and background studies

As already mentioned, the efficiency of the signal selection and the expected backgroundyield can be estimated applying the selection procedure to the MC samples described inSec. 2.7. We can also compare the performances for data and MC at different selectionstages. A good strategy to do that consist on performing a blinded analysis: events in theEextra signal region are removed from both the data and generic MC samples and only eventsin the sideband defined as 0.6 < Eextra < 1.5 GeV are retained. In this way, we are confidentto have a sample free of signal contribution, and we can compare data and MC independentlyon any assumption on the signal branching ratio. This allow to check the selection strategyand, if needed, to apply correction procedures, without introducing any bias in the finalresult.

76C

HA

PT

ER

4.

RE

CO

NST

RU

CT

ION

AN

DSE

LE

CT

ION

OFB→

K∗νν

Table 4.4: List of selection requirements.

K∗0 → K+π− K∗+ → K0Sπ+ K∗+ → K+π0

K0S→ π+π− K0

S→ π0π0

cos θB,Dl [-1.0,1.0] [-2.0,1.0]mD −mPDG

D D0 → K−π+π0: [−0.035,+0.035] [−0.020,+0.020](GeV/c2) other modes: [−0.020,+0.020]cos θDl,T [-0.996,0.998] [-0.990,0.996] [-0.977,0.973] [-0.987,0.997]R2 [0.004,0.797] [0.010,0.709] [0.021,0.789] [0.013,0.819]|~p ∗

l | (GeV/c) [0.835,2.478] [0.807,2.498] [0.272,2.395] [0.949,2.403]mK∗ (GeV/c2) [0.844,0.965] [0.845,0.954] [0.819,0.982] [0.825,0.969]mK0

S(GeV/c2) - [0.491,0.503] [0.440,0.572] -

E∗miss + c|~p ∗

miss| (GeV ) [5.112,9.007] [5.013,8.733] [4.900,9.643] [5.8124,8.823]cos(θmiss) [-0.951,0.886] [-0.875,0.850] [-0.787,0.959] [-0.900,0.875]


Table 4.5: K∗0 → K+π−: Expected background yields and observed data yields in the Eextra

sideband.Cut Generic MC data

Bsig Rec. 13172.9 13133cos θB,Dl 9453.8 9463mD 5220.6 5131∆M 4119.7 4043R2 4099.9 4025

Btag PID 3014.8 2877cos(θDl,T ) 2987.2 2858|~p ∗

l | 2929.6 2800mK∗ 2497.4 2346

E∗miss + c|~p ∗

miss| 818.2 835cos(θmiss) 653.1 697Eextra 360.3 398

In particular, we evaluated the expected yields in the Eextra sideband from the generic MCand compared them to the measured yields on data. The results are quoted in Tabb. 4.5–4.8.A good overall agreement is found. The already mentioned 5% discrepancy in the number ofK∗+ → K0

Sπ+ (K0

S→ π+π−) events disappears after the application of the refined tag side

PID requirements.Once the selection strategy is blindly checked, we can evaluate the effect of the selection on

data and MC in the full Eextra region used in the maximum likelihood fit (Eextra < 1.2 GeV).A detailed report of the results can be found in Tabb. 4.9–4.12, where we quote the numberof events passing the selection, and Tabb. 4.13–4.16, where these numbers are translatedin terms of efficiencies; here, the marginal efficiency is evaluated as the ratio between thenumbers of events we get applying sequentially all the cuts before the given one and thecuts up to the given one. Global efficiencies in the Generic MC samples have been evaluatedtaking into account the different luminosity scale factors.

In order to evaluate the signal efficiency, notice that the B0 → K∗0νν signal MC isgenerated only with K∗0 → K+π−, while the B± → K∗±νν signal MC is generated with ageneric K∗ decay. It means that a factor 0.6657 (corresponding to the K∗0 → K+π− BR) hasto be included in the calculation of the B0 → K∗0νν efficiency, and we do it when compilingthese tables.


Table 4.6: K∗+ → K0Sπ+ with K0

S→ π+π−: Expected background yields and observed data

yields in the Eextra sideband.

Cut Generic MC dataBsig Rec. 74136.9 78060cos θB,Dl 69041.4 72585mD 27433.9 28878∆M 27433.9 28878R2 26991.1 28506


l | 18536.7 18800mK∗ 13564.4 13818mK0

S1134.0 5280

E∗miss + c|~p ∗



S→ π0π0: Expected background yields and observed data

yields in the Eextra sideband.

Cut Generic MC dataBsig Rec. 6044.02 5840cos θB,Dl 5591.15 5404mD 2150.57 2119∆M 2150.57 2119R2 2091.43 2058


l | 1339.6 1281mK∗ 1315.58 1266mK0

S1303.55 1252

E∗miss + c|~p ∗



Table 4.8: K∗+ → K+π0: Expected background yields and observed data yields in the Eextra

sideband.Cut Generic MC data

Bsig Rec. 16315.09 16509cos θB,Dl 15124.61 15368mD 6043.31 6122∆M 6043.31 6122R2 5901 6028


l | 3673.54 3703mK∗ 3448.41 3479

E∗miss + c|~p ∗


80C

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PT

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4.

RE

CO

NST

RU

CT

ION

AN

DSE

LE

CT

ION

OFB→

K∗νν

Table 4.9: K∗0 → K+π−: Number of events that pass the selection cuts. In parenthesis, the numbers are scaled to theluminosity. We assumed the SM BR for B → K∗νν.

Cut SIGNAL B+B− B0B0 cc τ+τ− uds TOT MC datascaled

Btag Rec. 105312 49.86M 42.60M 17.67M 33329 3.481M 42.32M 40.88MBsig Rec. 9944 (7.417) 15610 (5031) 11131 (3550) 9547 (4915) 17 (18.2) 859 (864.9) 14379 14528cos θB,Dl 8561 (6.385) 11193 (3609) 8608 (2746) 6658 (3425) 9 (9.6) 575 (579) 10367 10526mD 7860 (5.863) 4976 (1604) 6641 (2121) 3608 (1855) 4 (4.3) 219 (222.4) 5807 5824∆M 7728 (5.764) 3661 (1181) 5512 (1760) 2919 (1501) 4 (4.3) 194 (196.7) 4644 4667R2 7724 (5.761) 3661 (1181) 5510 (1760) 2892 (1487) 3 (3.2) 188 (191 6) 4622 4646

Btag PID 7294 (5.440) 1958 (631.4) 4790 (1530) 2196 (1130) 1 (1.1) 122 (123.5) 3416 3347cos(θDl,T ) 7272 (5.424) 1951 (629.2) 4771 (1524) 2159 (1111) 1 (1.1) 119 (120.4) 3387 3323|~p ∗

l | 7185 (5.359) 1928 (621.7) 4709 (1504) 2077 (1069) 1 (1.1) 119 (120.4) 3316 3250mK∗ 6731 (5.020) 1590 (512.6) 3979 (1271) 1813 (932.3) 1 (1.1) 106 (107.0) 2824 2709

E∗miss + c|~p ∗

miss| 6556 (4.890) 622 (200.7) 1873 (597.5) 536 (275.9) 0 (0) 28 (28.7) 1103 1157cos(θmiss) 6194 (4.620) 567 (183.1) 1663 (530.7) 262 (135.0) 0 (0) 14 (14.0) 862.8 937Eextra 6173 (4.604) 216 (69.4) 1012 (323.2) 133 (68.3) 0 (0) 7 (7.1) 468.1 511

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S→ π+π−: Number of events that pass the selection cuts. In parenthesis, the numbers

are scaled to the luminosity. We assumed the SM BR for B → K∗νν.


Btag Rec. 149927 49.86M 42.60M 17.67M 33329 3.481M 42.32M 40.88MBsig Rec. 7475 (5.683) 92246 (29728) 72838 (23241) 43837 (22576) 47 (50.0) 4673 (4694) 80288 85153cos θB,Dl 7223 (5.491) 86919 (28010) 67958 (21682) 40429 (20819) 43 (45.6) 4298 (4316) 74872 79316mD 5858 (4.453) 38366 (12359) 26527 (8460) 15055 (7756) 12 (12.6) 1448 (1457) 30045 31919∆M 5858 (4.453) 38366 (12359) 26527 (8460) 15055 (7756) 12 (12.6) 1448 (1457) 30045 31919R2 5833 (4.434) 38277 (12330) 26441 (8432) 14422 (7428) 4 (4.4) 1362 (1371) 29566 31516

Btag PID 5407 (4.111) 27123 (8739) 17222 (5494) 10530 (5423) 3 (3.2) 1044 (1051) 20710 21279cos(θDl,T ) 5371 (4.083) 26888 (8663) 17093 (5453) 10259 (5283) 3 (3.2) 1018 (1024) 20426.5 20963|~p ∗

l | 5359 (4.074) 26823 (8642) 17050 (5439) 10177 (5241) 2 (2.2) 1011 (1017) 20342 20865mK∗ 4799 (3.648) 19617 (6323) 12406 (3960) 7514 (3867) 1 (1.1) 744 (749.8) 14901 15332mK0

S4118 (3.131) 7405 (2389) 4186 (1334) 3312 (1705) 0 (0) 293 (296.1) 5724 5868

E∗miss + c|~p ∗

miss| 3998 (3.039) 3224 (1040) 2066 (658.1) 1039 (535.2) 0 (0) 57 (58.2) 2291 2389cos(θmiss) 3644 (2.770) 2801 (902.6) 1784 (568) 572 (295.0) 0 (0) 22 (22.1) 1788 1890Eextra 3610 (2.744) 1262 (406.3) 843 (267.9) 281 (144.9) 0 (0) 8 (8.1) 827.2 872

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S→ π0π0: Number of events that pass the selection cuts. In parenthesis, the numbers are

scaled to the luminosity. We assumed the SM BR for B → K∗νν.


Btag Rec. 149927 49.86M 42.60M 17.67M 33329 3.481M 42.31M 40.88MBsig Rec. 1255 (0.954) 7027 (2264) 3867 (1234) 5686 (2929) 13 (13.7) 409 (413.0) 6854 6600cos θB,Dl 1216 (0.924) 6597 (2125) 3558 (1135) 5240 (2699) 13 (13.7) 386 (390.0) 6362 6131mD 966 (0.734) 2915 (940.3) 1306 (415.1) 1901 (977.1) 6 (6.3) 118 (118.8) 2458 2420∆M 966 (0.734) 2915 (940.3) 1306 (415.1) 1901 (977.1) 6 (6.3) 118 (118.8) 2458 2420R2 956 (0.727) 2885 (930.8) 1291 (410.3) 1809 (929.7) 5 (5.3) 111 (111.8) 2388 2357

Btag PID 878 (0.667) 1950 (629.4) 733 (233.4) 1390 (714.2) 5 (5.3) 89 (89.6) 1672 1595cos(θDl,T ) 855 (0.650) 1893 (610.9) 711 (226.3) 1185 (607.9) 2 (2.1) 76 (76.8) 1524 1467|~p ∗

l | 855 (0.650) 1893 (610.9) 711 (226.3) 1185 (607.9) 2 (2.1) 76 (76.8) 1524 1467mK∗ 849 (0.645) 1863 (601.2) 688 (218.9) 1169 (599.8) 2 (2.1) 75 (75.7) 1498 1446mK0

S844 (0.642) 1844 (595.1) 680 (216.4) 1159 (594.7) 2 (2.1) 75 (75.7) 1484 1432

E∗miss + c|~p ∗

miss| 832 (0.633) 1065 (344.2) 416 (132.3) 492 (251.9) 2 (2.1) 25 (25.4) 755.9 756cos(θmiss) 790 (0.601) 939 (303.7) 363 (115.4) 340 (174.3) 2 (2.1) 14 (14.0) 609.6 624Eextra 782 (0.594) 530 (171.1) 218 (69.5) 176 (90.0) 2 (2.1) 6 (5.9) 338.7 329

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Table 4.12: K∗+ → K+π0: Number of events that pass the selection cuts. In parenthesis, the numbers are scaled to theluminosity. We assumed the SM BR for B → K∗νν.


Btag Rec. 149927 49.86M 42.60M 17.67M 33329 3.480M 42.32M 40.88MBsig Rec. 7958 (6.050) 21347 (6869) 6517 (2078) 15170 (7814) 12 (12.7) 1285 (1289) 18063 18129cos θB,Dl 7677 (5.836) 20146 (6483) 6104 (1947) 13914 (7166) 12 (12.7) 1173 (1176) 16783 16776mD 6366 (4.840) 9248 (2974) 2239 (712.8) 5349 (2755) 6 (6.3) 396 (397.2) 6845 6886∆M 6366 (4.840) 9248 (2974) 2239 (712.8) 5349 (2755) 6 (6.3) 396 (397.2) 6845 6831R2 6334 (4.815) 9205 (2960) 2230 (709.9) 5147 (2650) 1 (1.0) 368 (369.5) 6691 6731

Btag PID 5923 (4.503) 6647 (2137) 1322 (420.5) 3749 (1930) 0 (0) 283 (285) 4773 4642cos(θDl,T ) 5872 (4.464) 6586 (2118) 1312 (417.5) 3641 (1875) 0 (0) 272 (273.5) 4684 4587|~p ∗

l | 5555 (4.223) 6231 (2003) 1223 (389.3) 3050 (1571) 0 (0) 224 (225.7) 4190 4168mK∗ 5389 (4.097) 5829 (1874) 1148 (365.0) 2873 (1480) 0 (0) 213 (214.8) 3934 3898

E∗miss + c|~p ∗

miss| 5237 (3.981) 2878 (924.5) 647 (204.6) 994 (510.9) 0 (0) 40 (40.7) 1681 1728cos(θmiss) 4906 (3.730) 2552 (820.3) 567 (179.6) 542 (278.2) 0 (0) 20 (20.0) 1298 1368Eextra 4776 (3.631) 1429 (458.7) 289 (91.4) 256 (131.8) 0 (0) 15 (14.8) 696.8 719

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Table 4.13: K∗0 → K+π−: Cumulative and Marginal Efficiencies in the signal MC, the generic MC and the data sample.

Cut SIGNAL GENERIC MC DATACumulative Marginal Cumulative Marginal Cumulative Marginal

Btag Rec. 0.0199833 0.0199833 0.0183042635 0.0183042635 0.0066332 0.0.0066332Bsig Rec. 0.0012561 0.0944241 0.0000062197 0.0003398 0.0000024 0.00036cos θB,Dl 0.0010814 0.8609222 0.0000044844 0.7210039 0.0000017 0.72453mD 0.0009929 0.9181163 0.0000025117 0.5601049 0.0000009 0.55330∆M 0.0009762 0.9832069 0.0000020086 0.7996638 0.0000008 0.80134R2 0.0009757 0.9994813 0.0000019991 0.9952812 0.0000008 0.99550

Btag PID 0.0009214 0.9443301 0.0000014775 0.7391054 0.0000005 0.72040cos(θDl,T ) 0.0009186 0.9969837 0.0000014644 0.9911502 0.0000005 0.99283|~p ∗

l | 0.0009076 0.9880364 0.0000014343 0.9794427 0.0000005 0.97803mK∗ 0.0008503 0.9368119 0.0000012215 0.8515924 0.0000004 0.83354

E∗miss + c|~p ∗

miss| 0.0008281 0.9740023 0.0000004770 0.3905072 0.0000002 0.42709cos(θmiss) 0.0007824 0.9447824 0.0000003732 0.7823999 0.0000002 0.80985Eextra 0.0007798 0.9966103 0.0000002025 0.5425076 0.0000001 0.54536

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Table 4.14: K∗+ → K0Sπ+ (K0

S→ π+π−): Cumulative and Marginal Efficiencies in the signal MC, the generic MC and the

data sample.


Btag Rec. 0.0193031 0.0193031 0.0183042613 0.0183042613 0.0066332 0.0066332Bsig Rec. 0.0009624 0.0498576 0.0000347287 0.0018973 0.0000138 0.0020829cos θB,Dl 0.0009300 0.9662873 0.0000323861 0.9325444 0.0000129 0.9314528mD 0.0007542 0.8110210 0.0000129960 0.4012828 0.0000052 0.4024283∆M 0.0007542 1.0000000 0.0000129960 1.0000000 0.0000052 1.0000000R2 0.0007510 0.9957314 0.0000127887 0.9840490 0.0000051 0.9873743


l | 0.0006900 0.9977640 0.0000087990 0.9958602 0.0000034 0.9953251mK∗ 0.0006179 0.8955025 0.0000064453 0.7325120 0.0000025 0.7348191mK0

S0.0005302 0.8580971 0.0000024757 0.3841115 0.0000010 0.3827289

E∗miss + c|~p ∗


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Table 4.15: K∗+ → K0Sπ+ (K0

S→ π0π0): Cumulative and Marginal Efficiencies in the signal MC, the generic MC and the

data sample.




l | 0.0001080 1.0000000 0.0000006592 1.0000000 0.0000002 1.0000000mK∗ 0.0001072 0.9929828 0.0000006478 0.9827387 0.0000002 0.9856851mK0

S0.0001066 0.9941097 0.0000006419 0.9908631 0.0000002 0.9903181

E∗miss + c|~p ∗


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Table 4.16: K∗+ → K+π0: Cumulative and Marginal Efficiencies in the signal MC, the generic MC and the data sample.




l | 0.0007152 0.9460156 0.0000018122 0.8945160 0.0000007 0.9104412mK∗ 0.0006938 0.9701166 0.0000017017 0.9390720 0.0000006 0.9352207

E∗miss + c|~p ∗


Chapter 5

Control samples

5.1 The Double Tag Sample

The Double Tag sample is widely used in these analyses that exploit the semileptonic recoiltechnique, in order to validate or correct the tagging efficiency evaluated in the signal andgeneric MC samples.

As already mentioned in Sec. 4.1, the double tag sample is composed by these eventswhere two different and independent B → D`ν(X) candidates can be reconstructed. As fortheB → K∗νν sample, the right flavour correlation is required between the two reconstructedcandidates. By construction, the double tag sample is completely independent w.r.t. theB → K∗νν sample; in fact, if it is possible to reconstruct at least one B → D`ν(X) pair inthe event, this is classified as a double tagged event and no B → K∗νν candidate is accepted.

Also in the double tag sample it is possible to reconstruct different BB pairs and a bestcandidate selection is applied. In order to preserve the consistency between the single tagand the double tag sample, we apply the same method described in Sec. 4.2 to select the bestBB pair, and we model the PDFs and the Priors using the the signal sample, with the onlydifference that in this case we simply distinguish the B0 → K∗0νν and the B± → K∗±ννsample. In particular:

1. For both B’s we use the same Vertex Probability PDF extracted for the tag side B inthe signal samples.

2. The P (i) priors are evaluated as:

PDT (TT ) = (Psig(TT ) + Psig(TF ))2 (5.1)

PDT (FF ) = (Psig(FT ) + Psig(FF ))2 (5.2)

PDT (TF ) = PDT (FT ) = (Psig(TT ) + Psig(TF ))× (Psig(FT ) + Psig(FF )) (5.3)

3. The two pch priors are proportional to the Btag reconstruction efficiencies in the chargedand in the neutral signal sample, i.e. we didn’t introduce a BR factor to distinguishthe semileptonic B0 and B± branching fractions, being them essentially equals.

89

90 CHAPTER 5. CONTROL SAMPLES

Table 5.1: Priors and pch factors in the double tag sample.

Channel pch P (TT ) P (TF ) P (FT ) P (FF )B0 tag 0.5173 0.5171 0.0789 0.2020 0.2020B± tag 0.4827 0.2947 0.2089 0.2482 0.2482

The results are summarized in Tab. 5.1 1

5.2 Data-MC Comparison in the Double Tag Sample

In this section we summarize the results of the data-MC comparison we performed in orderto validate the tagging efficiency by using the double tag sample. The results obtained herewill be used to correct the signal efficency for data-MC discrepancies in the tagging.

At first, a selection is applied in order to include in this correction any effect introducedby the Btag selection. The cuts on cos θB,Dl and cos θDl,T are applied to the first B only, theones on mD, ∆m and |~p ∗

l | are applied to both B’s. The cut on R2 is also applied to theevent and we require no tracks apart from these used to reconstruct the two B’s. Noticethat we have to evaluate one correction for each channel we study, because the cuts appliedon tag side are different.

Finally, we scale the MC yields to the data statistics and compare them with the doubletag yields on data, obtained applying the same cuts. Tab. 5.2 shows the ratios between dataand rescaled MC yields, and the corresponding square root that will be used to correct thesignal efficiency, assuming that, for a given tagging efficiency εtag, the efficiency for doubletag events is ε2

tag. A 1.1% error is added in quadrature to the error on the ratio to take into

account the uncertainty due to the overall MC normalization (i.e. the number of BB pairsproduced at the Υ (4S) resonance).

In evaluating the correction, we distinguish not only between the different decay channels,but also between events reconstructed as B0B0 and events reconstructed as B+B−. So, forthe K∗0 → K+π− channel we evaluate the correction using only B0B0 tag, while for theother channels we use only the B+B− tag. We have different corrections for the threeB± → K∗±νν modes, due to the different cuts that are applied on tag side (see Tab. 4.4).

5.3 Data-MC comparison in the mD sidebands

The cut applied on mD allows to define two sidebands, for values of mD lower and higherthan the cut. The events falling in these two regions can be used to perform a further data-MC comparison. They are interesting, in particular, to check the data-MC agreement forthe background Eextra shape that will be used in the ML fit (see Sec. 6.2.1).

1The B± double tag priors cannot be directly extracted from the values in Tab. 4.2. In fact, the formerare evaluated from the full B0 → K∗0νν sample, without separating the different K∗ modes.

5.4. DATA-MC COMPARISON IN THE MK∗ SIDEBANDS 91

Table 5.2: Data-MC ratio for double tags and the corresponding correction (square root ofthe ratio).

Channel data-MC ratio efficiency correctionK∗0 → K+π− 0.799 ± 0.026 0.894 ± 0.015

K∗+ → K0Sπ+ (K0

S→ π+π−) 0.858 ± 0.014 0.926 ± 0.008

K∗+ → K0Sπ+ (K0

S→ π0π0) 0.857 ± 0.014 0.926 ± 0.008

K∗+ → K+π0 0.861 ± 0.018 0.928 ± 0.010

In order to have enough statistics, we apply only the cut on E∗miss + c|~p ∗

miss|, that is theonly selection variable showing a correlation with Eextra.

The normalized Eextra distributions (we are interested on the shapes only) in the fourchannels, and the corresponding data-MC ratio can be found in Fig. 5.1.

5.4 Data-MC comparison in the mK∗ sidebands

An alternative data-MC comparison to check the Eextra shape in the background can beperformed in the sidebands of mK∗. Also in this case, we apply only the E∗

miss + c|~p ∗miss|

selection.The results of this comparison are shown in Fig. 5.2.


(GeV)extraE0 0.5 1

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range [0.05 GeV ,1.2 GeV ]). All the distributions are scaled to unit. From the top: K ∗0 →K+π−,K∗+ → K0

Sπ+ with K0

S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.

5.4. DATA-MC COMPARISON IN THE MK∗ SIDEBANDS 93

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range [0.05 GeV ,1.2 GeV ]). All the distributions are scaled to unit. From the top: K ∗0 →K+π−,K∗+ → K0

Sπ+ with K0

S→ π+π−, K∗+ → K0

Sπ+ with K0

S→ π0π0, K∗+ → K+π0.

Chapter 6

Results

In this chapter we describe the strategy adopted to extract a measurement of the B → K (∗)ννBR, based on a Bayesian approach described in Sec. 6.1. The method requires the definitionof a likelihood function, which in this analysis can be approximated by a gaussian function.The corresponding parameters are extracted by means of a maximum likelihood (ML) fitof the Eextra distribution. In Sec. 6.2 we describe in detail the fit strategy, which has beenvalidated as described in Sec. 6.2.2. The strategy is finally applied on real data (Sec. 6.2.3).In this chapter we also present the estimate of the systematic uncertainties affecting themeasurement (Sec. 6.3). Since no significant signal is observed, we set upper limits on theB → K(∗)νν BRs. Our results are also combined with the ones obtained by a similar analysisperformed in the recoil of a hadronic B decay (Sec. 6.4).

6.1 Bayesian approach for the BR measurement

The number Ns of expected signal events observed in a data set of NBB BB pairs is relatedto the BR by the formula:

B =Ns

ε ·NBB

, (6.1)

being ε the efficiency of the full analysis strategy for signal events, estimated from the signalMC as the ratio between generated and selected events.

Since the measured signal yield, whatever strategy we use to extract it, is affected by astatistical uncertainty, it has to be propagated to the branching ratio. The uncertainties onNBB and ε have also to be taken into account. As a consequence, it can be challenging togive a consistent statistical interpretation of the results, in particular when the estimator ofthe signal yield approaches zero or even takes an unphysical negative value.

A Bayesian approach allows to take into account all these effects in a self-consistentway. At first, we have to define a prior probability density function (PDF) for the BR,P (B), describing our previous knowledge of BR itself and taking into account the physicalconstraint B > 0. We chose:

{

P (B) flat B > 0P (B) = 0 B < 0

(6.2)

95

96 CHAPTER 6. RESULTS

At this point, given a single decay channel, the Bayes theorem allows to update the PDFfor the BR, producing a posterior PDF:

P (B|data) ∝ P (data|B)P (B) ∝∝

∫

dεdNBBL(data|Ns = B · ε ·NBB)P (ε)P (NBB)P (B) (6.3)

being L(data|Ns) the so-called likelihood function, defined as the probability of having theobserved data given a number of signal events equal to Ns (it will be described in detail inSec. 6.2).

P (ε) and P (NBB) are two PDFs describing our knowledge of efficiency and NBB . Forsimplicity, P (ε) will be a gaussian PDF centered at the MC efficiency value and as wideas the corresponding error (see Sec. 6.3 and Tab. 6.4 for details). Similarly, P (NBB) willbe a gaussian PDF centered in the nominal value of the BB counting and as wide as thecorresponding error (See Tab. 6.6).

The posterior PDF contains all the knowledge regarding the BR and can be used toextract upper limits or confidence intervals. For instance, a 90% upper limit (UL) can bedefined as:

∫ UL

0P(B) dB

/∫ ∞

0P(B) dB = 0.9 . (6.4)

The integral in Eq. (6.3) can be evaluated numerically. The implementation is verysimple. We proceed as follows:

1. generate a random positive value for B according to a flat distribution;

2. generate ε and NBB according to their gaussian distributions;

3. associate to B a weight given by the Ns likelihood;

4. iterate several times;

5. the weighted B distribution is the posterior we are looking for.

If, for a given mode (B0 or B±) we have different channels, this Bayesian approach allowsalso to combine them. We just have to generalize Eq. (6.3), writing:

P (B|data) ∝∫

dNBBP (NBB)P (B)×

×[

∏

α

∫

dεsig,αL(Ns,α = B · εsig,α ·NBB)P (εsig,α)

]

P (NBB)P (B) (6.5)

In this case, a different εsig,α value will be generated for each channel, and the weight willbe given by the product of the likelihoods. We need to use this generalized equation forB± → K∗±νν, where:

α ∈ {K∗+ → K0Sπ+ (K0

S→ π+π−), K∗+ → K0

Sπ+ (K0

S→ π0π0), K∗+ → K+π0} (6.6)

6.1. BAYESIAN APPROACH FOR THE BR MEASUREMENT 97

Table 6.1: Cross-feed efficiencies (× 10−4).

Prod. Mode K∗0 → K+π− K∗+ → K0Sπ+ K∗+ → K+π0

K0S→ π+π− K0

S→ π0π0

B0 → K∗0νν - 0.133 ± 0.016 0.008 ± 0.004 0.118 ± 0.016B± → K∗±νν 0.057 ± 0.009 - - -

Another effect that can be treated in this approach is the cross-feed between differentchannels. We found that a small but not negligible fraction of B0 → K∗0νν events can bereconstructed in one of the B± → K∗±νν channels and vice versa. Let εi→α be the efficiencyfor an event produced in the mode i (i ∈ {B0, B±}) to be reconstructed in the channelα (again α ∈ {K∗+ → K0

Sπ+ (K0

S→ π+π−), K∗+ → K0

Sπ+ (K0

S→ π0π0), K∗+ → K+π0}).

The results obtained in the MC are summarized in Tab. 6.1.

It means that the number of events expected in the channel α is:

Ns,α =∑

i

εi→α · Bi ·NBB (6.7)

This formula can be used to get a further generalization of (Eq.( 6.5)). Also without writingdown this complicated equation, this is the recipe we can follow:

1. generate a random positive value for BB0 according to a flat distribution;

2. generate a random positive value for BB± according to a flat distribution;

3. generate all the efficiencies (including the cross-feed ones) and the BB counting ac-cording to their gaussian distributions;

4. evaluate Ns,α from Eq. (6.7);

5. associate to the BR pair a weight given by the product of all the likelihoods (evaluatedat Ns,α);

6. iterate several times;

7. the weighted (BB0 ,BB±) distribution is a 2-dimensional posterior for the two BR, withsystematic errors and cross-feed taken into account.

Notice that some systematic uncertainties for different channels can be correlated, inthe sense that their effect can be in the same direction (not necessarily the same entity)for all the channels. It can be properly treated generating the various efficiencies with fullcorrelation.


6.2 Maximum likelihood fit

In this section we will define in detail the construction of the likelihood to be used in theBayesian approach.

Let x be a continuous variable that can assume values in a given range. Let Psig(x|~psig)be a continuous function, depending on a set of known parameters ~psig, and defining the

PDF of this variable in the signal sample. Similarly, let Pbkg(x|~Pbkg) be the PDF in thebackground sample, with known parameters ~pbkg. Given a sample of N data events, theprobability of observing the values xi, i = 1 . . . N , assuming that the sample is composed byNs signal events and Nb background events is:

L(Ns, Nb) =e−[Ns+Nb]

N !×

N∏

i=1

[Psig(xi|~psig)Ns + Pbkg(xi|~pbkg)Nb] , (6.8)

which, according to the definition given in Sec. 6.1, can be taken as the likelihood functionwe need in our bayesian approach (after integrating with respect to Nb).

The variable x that we want to use is Eextra. Considering that we use only photons withenergy greater than 0.050 GeV when calculating it, the distribution of this variable cannotbe continuous. In fact, if an event has zero extra photons, the value of Eextra will be 0,otherwise it will be something greater than the energy lower bound. Hence, it is not possibleto define the likelihood as done in Eq. (6.8) by means of continuous functions.

An alternative consists in adopting a binned likelihood. In this case, the values of Eextra

are organized in n intervals (bins), and a Poisson probability is assigned to the number ofevents in each bin. Anyway, this strategy reduces the available information and, duringpreliminary studies, presented problems that will be discussed in Sec. 6.2.2.

Finally, we decided to write the Eextra likelihood as:

L(Ns, Nb) =e−[(1−fs)Ns+(1−fb)Nb]

N1!

×N1∏

i=1

[Psig(Eextra,i|~psig)(1− fs)Ns + Pbkg(Eextra,i|~pbkg)(1− fb)Nb]

× (fsNs + fbNb)N0e−(fsNs+fbNb)

N0!, (6.9)

where fs and fb are the fractions of signal and background events with Eextra = 0, andare fixed from the MC; N0 and N1 the numbers of selected events with Eextra = 0 andEextra > 50MeV respectively; Psig and Pbkg the PDFs for the signal and the background.

The first two terms in Eq. (6.9) represent a standard likelihood for Eextra > 50MeV , thethird one a specific Poisson likelihood for Eextra = 0. The negative natural logarithm of thelikelihood NLL = − logL is useful for calculations, and can be written as:

NLL = NLL(Eextra = 0) +NLL(Eextra > 50MeV )

= −N0 log(fsNs + fbNb) + (fsNs + fbNb) +NLL(Eextra > 50MeV ) (6.10)

6.2. MAXIMUM LIKELIHOOD FIT 99

where NLL(Eextra > 50MeV ) is the negative natural logarithm of the first two terms inEq. (6.9).

By applying this strategy on a few MC samples including both signal and backgroundevents, we could verify that NLL is well described by a parabolic function of Ns, i.e. thelikelihood is described by a gaussian function. A further validation which will be describedin Sec. 6.2.2 actually proved that this assumption is reliable. Hence, we can proceed onreal data as follows: the MIGRAD and MINOS algorithms provided by MINUIT are usedto identify the value of Ns that minimizes the NLL (N fit

s ), corresponding to the mean ofthe gaussian. The same algorithms provide also an error σ(N fit

s ), defined as the differencebetween N fit

s and an N1/2s such that L(N fit

s ) = L(N fits ) + 1/2. This error corresponds to

the width of the gaussian. In other word, the procedure that is usually called Maximumlikelihood fit easily allows, in our case, to extract a parameterization of the likelihood to beused in our bayesian approach.

6.2.1 Signal and background shapes

The fit is performed in the range 0GeV ≤ Eextra < 1.2GeV . In this region, the backgroundshape is well described by a first order polynomial for all channels:

Pbkg(Eextra) ∝ 1 + p1Eextra (6.11)

On the other hand, the signal shape requires different parameterizations in the fourdifferent channels. In fact, a soft photon coming from the D∗0 decay can contribute to Eextra

if it has been not associated with the tag side D0, and it introduces a deformation of theEextra distribution in the B± → K∗±νν channels.

So, we find that in the K∗0 → K+π− channel the signal MC is well described by anexponential PDF, while in the neutral channels the Eextra distribution is well described byan exponential distribution summed to a Landau PDF:

Psig(Eextra) = f · λe−λEextra + (1− f) · Landau(Eextra, µl, σl) (6.12)

The parameters of Pbkg and Psig can be found by maximizing the likelihood functionwith respect to these parameters in a background MC sample and in a signal MC samplerespectively. They are affected by statistical errors provided as before by MINUIT. Alsotheir correlations are provided by MINUIT through the HESSE algorithm.

The results of the fits are quoted in Tab. 6.2 and the resulting PDF are plotted inFigg. 6.1–6.4, superimposed to the MC. These figures show also the difference between thefitted function and the MC points. The background sample used in the fits is a cocktail of thedifferent generic MC sample, the contribution of each one being proportional to the expectedrelative contribution, extracted from Tabb. 4.9–4.12 after all cuts. To take into account thecross-feed between the different channels (see Sec. 6.1), we also included in the K∗0 (K∗+)signal sample a contamination from the B± → K∗±νν (B0 → K∗0νν) MC, proportional tothe cross-feed observed in the MC.

The parameters obtained in the MC are fixed when applying the maximum likelihood fitstrategy to the real data and only Ns and Nb are fitted.


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Figure 6.1: TOP: Results of the fit in the MC samples, for signal (left) and background (right)for the K∗0 → K+π− channel. The lines represent the fitted PDF. BOTTOM: differencebetween MC points and fitted function.


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Figure 6.2: TOP: Results of the fit in the MC samples, for signal (left) and background(right) for the K∗+ → K0

Sπ+ (K0

S→ π+π−) channel. The lines represent the fitted PDF.

BOTTOM: difference between MC points and fitted function.


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Figure 6.3: TOP: Results of the fit in the MC samples, for signal (left) and background(right) for the K∗+ → K0

Sπ+ (K0

S→ π0π0) channel. The lines represent the fitted PDF.

BOTTOM: difference between MC points and fitted function.


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Figure 6.4: TOP: Results of the fit in the MC samples, for signal (left) and background (right)for the K∗+ → K+π0 channel. The lines represent the fitted PDF. BOTTOM: differencebetween MC points and fitted function.


Table 6.2: Results of the Fit in the MC.

K∗0 → K+π− K∗+ → K0Sπ+ K∗+ → K0

Sπ+ K∗+ → K+π0

(K0S→ π+π−) (K0

S→ π0π0)

fs 0.415 ± 0.006 0.308 ± 0.008 0.313 ± 0.017 0.306 ± 0.007fb 0.046 ± 0.008 0.045 ± 0.006 0.037 ± 0.008 0.053 ± 0.007f - 0.20 ± 0.10 0.928 ± 0.013 0.03 ± 0.04

µL (GeV ) - 0.165 ± 0.015 0.94 ± 0.005 0.092 ± 0.008σL (GeV ) - 0.048 ± 0.004 0.09 ± 0.03 0.058 ± 0.004λ (GeV −1) 5.27 ± 0.09 20 ± 11 5.7 ± 0.3 0.4 ± 2.3p1 (GeV −2) 0.41 ± 0.17 0.85 ± 0.19 2.3 ± 0.7 0.73 ± 0.19

6.2.2 Fit validation

In order to validate the fit strategy, we use the so-called Toy MC studies. In these studies,values of Eextra are randomly generated for N events (a toy experiment) accordingly to theexpected distribution.

In our case, a toy experiment is generated as follows:

1. N0 is generated according to a Poisson distribution with expected value fsNgens +

fbNgenb , where N gen

s and Ngenb are equal to the signal and background yields expected

in the data sample, using the SM prediction for the signal;

2. N1 is generated according to a Poisson distribution with expected value (1−fs)Ngens +

(1− fb)Ngenb ;

3. N1 events with Eextra > 50MeV are generated according to the signal + backgroundPDF (see the factor of the product in the second line of Eq. (6.9)).

Then, the fit procedure is applied to the generated events and an estimate of Ns andNb with errors is extracted. Several toy experiments are generated and fitted. Finally, thedistribution of the following variables is studied:

signal pull =Nfit

s −Ngens

σ(Nfits )

, (6.13)

background pull =Nfit

b −Ngenb

σ(Nfitb )

. (6.14)

The distribution of the signal pull, in particular, is expected to be a gaussian distributioncentered in 0 with σ = 1, under the hypothesis that the likelihood can be described by agaussian function centered in N fit

s and as wide as σ(N fits ). Hence, by studying the pull, we

can validate the proposal of parameterizing the likelihood by a gaussian function.We realize 1000 toy experiments for each channel. The PDF shapes are fixed from the

MC results and the signal and background yields are the only floating parameters. The


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Figure 6.5: K∗0 → K+π−: Results of the toy MC experiments. Signal Yield (top left), SignalError (top middle), Signal Pull (top right), Background Yields (bottom left), BackgroundError (bottom middle), Background Pull (bottom right).

results are summarized in Figg. 6.5–6.8. The pull distributions are correctly described bygaussian PDFs, providing a successful validation of the fit strategy.

When we tried to validate with a similar approach the binned likelihood strategy, theaverage of the resulting pulls showed a significant deviation from 0. It indicates, mostprobably, a non-gaussianity of the likelihood, precluding the possibility of using the fit resultsfor a correct gaussian parameterization of the likelihood itself. Hence, we decided to use thedefinition in Eq. (6.9) which, as we have just shown, is not affected by this problem.

A further validation is also performed. For each channel, the fit procedure is applied ona few samples composed by Ns MC signal and Nb MC background events, where Nb is equalto the background yield expected in the data sample and Ns goes from the SM expectationto a few hundred events. No significant bias is observed in the fitted yields with respect tothe true ones.


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Figure 6.6: K∗+ → K0Sπ+ (K0

S→ π+π−): Results of the toy MC experiments. Signal Yield

(top left), Signal Error (top middle), Signal Pull (top right), Background Yields (bottomleft), Background Error (bottom middle), Background Pull (bottom right).


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Figure 6.7: K∗+ → K0Sπ+ (K0

S→ π0π0): Results of the toy MC experiments. Signal Yield

(top left), Signal Error (top middle), Signal Pull (top right), Background Yields (bottomleft), Background Error (bottom middle), Background Pull (bottom right).


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Figure 6.8: K∗+ → K+π0: Results of the toy MC experiments. Signal Yield (top left), SignalError (top middle), Signal Pull (top right), Background Yields (bottom left), BackgroundError (bottom middle), Background Pull (bottom right).

6.3. SYSTEMATIC UNCERTAINTIES 109

6.2.3 Fit results

The fit strategy has been applied to the real data sample. The results of the fit are quotedin Tab. 6.3 and plotted in Figg. 6.9–6.12.

In the table we also quote:

• the expected signal and background yields, assuming the SM hypothesis for the signal;

• the signal efficiency according to Tabb. 4.13–4.16, corrected for systematic effects de-scribed in Sec. 6.3;

• the number of BB pairs NBB .

Table 6.3: Approximated expected yields from MC studies and results of the data fit, alongwith the signal efficiencies, corrected for systematic effects (see Sec. 6.3), and the number ofBB pairs. Expected signal yields are evaluated according to the SM expected BR. The firsterror on the fitted signal yield is statistical, the second is systematic.

K∗0 → K+π− K∗+ → K0Sπ+ K∗+ → K0

Sπ+ K∗+ → K+π0

(K0S→ π+π−) (K0

S→ π0π0)

Expected YieldsNs 4.04 2.51 0.53 3.31Nb 468 827 339 697

Fit ResultsNs 35 ± 13 ± 9 3 ± 17 ± 15 -9 ± 8 ± 15 -22 ± 16 ± 14Nb 476 ± 25 869 ± 34 338 ± 20 754 ± 32

ε (×10−4) 6.9 ± 0.8 4.3 ± 0.6 0.90 ± 0.20 5.6 ± 0.7NBB (×106) 454± 5

6.3 Systematic uncertainties

Given the Branching Ratio Formula:

BR =Ns

ε ·NBB

(6.15)

we can distinguish three different sources of systematic uncertainties:

1. Systematic uncertainty associated with the number of BB pairs, NBB ;

2. Systematic uncertainties associated with the signal efficiency;

3. Systematic uncertainties associated with the signal yield;


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Figure 6.11: Results of the fit in the data sample (right) and the corresponding pulls (left)in the K∗+ → K0

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Figure 6.12: Results of the fit in the data sample (right) and the corresponding pulls (left)in the K∗+ → K+π0 mode.


As discussed in Sec. 6.1, the Bayesian approach allows to treat the first two types ofsystematic uncertainties simply introducing a suitable PDF for NBB and the signal efficiency(for simplicity a gaussian PDF centered in the nominal value and as wide as the error on NBB

and ε respectively), and integrating (numerically) the posterior PDF over them. Instead, thesystematic uncertainty associated with the signal yield can be treated applying a gaussiansmearing to the likelihood, i.e. convolving it with a gaussian PDF centered in 0 and as largeas the systematics. Since the likelihood is modeled using a gaussian PDF, the smearing justproduces a new gaussian whose width is given by the sum in quadrature of statistical andsystematic uncertainties.

In this section we discuss and evaluate the different sources of systematics. Tab. 6.6 sum-marize the corresponding results. We also distinguish between correlated and uncorrelatedsystematics, according to the definition given in Sec. 6.1.

6.3.1 Normalization

The procedure adopted by the BABAR collaboration in order to evaluate the number ofBB pairs in the data sample collected at the Υ (4S) resonance is documented in [32]. Thisprocedure consist on counting the number of events passing a selection optimized for e+e− →hadrons events. In particular, the selection requires a total visible energy of at least 4.5 GeV,R2 < 0.5 and at least three tracks with 0.41 < θ < 2.54 rad. The number of BB pairs canbe obtained by subtracting to the total number of selected events the expected number ofcontinuum events (extrapolated from the off-peak data and normalized according to theluminosity, evaluated using e+e− → µ+µ− events), and dividing by the efficiency of theselection on a generic BB MC sample. The total relative error associated with this strategyis 1.1%.

6.3.2 Efficiency

The signal efficiency is firstly affected by an uncertainty due to finiteness of the MC statistics,which we will call the MC statistical error. The corresponding percent error can be evaluatedfrom the formula:

δε

ε=

√

1− εε ·Ngen

(6.16)

being Ngen the number of generated MC events 1. On top of this error, we have to addthe systematic uncertainties coming from the imperfect knowledge of the detector and thepresence of some disagreement between data and MC.

We describe in this section these possible sources of systematic errors. Some of therecipes described here allows to evaluate a correction (and the corresponding systematics)to be applied to the signal efficiency. The corrected efficiencies are quoted in Tab. 6.4.The global percent error on the efficiency is obtained adding in quadrature the percent MCstatistical error and all the percent systematic errors.

1In the K∗0 → K+π− channel the efficiency has a contribution coming from the corresponding BR.Eq. (6.16) has to be applied before introducing this factor.


Table 6.4: Summary of corrected efficiencies.

K∗0 → K+π− K∗+ → K0Sπ+ K∗+ → K+π0

(K0S→ π+π−) (K0

S→ π0π0)

Efficiency (×10−4) 6.9 ± 0.8 4.3 ± 0.6 0.90 ± 0.20 5.6 ± 0.7

Tagging efficiency

The Double Tag studies provide a correction to be applied to the Signal Efficiency. Onthe other hand, other analyses performed by the BABAR collaboration [33] used also alter-native methods to evaluate this correction, finding differences up to ∼ 8% among differentcorrections. Hence, we decided to apply a conservative 10% uncertainty on that.

Systematic Error on the Signal Selection Criteria

Concerning the tag side selection cuts, most of them are included in the selection of theDouble Tag sample. Hence, any data-MC disagreement in their selection efficiency is takeninto account by the Double Tag correction. There, for technical reasons, the cos θB,Dl and thecos θDl,T cuts are applied on one side only. Since the correction is taken as the square root

of the data/MC ratio, it means that this correction is good apart from a factor√

ε′data/ε′MC ,

being ε′ the marginal efficiency of the two cuts. Therefore, we considered the possibility of afurther correction given by this square root, evaluating also these marginal efficiencies fromthe Double Tag sample. Anyway, since no significant discrepancy can be found at the permille level, no correction is applied and no systematic uncertainty is included.

Concerning the event shape and the signal side selection, the cut on R2 is included in theDouble Tag selection and does not need a further systematics. Several data-MC comparisonsfor Eextra will be discussed later. The only cuts that need a systematics here are E∗

miss+p∗miss,

cos(θmiss), mK0S

and mK∗.

Let a and b be the lower and upper selection bounds for one of these variables. A data-MC disagreement can produce a deformation of the distribution in such a way that the realdata falling in the [a, b] range correspond to the simulated events falling in some [a± δ, b± δ]range. It means that a reasonable estimate of the corresponding systematics can be obtainedmoving both bounds by a given amount δ and looking at the difference in the signal MCefficiency. In particular, for each cut we evaluate the efficiency for the range [a − δ, b + δ]and the range [a + δ, b − δ]. The maximum discrepancy w.r.t. the nominal efficiency istaken as a systematics. Then the systematics corresponding to different cuts are summed inquadrature. Here the values that have been chosen for δ:

• E∗miss

+ c|~p ∗miss| : Looking at Fig. 4.11, data-MC disagreements in the background are

not expected to exceed ∼ 0.1 GeV. Assuming the same order of magnitude for thedeviations in the signal, we use δ = 100 GeV;

• cos(θmiss) : With similar motivations, looking at Fig. 4.12 we use δ = 0.05 GeV/c2;


• mK∗ : A data-MC disagreement can be produced by a different resolution. Since theexpected resolution for this decay is of the order of few MeV/c2, we conservatively setδ = 0.005 GeV/c2;

• mK0

S

: With similar motivations, we set δ = 0.001 GeV/c2.

Systematic Errors on Selectors and PID

The correction applied to the tagging efficiency using the double tag control sample correctany systematic disagreement between data and MC due to the reconstruction and the se-lection of the particles on the tag side, hence we only have to care here about the signalside reconstruction and PID. The following sources of systematic errors have been taken intoaccount:

• Tracking Efficiency: The systematics associated to the tracking efficiency can bemeasured by means of e+e− → τ+τ− events with a topology consistent with the 3 – 1hypothesis: one of the two τ has decayed in a channel with 3 tracks, while the otherone has decayed in a single track channel. These events are selected allowing also 3 or5 charged tracks. In the events with an odd number of tracks there is a missing or anextra track. Hence, we can estimate the efficiency of missing a track or reconstructing afake track. By comparing these efficiencies for data and MC it is possible to determinea systematic uncertainty for the tracking efficiency. By using this method, the BABAR

collaboration estimates an error of 0.34% for each track.

• K0

Sreconstruction efficiency: Correction factors and systematic errors associated

to the K0S

reconstruction can be evaluated by fitting the number of K0S

in data andgeneric MC samples in different bins of K0

Smass, transverse momentum, polar angle

and transverse distance between the primary vertex and the K0S

vertex.

• π0 reconstruction efficiency: Several control samples are used by the collabora-tion in order to estimate an efficiency correction factor of (0.984 ± 0.030) for eachreconstructed π0.

• Kaon PID: The systematic error associated to the efficiency of the charged kaonPID selection has be estimated by means of a tweaking method: a previously rejectedK± candidate can be randomly accepted and a previously accepted candidate can berandomly rejected with probabilities extracted from control samples. A new efficiencyis evaluated and the difference with respect to the nominal efficiency is taken as asystematic uncertainty.

Systematic Error on the Best Pair Selection

The Best Pair selection described in Sec. 4.2 rely on the vertex χ2 probability distribution.A systematic uncertainty on the efficiency can arise from a data-MC disagreement in thisdistribution. It can be tested, for the tag side, using the Double Tag sample and, for thesignal side, using the mD sidebands. Fig. 6.13 and Figg. 6.14–6.17 show some disagreement


between data and MC. Its impact can be evaluated by multiplying the PDFs used in the bestcandidate selection by the ratio of the data and MC distributions, and evaluating the changeof the signal efficiency. The ratio has been modeled with a first order polynomial, exceptingfor the K∗+ → K+π0 channel, where the discrepancy is concentrated in the first bin. Inthis case, we just apply a correction factor when the probability is under 0.04. The percentdiscrepancy between the new efficiency and the nominal one can be taken as a systematicuncertainty associated with the Best Pair Selection.

Model dependence

In order to evaluate the model dependence of our measurement, induced by the effect ofthe NP in the decay kinematics, we apply a MC correction from the phase space kinematics(used to generate the MC and get the nominal efficiencies) to:

1. the Standard Model kinematics;

2. a SUSY kinematics with CνL = −4.0 and Cν

R = +1.0;

Fig. 6.18 shows the s distribution in the B0 → K∗0νν signal MC (from the MC truth infor-mation before the reconstruction and selection) and the expected SM distribution, accordingto Eq. (1.42). Similar distributions hold for B± → K∗±νν. We developed two techniques tocorrect the MC:

Re-weighting Each event is assigned a weight, such that the re-weighted s distributionmatches the expected one. The weight is proportional to ratio of the two distributionsshowed in Fig. 6.18.

Hit/Miss Each event is accepted or rejected with a probability proportional to the ratioof the two distributions showed in Fig. 6.18, so that the s distribution of the acceptedevents matches the expected one.

The re-weighting procedure ensures higher statistics, since the hit/miss procedure has anintrinsic efficiency and is equivalent to using a lower number of generated events.

We want to stress here that the MC correction has to be performed by using the MCtruth information, in order to avoid to absorb reconstruction effects in this correction.

The signal efficiency has been evaluated in the SM and NP configurations described aboveand compared to the nominal efficiency extracted from Tabb. 4.9–4.12. The two correctionstrategies (Hit/Miss and Re-weighting) give completely consistent results. The results of thecomparison applying the SM correction can be find in Tab. 6.5. The SUSY scenario givesvery similar results. The relative discrepancies listed in this table are used as systematicuncertainties due the model dependence.

A 18% discrepancy show up in the K∗+ → K0Sπ+ (K0

S→ π0π0) mode. This discrepancy

already appears before the selection is applied and hence it is not related to the reconstructionstrategy. It is probably due, in particular, to the K0

S→ π0π0 reconstruction, which relies on

the kinematical properties of the K0S, like energy and transversal momentum.

Apart from this channel, we are able to keep the model dependence at a few percentlevel, demonstrating that we are actually performing a model independent measurement.


Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

000

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tautau

uds

ccbar

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Btag VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio

0

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Ratio

0

0.2

0.4

0.6

0.8

1

1.2

Figure 6.13: Top: Data-MC comparison for the Btag vertex probability in the Double Tagsample for neutral tags (left) and charged tags (right). The distributions are normalized tounit. Bottom: ratio of the distributions.


Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

000

0

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uds

ccbar

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B0B0

Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio

0

0.2

0.4

0.6

0.8

1

1.2

Figure 6.14: Left: Data-MC comparison for the Bsig vertex probability in the mD sidebandin the K∗0 → K+π− sample. The distributions are normalized to unit. Right: ratio of thedistributions.

Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

000

0

0.05

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0.4tautau

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ccbar

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Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio

0

0.2

0.4

0.6

0.8

1

Figure 6.15: Left: Data-MC comparison for the Bsig vertex probability in the mD sidebandin the K∗+ → K0

Sπ+ (K0

S→ π+π−) sample. The distributions are normalized to unit. Right:

ratio of the distributions.


Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

000

0

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ccbar

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Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Figure 6.16: Left: Data-MC comparison for the Bsig vertex probability in the mD sidebandin the K∗+ → K0

Sπ+ (K0

S→ π0π0) sample. The distributions are normalized to unit. Right:

ratio of the distributions.

Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N.e

v./0

.040

000

0

0.01

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ccbar

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B0B0

Bsig VtxProb0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio

0

0.2

0.4

0.6

0.8

1

1.2

Figure 6.17: Left: Data-MC comparison for the Bsig vertex probability in the mD sidebandin the K∗+ → K+π0 sample. The distributions are normalized to unit. Right: ratio of thedistributions.


s0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

P(s)

0

0.5

1

1.5

2

2.5

3

Figure 6.18: True s distribution in the signal B0 → K∗0νν MC (black dots) and the expectedSM distribution (black line). The expected distribution is affected by theoretical uncertaintiesthat we don’t show here.

Table 6.5: Efficiency with and without the signal MC kinematical correction and relativediscrepancy.

Mode Uncorrected Corrected Discrepancyefficiency (×10−4) efficiency (×10−4)

K∗0 → K+π− 7.798 7.695 1.3%K∗+ → K0

Sπ+ (K0

S→ π+π−) 4.648 4.423 4.8%

K∗+ → K0Sπ+ (K0

S→ π0π0) 1.007 0.828 18%

K∗+ → K+π0 6.149 5.873 4.5%

6.3.3 Signal yields

Systematic Error on the Eextra parameterization

The fit parameters extracted from the MC samples and fixed on the data fit are affected byan uncertainty, related to the MC statistics, which has to be propagated to the fitted yield.

The background PDF has two parameter, p1 and fb, determined from a suitable MCcocktail. They are affected by a statistical uncertainty, which can be extracted from theMC fit and are quoted in Tab. 6.2, and a systematic one, related to the composition of thecocktail, i.e. the relative amount of each background species. The latter can be estimatedchanging the composition of the cocktail, according to the uncertainty on the expected yieldsof each kind of background. In particular, the number of events in the cocktail for a givensample i is calculated as Ni = NMC

i · f , being NMCi the number of events selected in the


MC and f the luminosity normalization factor. To evaluate the systematic uncertainty, wegenerate a random set of Poisson distributed NMC

i and use them to build a new cocktail andmake a new fit. We repeat this operation 100 times and extract a distribution for p1, and fb,whose RMS is the uncertainty we are looking for. The effect is found to be marginal. Theglobal uncertainties on p1 and fb, obtained as the sum in quadrature of the statistical andsystematic contributions, is:

δfb = 0.008 δp1 = 0.18GeV −2 in K∗0 → K+π−

δfb = 0.006 δp1 = 0.19GeV −2 in K∗+ → K0Sπ+ (K0

S→ π+π−)

δfb = 0.008 δp1 = 0.7GeV −2 in K∗+ → K0Sπ+ (K0

S→ π0π0)

δfb = 0.007 δp1 = 0.20GeV −2 in K∗+ → K+π0

(6.17)

The corresponding uncertainties on the signal yield are obtained moving the values of p1

and fb in the data fit by ±δp1 and ±δfb respectively, and taking for each parameter thelarger difference w.r.t. the nominal yield value. The two uncertainties are then summedin quadrature, considering that the MC fit does not show any correlation between the twoparameters.

In order to evaluate the systematic error associated with the signal PDF, we have totake into account the significant correlations between the different parameters ~p. It can bedone diagonalizing the covariance matrix V obtained from the MC fit. The matrix M thatdiagonalizes V provides a transformation from the set ~p to a new set ~p ′ of uncorrelatedparameters, and the corresponding errors. For each uncorrelated parameter p ′

i, we generatea set of 100 values, according to a gaussian distribution centered in its nominal value andas wide as the error. For each generated value, the set ~p ′ is transformed back in a newset ~p and the fit is repeated. Hence we get a distribution of 100 fitted values of Ns, whoseRMS is taken as the systematic uncertainty for p ′

i. In this way, each parameter p ′i gives an

independent systematic uncertainty on the signal yield. All these uncertainties are summedin quadrature to get the global error due to the signal parameterization.

Systematic Error on the Eextra shape from data-MC disagreements

We also take into account the possibility of having a data-MC discrepancies in the modelingof the Eextra distribution.

To evaluate the impact of such effects on the signal shape, we compare the data and MCEextra distributions in the Double Tag sample, as shown in Fig. 6.19. Here the distributions,separated for charged and neutral tags, are normalized to unit, since we are interested onthe shape only. The data-MC agreement is good, a part from a significant deviation in thefirst bin for the charged tags. So, we decided to apply a correction only to the parameter fs

and only to the charged modes. This correction is equal to the ratio between data and MCin the first bin, and a conservative 100% systematic error is associated with it. Hence, weuse the following values are:

fs = 0.348± 0.008± 0.040 in K∗+ → K0Sπ+ (K0

S→ π+π−)

fs = 0.351± 0.017± 0.038 in K∗+ → K0Sπ+ (K0

S→ π0π0)

fs = 0.343± 0.007± 0.037 in K∗+ → K+π0(6.18)


(GeV)extraE0 0.2 0.4 0.6 0.8 1 1.2

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B+B-

B0B0

BABARpreliminary

Figure 6.19: Data-MC comparison for Eextra in the Double Tag sample for neutral tags (left)and charged tags (right). The distribution are normalized to unit.

where the first error is the MC statistical one, the second error is systematic. The two errorsare summed in quadrature and this global error is used in the procedures described in theprevious paragraph.

Concerning the background shape, the data-MC comparison performed on the mD side-band (Sec. 5.3) is used. In particular, the background PDF used in the nominal fit ismultiplied by the data-MC ratio showed in Fig. 5.1 (modeled by an order 1 Polynomial) anda new fit is performed. The change in Ns w.r.t. the nominal value is used as a systematicuncertainty.

A further systematic uncertainty is introduced to take into account the possibility ofhaving, in the background, a component that peaks in Eextra like the signal. A possible sourceis, for instance, the already mentioned B → τν decay. This decay can easily fake the signalsignature, in particular if a hadronic τ decay occurs. After applying the signal selection,the number of expected B → τnu events, assuming a B → τν BR of 9 × 10−5, is about0.62 events in the K∗+ → K0

Sπ+ (K0

S→ π+π−) channel, 0.28 events in the K∗+ → K0

Sπ+

(K0S→ π0π0) channel and 0.91 events in the K∗+ → K+π0 channel. Since these numbers are

small with respect to the error on on the signal yield, we do not adopt any specific treatment.Anyway, considering that this and possibly other peaking backgrounds are included in theMC, we performed some studies, adding an exponential contribution in the backgroundparameterization, weighted by a fraction fpeak. In the MC we obtain values of fpeak consistentwith 0 within 1σ, where the error σ is at the level of few 0.01, depending on the specificchannel, with the exception of K∗+ → K0

Sπ+ (K0

S→ π0π0) where the effect is larger, with

a negative fpeak. We conservatively repeat the data fits adding an exponential backgroundcomponent with fpeak = 0.5σ and take the deviations from the standard fits as a systematic


)ν ν 0 K*→ 0BR(B

0 0.2 0.4-310×

Pro

bab

ility

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sity

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BABARpreliminary

)ν ν + K*→ +BR(B0 0.2 0.4

-310×

Pro

bab

ility

den

sity

0

0.0005

0.001

0.0015

0.002

Figure 6.20: Posterior PDF for the B0 → K∗0νν BR (left) and the B± → K∗±νν BR (right)including all systematics. The dark (light) filled area shows the 90% (95%) CL region.

uncertainty.

6.4 Final results

As quoted in Tab 6.2.3, no significant signal is observed. Hence, we use the bayesian tech-nique described in Sec. 6.1 in order to set upper limits on the B → K∗νν BRs. Due to thelarge systematic uncertainties and the low sensitivity of the K∗+ → K0

Sπ+ (K0

S→ π0π0)

channel, we do not use this channel to get the final results.

The extracted posterior PDFs are showed in Fig. 6.20. The corresponding 90% ULs are:

BR(B0 → K∗0νν) < 18× 10−5

BR(B± → K∗±νν) < 9× 10−5. (6.19)

These results can be combined with the ones obtained by the BABAR collaboration bylooking for B → K∗νν in the recoil of a hadronic B decay [43]. In this analysis one of thetwo B produced in the Υ (4S) decay is reconstructed in about 1000 different decay channels,looking for B → DY , where D refers to a charm meson, and Y represents a collection ofhadrons with a total charge of±1, composed of n1π

±+n2K±+n3K

0S+n4π

0, where n1+n2 ≤ 5,n3 ≤ 2, and n4 ≤ 2. The results of this analysis are summarized in Tab. 6.7. A differentBR normalization is used here: exploiting the kinematical variables available from the fullBtag reconstruction, it is possible to evaluate the number of reconstructed Btag (NBtag

) witha data driven approach, in order to remove the systematic uncertainties associated with thetagging efficiency. Hence, the BR is written as:

B =Ns

εBsig·NBtag

·εBB

Btag

εK∗ννBtag

, (6.20)

6.4

.FIN

AL

RE

SU

LT

S123

Table 6.6: Summary of the systematic uncertainties (in percent).

Source K∗0 → K+π− K∗+ → K0Sπ+ K∗+ → K0

Sπ+ K∗+ → K+π0

(K0S→ π+π−) (K0

S→ π0π0)

NORMALIZATION ERRORSB counting 1.1 1.1 1.1 1.1

EFFICIENCY ERRORS (UNCORRELATED)MC Statistics 1.3 1.7 3.6 1.4

Model Dependence 1.3 4.8 17.8 4.5Best Pair Selection 0.0 0.0 0.5 0.2Selection Criteria 5.1 7.3 3.2 5.0

Total Uncorrelated error(excepting MC statistics) 5.3 8.7 18.1 6.7Total Uncorrelated Error 5.4 8.9 18.4 6.9

EFFICIENCY ERRORS (CORRELATED)Tagging Efficiency 10 10 10 10Tracking Efficiency 0.7 1.0 0.3 0.3π0 reconstruction - - 6.0 3.0K0

Sreconstruction - 2.5 - -Kaon ID 0.4 - - 0.4

Total Correlated Error 10.0 10.4 11.7 10.4

YIELD ERRORSSignal Param. 0.17 1.4 0.7 0.7

Background Param. 7.7 11.4 5.7 11.0Background Shape 2.8 4.9 5.0 6.4

Peaking Background 3.9 7.9 13.5 4.6Total Yield Error 9 15 15 14


where εBsigis the efficiency related to the signal side only, while εBB

Btagand εK∗νν

Btagare the Btag

reconstruction efficiencies in events with generic BB decays and events containing the signalprocess, respectively; to account for differences among them, observed in the MC, their ratioεK∗ νν

Btag/εBB

Btagis used in Eq. (6.20) as a correction factor.

Table 6.7: Approximated expected yields from MC studies and results of the data fit, alongwith the signal efficiencies, for the hadronic recoil analysis. Expected signal yields are eval-uated according to the SM expected BR. The first errors on and on Ns and NBtag

arestatistical, the second ones are systematic.

K∗0 → K+π− K∗+ → K0Sπ+ K∗+ → K+π0

(K0S→ π+π−)

Expected YieldsNs 0.79 0.72 1.65Nb 46 35 73

Fit ResultsNs 5 ± 6 ± 4 3 ± 7 ± 4 -10 ± 9 ± 6Nb 39 ± 9 51 ± 10 77 ± 13

εBsig(×10−2) 6.7± 0.6 6.1± 0.7 19.2± 1.6

NBtag(×105) 8.933± 0.009± 0.357 6.330± 0.008± 0.227

Since the semileptonic and hadronic approach are independent, in the sense that it hasbeen proved that the probability of reconstructing the same signal event with both techniqueis completely negligible, the two analysis can be combined. We use the bayesian algorithmtreating the two analysis like different channels. Moreover, the two analysis have beenrealized in close synergy, in order to properly take into account the correlated systematics.

The combined ULs are:

B(B0 → K∗0νν) < 12× 10−5 (6.21)

B(B± → K∗±νν) < 8× 10−5 .

We also set a combined UL for a generic B → K (∗)νν decay, by using together thecharged and neutral channels:

B(B → K(∗)νν) < 8× 10−5 ,

(6.22)

largely dominated by the semileptonic B± → K∗±νν BR. These results represent the moststringent upper limits reported to date [15].

Since no constraints were applied to the kinematics of the final state K∗ meson, or thehypothesized νν system, and a systematic uncertainty is associated to the model dependenceof this measurement, these results can be interpreted in the context of new physics modelswhere invisible particles, other than neutrinos, are responsible for the missing energy [20,23, 24].

Chapter 7

The b→ s νν and b→ s `+`− decays ata Super B-Factory

Flavour-changing neutral currents producing b → d and b → s transitions are among themain topics of aB-Factory experiment. The results obtained in the last decade by BABAR andBelle allowed to strongly constrain possible NP effects in b→ d transitions, by investigatingthe B0B0 mixing. When operating a B-Factory at the energy of the Υ (4S) resonance, b→ stransitions can be investigated through rare B decays like B → K (∗)νν, B → K(∗)`+`− andB → sγ.

In this chapter, we will illustrate the prospects for B → K (∗)νν and B → K(∗)`+`−

measurements at a Super B-Factory, running with a luminosity 100 times larger than presentB-Factories. In Sec. 7.1 we will briefly introduce a project, called SuperB [34], that aims at aluminosity of about 1036 cm−2s−1. In Sec. 7.2 we will describe how the detector improvementswith respect to the present experiments can affect a recoil analysis. Finally, in Sec. 7.3-7.4the expected sensitivity on some specific b→ s νν and b→ s `+`− studies are extracted.

7.1 The SuperB project

A Conceptual Design Report as been recently published for SuperB: a B-Factory projectaiming at a luminosity above 1036 cm−2s−1 [34], to be built and operated in the next decade.

Such an experiment would allow to collect about 15 ab−1 of integrated luminosity per yearat the Υ (4S) resonance, increasing by almost two orders of magnitude the present BABAR

integrated luminosity.

Moreover, an improvement of the detector is possible thanks to the experience with thepresent B-Factory experiments and the most recent developments in detector physics.

The baseline detector design for SuperB, based on the BABAR design, involve:

1. a tracking system composed by a silicon vertex detector (SVT) and a drift chamber(DCH);

2. a Cerenkov-based PID detector inspired to the BABAR DIRC;

125

126 CHAPTER 7. b→ s νν AND b→ s `+`− AT A SUPER B-FACTORY

γβ0.1 0.2 0.3 0.4 0.5 0.6

t si

gm

a (p

s)∆

0

0.2

0.4

0.6

0.8

1

1.2

1.4

r = 0.7 cmr = 1.2 cmr = 1.7 cm

Figure 7.1: ∆t resolution for as a function of the boost with a MAPS layer 0 at differentradii. The dashed line represents the BABAR reference value.

3. an electromagnetic calorimeter (EMC);

4. a muon detector integrated in the solenoid flux return (IFR).

Anyway, with respect to the BABAR design, several improvements are under study. Amongthem:

1. Concerning the SVT, the possibility of adding a Layer 0 of 1.2 to 1.5 cm radius wouldsignificantly improve the vertex resolution. Two different technologies are under study:high resistivity silicon sensors with short strips (striplet detectors) and CMOS mono-lithic active pixel sensors (MAPS). in both cases a single hit resolution of about 10µmis achievable and a fine segmentation is possible, as needed in order to ensure a lowoccupancy even at the high event rate of SuperB. The ∆t resolution that can be ob-tained with the MAPS solution, as a function of the boost βγ, is shown in Fig. 7.1.This is a crucial issue for the measurement of time-dependent CP asymmetries, andsuch performances would allow to reduce the boost with respect to BABAR down toβγ ∼ 0.28.

2. The possibility of adding a forward endcap PID system could be considered. A time-of-flight system is the candidate.

3. The forward endcap calorimeter would be rebuilt using a faster and more radiationresistant crystal, like L(Y)SO. The possibility of adding a backward calorimeter hasbeen also considered. It would extend the EMC coverage in the backward down to 300

7.2 RECOIL ANALYSES: IMPACT OF DETECTOR IMPROVEMENTS 127

Backward EMC Extent (rad)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Back

grou

nd-to

-Sig

nal R

atio

2

2.5

3

3.5

4

4.5

5

Figure 7.2: Background over signal ratio for the B → τν search in the hadronic recoil asa function of the backward extent of the EMC. The energy resolution is degraded below 700mrad to simulate the performance of a veto device.

mrad with respect to the beam axis, to be compared with the 600 mrad of BABAR.This detector would be primarily used as a veto device in the recoil analysis, wherethe detection of extra photons not expected from signal events is critical to reject thebackground. As a benchmark, one can consider the B → τν search in the hadronicrecoil. As shown in Fig. 7.2, the presence of a backward EMC, also with a worseenergy resolution than the barrel EMC, would allow to reduce the background oversignal ratio by ∼ 30% (see Sec. 7.2 for a detailed discussion).

4. The RPC/LST technologies for the IFR would be replaced by scintillating crystals inorder to improve the high rate capability. Moreover, the detector segmentation wouldbe reoptimized, since the BABAR segmentation is suboptimal for muon identification,and it would significantly increase the µ/π discrimination.

7.2 Recoil analyses: impact of detector improvements

All the detector improvements listed in the previous section would have a significant impacton the sensitivity of the recoil analyses. The most important effect would be producedby the presence of a backward EMC. As we have already shown, a 30% reduction of thebackground in the recoil analyses seems to be possible. In fact, the most discriminatingvariable in these analysis is Eextra, the sum of the energies of the neutral EMC clusters notassociated either to the tag or signal side. When a photon from a background event escape


the detector acceptance, the value of Eextra is lower, i.e. similar to the values expected in thesignal, and it is easier to select this event when applying the Eextra selection requirement.By introducing a photon veto in the backward region we reduce this possibility. Notice thatthis improvement essentially does not dependent on the specific signal channel we look for.

On the other hand, there are analyses (like the one described in this thesis) that usethe Eextra shape in a maximum likelihood fit. By introducing a backward EMC we increasethe probability of having a random activity, producing higher values of Eextra also for thesignal. In other words, the Eextra shape could be modified in a direction that reduces itsdiscriminating power. In order to test the impact of this effect, we use as a benchmarkthe K∗0 → K+π− channel of the analysis described in this work. We take the signal andbackground MC samples and add random photons to the Eextra calculation. Then, werepeat the MC fits of Sec. 6.2.1, we extract new results for the signal and backgroundparameterizations, and we use them in the toy MC studies. Finally, we compare the averagesignal yield error in the new toy studies with the ones showed in Fig. 6.5. If the presence ofnew photons degrades significantly the Eextra discriminating power, we expect a significantlyhigher error.

The number of new random photons is generated for signal and background accordingto a Poisson distribution, with an expectation value given by:

〈N〉 = 〈NMC〉(

εgeom(SuperB)

εgeom(BABAR)− 1

)

(7.1)

where 〈NMC〉 is the average number of photons in each MC event, while εgeom(BABAR)and εgeom(SuperB) are the geometrical BABAR and SuperB acceptances. The energy of thephotons is generated according to an exponential distribution, with an expectation valueextracted from the energy spectrum of photons in the MC.

The new toy MC studies show a slight but not significant increase of the signal yielderror (up to a 10% relative increase), proving that the effect under study can be neglected.

The other detector improvements can also help in rejecting the background. For instance,vertexing informations are poorly used at present. Instead, the new SVT could allow asignificant continuum rejection thanks to the possibility of separating the B and D verticesin B → D decays and including the D flight length in the topological algorithms used todiscriminate continuum and BB events.

Finally, as shown in Tab. 4.3, a significant amount of background for channels like B →K∗νν comes from particle mis-identification. Hence, an improved muon PID and a newbackward PID device could help to further reduce the contamination.

On the basis of the remarks given above, we decided to evaluate the potential of SuperBin the search for rare b → s decays, in particular b → s νν and b → s `+`−, for variousintegrated luminosities and in three background scenarios:

BABAR scenario We assume the same background over signal ratio than the present BABAR

analysis. Hence, we assume for simplicity the same signal and background efficiencieswe have now. This scenario is motivated considering that some of the improvementslisted above could be removed from the final project, and the machine backgroundcould become significant at SuperB.

7.3 PROSPECTS FOR b→ s νν AT SuperB 129

30% scenario We assume a 30% reduction of the background over signal ratio, on the basisof the expected impact of a backward calorimeter. In particular, we assume the samesignal efficiency of BABAR and a 30% reduction of the background.

50% scenario We assume a 50% reduction of the background over signal ratio, realizedagain with a 50% reduction of the background and the same signal efficiency of BABAR.This scenario is realistic, considering the possibility of improvements from vertexingand PID.

A luminosity from 1 to 50 ab−1 and the same analysis techniques used by the BABAR col-laboration are assumed, but significant improvements could derive from using different ap-proaches that become feasible when higher statistics is available.

7.3 Prospects for b→ s νν at SuperB

As already mentioned in the introduction of this thesis, the study of the b→ s νν transitionscan provide a clean test of the SM. As usual, theoretical predictions for inclusive BR mea-surements are affected by smaller uncertainties with respect to the exclusive BRs, due to thepoor knowledge of the form factors. On the other hand, the inclusive B → Xsνν BR is reallyhard to measure or constrain, also with a very high statistics. In fact, since neutrinos arenot detected, it would be difficult to apply any request on the signal side without hypothesison the Xs system. Hence, a large background would remain, also using a recoil technique.By comparison, B → Xsγ and B → Xs`

+`− are much easier to search for, looking respec-tively for an high energy photon or a pair of leptons coming from the same vertex. As aconsequence, inclusive b → s νν searches have never been performed and probably wont beat SuperB. So, let us concentrate on exclusive searches for B → Kνν and B → K∗νν. Bothsearches are performed at BABAR in the recoil of a hadronic or semileptonic B decay.

The B → K∗νν analysis has been already described in detail. The expected signal andbackground yields per ab−1 are quoted in Tab. 7.1 assuming the SM BR for the signal andthe BABAR scenario for the background. They refers to the full fit regions. Toy experimentslike the ones described in Sec. 6.2.2 are performed in order to evaluate the expected statisti-cal errors on the signal yields at high integrated luminosity. Then, assuming to observe theSM yields, the bayesian approach of Sec. 6.1 is used to extract ULs or BR measurements.Here we need to include the large systematic uncertainties coming from the background pa-rameterization. They mostly depend on the MC statistics and are expected to go down whenincreasing the data sets. Hence, in this particular case, it is realistic to assume a systematicerror that scales like the statistical error. Considering that their absolute value is also quitesimilar, for simplicity we assume them to be equal. The results are graphically representedin Fig. 7.3. The observation is expected between 20 and 30 ab−1 in the neutral channel,with an error ∼ 28% at 50 ab−1 in the most conservative scenario. Instead, significant im-provements with respect to the BABAR scenario seems to be needed in order to observe thecharged mode.

The B → Kνν search has been performed at BABAR in the charged channel only [16].The neutral B0 → K0

Sνν will be probably investigated in the next future, but at present


]-1Integrated Luminosity[ab0 10 20 30 40 50

]-5

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→ 0BR

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]-5

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]-5

10

×) [ν ν +

K*

→ +BR

(B

0

1

2

3

4

56

78

9

10

SM

Figure 7.3: Expected performances for the B → K∗νν searches at SuperB as a function of theintegrated luminosity and for three different background scenarios. A bar without a markershows that an UL is expected and indicates its value. When a marker is shown, the errorbars represents the expected error. From the top to the bottom: B0 → K∗0νν, B± → K∗±ννwith K∗+ → K0

Sπ+ and B± → K∗±νν with K∗+ → K+π0. From the left to the right:

BABARscenario, 30% scenario and 50% scenario. The yellow belt shows the SM prediction.

7.4 PROSPECTS FOR b→ s `+`− AT SuperB 131

Table 7.1: Expected signal and background yields per ab−1 for the B → K(∗)νν searchesagainst semileptonic and hadronic tags. We assume here the SM BR for the signal and theBABAR scenario for the background.

Channel recoil type submode Ns Nb

B0 → K∗0νν semilep. 10 1584had. 3.7 163

B+ → K∗+νν semilep. K∗+ → K0Sπ+ 6 2057

K∗+ → K+π0 8.5 2171had. K∗+ → K0

Sπ+ 1.7 78

K∗+ → K+π0 1.9 102B+ → K+νν semilep. 6.4 84

had. 2.6 60

there is no reliable estimate of the sensitivity, so we will ignore this channel. The signatureof B+ → K+νν is given by one and only one track in the ROE. In the present analyses,apart from the tag side selection, the main requirements are applied on the kaon momentum,the missing energy and Eextra. The signal yields are extracted by comparing the observedevents and the expected background. The expected signal and background yields are quotedin Tab. 7.1. Toy experiments have been used in order to extract the expected upper limit.For each toy experiment we generate the number of observed events according to a Poissondistribution, using the numbers in Tab. 7.1, then we apply a bayesian approach, similar tothe one described in Sec. 6.1, adapted to a counting analysis, and extract an upper limit or aBR measurement. Then, the average UL or the average BR error over 1000 toy experimentsis taken as the expected one. Here, systematic uncertainties can be ignored, being largelycovered by the statistical ones. The results are graphically represented in Fig. 7.4, obtainedcombining both the semileptonic and hadronic analyses. The observation of the processis expected between 10 and 20 ab−1 and an 18% error is expected at 50 ab−1 in the mostconservative scenario. Notice that in this case a maximum likelihood fit technique could beapplied when higher statistics is available and could provide better performances.

7.4 Prospects for b→ s `+`− at SuperB

As already mentioned, the inclusive B → Xs`+`− BR can be measured looking for lepton

pairs coming from the same vertex. Some feasibility studies have been performed [35] usinga multivariate analysis and looking at the region mll > 0.2 GeV, being mll the di-leptoninvariant mass. The number of expected signal events per ab−1 is ∼ 43 versus ∼ 65 back-ground events. It means that the inclusive BR can be easily measured at low luminosity, asshown in Fig 7.51. This possibility makes less interesting the measurement of the exclusive

1In this case, since the analysis is not performed in the recoil, the 30% and 50% improvements in thebackground rejection could be unrealistic. Anyway, we show their effect as well.



]-6

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×) [ν ν +

K→ +

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]-5

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]-5

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0

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Figure 7.4: Expected performances for the B → Kνν searches at SuperB as a function of theintegrated luminosity and for three different background scenarios. A bar without a markershows that an UL is expected and indicates its value. When a marker is shown, the errorbars represents the expected error. From the left to the right: BABAR scenario, 30% scenarioand 50% scenario. The yellow belt shows the SM prediction.

BRs of B → K(∗)νν. On the other hand, it has been pointed out by many authors [14, 36]that several interesting observables can be extracted by studying the exclusive B → K∗ννmode. In particular, rate asymmetries can be studied, the most interesting one being theforward-backward asymmetry:

dA(B)FB(s)

ds=

1

dΓ(B → K∗µ+µ−)/ds

∫ 1

−1d cos θ

d2Γ(B → K∗µ+µ−)

ds d cos θsgn(cos θ) , (7.2)

where θ is the angle between the momenta of µ+ and B in the di-lepton center-of-mass frameand s = m2

ll/m2B. Most of the uncertainties due to the form factors cancel when studying the

a rate asymmetry and the theoretical predictions become quite clean. A detailed descriptionof these measurements and their expected sensitivity goes beyond our purposes. Anyway,Fig. 7.6 shows the expected results at 50 ab−1, in four s = m2

`` regions assuming the BABAR

performances.

7.4 PROSPECTS FOR b→ s `+`− AT SuperB 133


]-6

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× )

[- l+ l s

X→

BR(B

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]-6

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]-6

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× )

[- l+ l s

X→

BR(B

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SM

Figure 7.5: Expected performances for the measurement of the B → Xs`+`− BR at SuperB

as a function of the integrated luminosity and for three different background scenarios. Abar without a marker shows that an UL is expected and indicates its value. When a markeris shown, the error bars represents the expected error. From the left to the right: BABAR

scenario, 30% scenario and 50% scenario. The yellow belt shows the SM prediction.

]2 [GeVll2m

0 2 4 6 8 10 12 14 16 18 20

FBA

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 7.6: Expected performances for the measurement of the forward-backward asymmetryin B → K∗`+`− at SuperB in four m2

`` regions assuming to observe the SM values with theBABAR performances and 50 ab−1 of integrated luminosity.

Chapter 8

Phenomenological constraints

The new limits set by this work on the B → K∗νν BRs can be used to constraint thepresence on NP effects competing with the SM Z0-penguins in b→ s transitions. Moreover,these results can be combined with other measurements recently published by the BABAR

and Belle collaborations and involving similar penguin diagrams.In this chapter we present the constraints that can be set by using the results currently

available for some exclusive B decays. Apart from the measurements presented in this thesis,we will refer to the new B → Kνν upper limits [15, 16], the recent updates for the B → K∗γand B → K∗`+`− BRs [37, 38], and the recently updated B → K∗`+`− forward-backwardasymmetry AFB [39].

In the first part, we will work in a MFV scenario and will neglect possible NP effectsentering other processes than Z0-penguins and magnetic penguins in b → s transitions.The latter assumption is reasonable, considering that NP contributions in other sectors arealready strongly constrained or are argued to not be irrelevant in B decays, as we will detailin Sec. 8.1.

In the second part, we will use our B → K∗νν measurements in order to set a limit onthe mass and couplings of a light scalar dark matter candidate.

8.1 General approach

We start from the amplitude Eq. (1.35), which we rewrite here:

A(M → F ) =∑

i

BiηiQCDV

iCKMFi(υ) . (8.1)

As already mentioned, each of the Inami-Lim functions Fi(υ) represents a particular kind ofdiagrams. In the SM, the relevant functions for weak decays depend on xt = m2

t /M2W and

can be defined as:

• C(xt) for Z0-penguins;

• D(xt) and D′(xt) for γ-penguins and magnetic penguins respectively;

135

136 CHAPTER 8. PHENOMENOLOGICAL CONSTRAINTS

C∆0.75 0.8 0.85 0.9 0.95

D’

∆

-5.2

-5.1

-5

-4.9

-4.8

-4.7

-4.6

C∆0.75 0.8 0.85 0.9 0.95

D’

∆

-5.2

-5.1

-5

-4.9

-4.8

-4.7

-4.6

Figure 8.1: SM prediction for C(υ) vs. D′(υ). The dark (light) area shows the 68% (95%)probability region.

• E(xt) and E ′(xt) for gluon-penguins and chromomagnetic penguins respectively;

• S(xt) for ∆B = 2 and ∆S = 2 box diagrams.

• B(xt) for semileptonic box diagrams.

In principle, any weak decay amplitude can be expressed in the SM in terms of thesefunctions, in the form of Eq. (8.1). By definition, it applies also in a MFV scenario, with NPentering only through corrections to these master functions. Anyway, NP contributions toS(υ) are strongly constrained by the measurements involving B0 and K0 mixing. Also, it hasbeen argued [40] that NP contributions to B(υ), D(υ), E(υ) and E ′(υ) should be irrelevantin the low-energy phenomenology. Hence, we will concentrate on NP contributions affectingC(υ) and D′(υ) only, whose SM predictions are shown in Fig. 8.1

From the practical point of view, relations in the literature are often expressed in termsof Wilson coefficients. It means that, in order to constraint the NP contributions to theInami-Lim function, we have to proceed in the following way:

1. the SM values of the Inami-Lim functions are evaluated;

2. NP contributions ∆C and ∆D′ are added to the SM predictions for C(υ) and D′(υ);

3. the matching results are used in order to write the Wilson coefficients at the high scaleµ0 ∼ O(MW ) in terms of the Inami-Lim functions;

4. the Wilson coefficients are runned down to the low scale µ ∼ O(mb) using the RGequations;

8.2 CONSTRAINTS ON NP IN Z AND MAGNETIC PENGUINS 137

5. the theoretical expectations for the experimental observables are evaluated from theWilson coefficients at the low scale;

6. the theoretical expectations are compared to the experimental results in order to con-strain ∆C and ∆D′.

In particular, we adopt a Bayesian approach to set the constraints:

1. the values of ∆C and ∆D′ are randomly generated according to flat priors in reasonableranges (which we will specify later);

2. Any other parameter entering the calculation is generated according to its presentexperimental knowledge (See Tab. 8.1);

3. the calculation of the theoretically expected observables (Oth1 . . . Oth

n ) is performed asdetailed before;

4. the experimental likelihoods are used in order to assign a weight w to the generatedvalues of ∆C and ∆D′: w = L(data|Oth

1 . . . Othn );

5. the procedure is iterated and a two-dimensional weighted histogram for ∆C vs. ∆D′

is filled using the weights w: once normalized, this histogram corresponds to the two-dimensional posterior PDF for ∆C and ∆D′.

The literature provides the needed equations for the matching and the running [41], as wellas the expressions for the specific observables.

As anticipated, the B → K(∗)νν BRs can also be used to constraint NP scenarios withexotic sources of missing energy. In this case, the MFV hypothesis is broken and we proceeddifferently: the approach described above is used for extracting the SM predictions, then theexotic contribution to the BR is calculated (by generating the parameters of the NP modelaccording to flat priors) and added.

8.2 Constraints on NP in Z- and magnetic-penguins

from exclusive b→ s decays

8.2.1 B → K(∗)νν

By integrating the differential rates of Eq. (1.41) and Eq. (1.42), the expected B → K (∗)ννBRs (Bth) can be expressed, in MFV, in terms of the Wilson coefficient CL, given by:

CνL|SM =

4B(υ)− C(υ)

sin2 θW

, (8.2)

We have already noticed that this coefficient is scale-independent, in the sense that it does notchange in the running from the high to the low scale. Anyway, as pointed out in [12], the SMprediction can depend significantly on the matching scale µ0, due to the top mass running,


Table 8.1: Parameters used in the phenomenological analysis. Here, ρ = (1 − λ2

2)ρ and

η = (1− λ2

2)η.

Parameter Value Parameter ValueGF [GeV−2] 1.16637× 10−5 τB0 [ps] 1.530α 1/137 τB+ [ps] 1.638αs(mZ) 0.119± 0.003 ρ 0.167± 0.051mW [GeV] 80.425 η 0.386± 0.035mZ [GeV] 91.1867 λ 0.2258± 0.0014sin(θW ) 0.23154 mt [GeV] 161.2± 1.7mB0 [GeV] 5.2794 mb [GeV] 4.21± 0.08mB+ [GeV] 5.279 mc [GeV] 1.3± 0.1mK [GeV] 0.494 ms [GeV] 0.95± 0.25mK∗ [GeV] 0.892 µ0 [GeV] 80.425

µ [GeV] 4.6

and the O(αs) expressions for the SM master functions are need in order to reduce this scaledependence. Given these SM predictions, the B → K (∗)νν decays can be easily used toconstraint NP contributions to C(υ), under the assumption that B(υ) is not significantlyaffected.

At present, none of these decays has been observed and only ULs are available. In general,it is difficult to extract an experimental BR likelihood from an UL. Hence, the experimentalobservables used in this case are not the BRs but:

• the number of observed events (Nobs) if the analysis is performed with a countingprocedure;

• the fitted number of signal events (Ns) if a ML fit is used.

In the first case, the likelihood is given by the Poisson distribution:

L(Nth|Nobs) =(Nth)

Nobse−Nth

Nobs!, (8.3)

where Nth = Bth · ε ·NBB +Nb, being ε, NBB and Nb the signal efficiency, the number of BBpairs and the expected background events. In our procedure they are generated accordingto gaussian distributions as wide as their errors.

In the second case, the likelihood for Ns is built from the ML fit like in Sec. 6.2, byadding the systematic uncertainties in quadrature to the statistical error.

The experimental results used in this analysis are summarized in Tabb. 8.2-8.3; theparameters used in the BR calculation are quoted in Tab. 8.1. The form factors are param-eterized in the form:

F (s) = F (0) exp[c1s+ c2s2 + c3s

3] , (8.4)


]-610×)[ννK→BR(B0 2 4 6 8 10

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0.001

Figure 8.2: SM predictions for B(B → Kνν) (left) and B(B → K∗νν) (right). The dark(light) area shows the 68% (95%) probability region.

where the parameters are generated according to flat distributions in the ranges given in[18].

The SM prediction for the isospin averaged BRs 1 are shown in Fig. 8.2, and are consistentwith the results in [14], small differences coming form the up to date SM parameters usedin our work. The experimental ULs are still consistent with these prediction.

Given the experimental inputs, the procedure described in Sec. 8.1 is followed, by gener-ating the NP contribution ∆C according to a flat distribution in the range [−10, 10], and itgives the constraint represented in Fig. 8.3 (left). The comparison with the SM predictionof Fig. 8.1 allows to exclude at 95% C.L. NP effects as large as 6 times the SM.

The constraint obtained without including the results of the BABAR B → K∗νν analysesis also represented in Fig. 8.3 (right), in order to point out the impact of the measurementsdescribed in this thesis.

1By isospin averaged BR we mean the average of the charged neutral B BRs. In the absence of adynamical isospin asymmetry introduced by EW interactions between the b quark and the light quark insidethe B meson, the only difference between the two BRs is related to the B0 and B+ lifetimes. It is taken intoaccount in the extraction of the constraints


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Figure 8.3: Constraint on ∆C from B → K (∗)νν decays with all measurements included(left) and without the BABAR B → K∗νν measurements (right). The dark (light) areas showthe 68% (95%) probability region.

8.2

CO

NST

RA

INT

SO

NN

PIN

ZA

ND

MA

GN

ET

ICP

EN

GU

INS

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Table 8.2: Experimental results for B → K (∗)νν decays (counting analyses)

Channel Nobs ε NBB Nb Collaboration Ref.B+ → K+νν 10 (26.7± 2.9)× 10−5 (535± 7)× 106 20.0± 4.0 Belle [15]B+ → K+νν 38 (1.64± 0.22)× 10−3 (351± 4)× 106 30.7± 0.7 BABAR [16]B0 → K0

Sνν 2 (5.0± 0.3)× 10−5 (535± 7)× 106 2.0± 0.9 Belle [15]

B+ → K∗+νν 4 (5.8± 0.7)× 10−5 (535± 7)× 106 5.6± 1.8 Belle [15]B0 → K∗0νν 7 (5.1± 0.3)× 10−5 (535± 7)× 106 4.2± 1.4 Belle [15]

142

CH

AP

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R8.

PH

EN

OM

EN

OLO

GIC

AL

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RA

INT

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Table 8.3: Experimental results for B → K (∗)νν decays (fit analyses)

Channel Ns ε NBB Collaboration Ref.B+ → K∗+ννK∗+ → K0

Sπ+ (SL) 3± 23 (4.3± 0.6)× 10−4 (454± 5)× 106 BABAR [43]

K∗+ → K+π0 (SL) −22± 21 (5.6± 0.7)× 10−4 (454± 5)× 106 BABAR [43]K∗+ → K0

Sπ+ (HAD) 3± 8 (6.1± 0.7)× 10−4 (8.9± 0.4)× 105 BABAR [43]

K∗+ → K0Sπ+ (HAD) 5± 7 (6.7± 0.6)× 10−4 (8.9± 0.4)× 105 BABAR [43]

B0 → K∗0ννK∗0 → K+π− (SL) 35± 16 (6.9± 0.8)× 10−4 (454± 5)× 106 BABAR [43]K∗0 → K+π− (HAD) −10± 11 (19.2± 1.6)× 10−4 (6.3± 0.3)× 105 BABAR [43]


]-610×)[-l+K*l→BR(B0 0.5 1 1.5 2

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Figure 8.4: SM predictions for the partial B(B → K∗`+`−) in the range 0.10 < m2`` <

7.02 GeV2. The dark (light) area shows the 68% (95%) probability region.

8.2.2 B → K∗`+`−

The B → K∗`+`− decays present a much cleaner experimental signature with respect to theB → K(∗)νν decays, but they are also much harder to face from a theoretical point of view.

The state of the art is presented, for instance, in [17]. At first, we have penguin andbox diagrams similar to the ones contributing to B → K (∗)νν, with the caveat that, in thepenguin diagram, the Z0 meson can be also replaced by a photon. Additional contribu-tions come from the four-quarks operators, through diagrams where the b→ s transition isprovided by the four-quarks vertex and a photon is emitted from one of the external legs.Moreover, more complex diagrams can contribute, whose feature is that their effect cannotbe parameterized by form factors and need to be explicitly calculated. It has been done inthe limit of a large b quark mass, with expansions in powers of 1/mb and taking the leadingorder results, even though, in principle, the subleading contributions can be significant. Inthe absence of systematic studies about these corrections, we adopt the present results, butit implies, for instance, that only the predictions for small values of q2/m2

b can be used, beingq2 = m2

`` the momentum of the intermediate photon. Moreover, the possibility of a largebias in the theoretical prediction has to be taken into account in the interpretation of theresult.

From the experimental point of view, only the BABAR collaboration provided the partialBRs in the low m2

`` region (0.10 < m2`` < 7.02 GeV2) [37]. We use the average of B+ →

K∗+`+`− and B0 → K∗0 `+`−:

B(B0 → K∗`+`−) = (0.42± 0.10± 0.03)× 10−6 (8.5)


C∆-10 -5 0 5 10

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C∆-10 -5 0 5 10

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Figure 8.5: Constraint on ∆D′ vs. ∆C from the B → K∗`+`− BRs. The dark (light) areashows the 68% (95%) probability region.

Since these results have been extracted by means of ML fits and the quoted errors aresymmetric, it is worth to built from them gaussian experimental likelihoods for the BRs, aswide as the sum in quadrature of the statistical errors and the systematic errors. Hence, inthis case the observables used in our phenomenological analysis is directly the BR, whosetheoretical prediction is extracted from the formulas in [17], by using again the parametersof Tab. 8.1 and the form factors of [18]. The isospin averaged BR is showed in Fig. 8.4 andthe experimental measurements are still consistent with it.

Since both C(υ) and D′(υ) enter the calculation, we can set a two-dimensional con-straint. ∆C and ∆D′ are extracted according to flat distributions in the ranges [−10, 20]and [−10, 10], respectively. The resulting constraint is represented in Fig. 8.5 for the NPcontributions, to be compared with the SM predictions of Fig. 8.1. It allows to exclude at95% C.L. NP effects as large as 3 times the SM for C ′(υ) and half the SM for D′(υ).

Part of the theoretical uncertainties affecting the B → K∗`+`− channels can be eliminatedby calculating rate asymmetries like the forward-backward asymmetry AFB introduced inSec. 7.4. It is also predicted in [17] for small values of m2

``, hence we can use the availableBABAR and Belle results in order to set a further constraint. The experimental informationsare given by [39]:

AFB = 0.24+0.10−0.23 ± 0.05 0.10 < m2

`` < 6.25 GeV2 BABAR (8.6)

AFB = 0.47+0.26−0.32 ± 0.03 0 < m2

`` < 2 GeV2 Belle (8.7)

AFB = 0.14+0.20−0.26 ± 0.07 2 < m2

`` < 5 GeV2 Belle (8.8)

AFB = 0.47+0.16−0.25 ± 0.14 5 < m2

`` < 8.68 GeV2 Belle (8.9)

but unfortunately the Belle result in the first region cannot be used in this analysis since


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Figure 8.6: SM predictions for the B → K∗`+`− forward-backward asymmetry AFB in threem`+`− regions: 0.10 < m2

`` < 6.25 (left, used by BABAR), 0 < m2`` < 4.0 GeV2 (center, used

by Belle) 4 < m2`` < 8.6 GeV2 (right, used by Belle). The dark (light) area shows the 68%

(95%) probability region.

C∆−10 −8 −6 −4 −2 0 2 4 6 8 10

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Figure 8.7: Constraint on ∆D′ vs. ∆C from the B → K∗`+`− forward-backward asymmetryAFB. The dark (light) area shows the 68% (95%) probability region.


the m2`` range spread down to the very low region, where the theoretical predictions cannot

be used, being based on the ultrarelativistic limit for what concern the leptons.The corresponding SM predictions are shown in Fig. 8.6. We interpret the asymmetric

statistical error by assigning a likelihood given by:

L(AFB|AthFB) ∝

exp[

− (AFB−AthFB

)2

2(σ2++σ2

syst)

]

AthFB > AFB

exp[

− (AFB−AthFB

)2

2(σ2−

+σ2syst)

]

AthFB < AFB

(8.10)

where σ+ and σ− are the positive and negative statistical errors.The two-dimensional constraint is represented in Fig. 8.7. Notice that the experimental

measurements are not able push the likelihood at zero outside the ∆C and ∆ ranges, hencethe extent of the probability regions in this figure strongly depend on the arbitrarily upperbounds. Anyway, values larger than 10 are well excluded, in the scenario we are considering,by the measurements previously presented, and it makes our ranges conservative, in thesense that the regions excluded at 95% C.L. (white in the figure) are smaller than they couldbe if we would use tighten ranges.


]-610×)[γK*→BR(B0 50 100 150 200

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Figure 8.8: SM prediction for the B → K∗γ BR. The dark (light) area shows the 68% (95%)probability region.

8.2.3 B → K∗γ

The theoretical treatment of the B → K∗γ decay is strictly related to the one of the B →K∗`+`− decays and is also described in [17]. In this case, anyway, the limitations to smallvalues of the photon momentum does not apply and the full BR can be considered. Theexperimental status is given by [42]:

B(B0 → K∗0γ) = (45.8± 1.0± 1.6)−6 BABAR (8.11)

B(B0 → K∗0γ) = (40.1± 2.1± 1.7)−6 Belle (8.12)

B(B+ → K∗+γ) = (47.3± 1.5± 1.7)−6 BABAR (8.13)

B(B+ → K∗+γ) = (42.5± 3.1± 2.4)−6 Belle (8.14)

(8.15)

Also in this case we interpret these results by introducing gaussian likelihoods. The SMprediction for the isospin averaged BR is shown in Fig. 8.8. This channel is found to besensitive to ∆D′ only, and the corresponding constraint is shown in Fig. 8.9. Two peaksare present, one peak centered at zero (corresponding to the SM solution) and another onearound 2.5. Although the SM peak seems to be disfavored, is is not excluded even at a 68%level.

8.2.4 Combined constraints

All the measurements used in the previous sections can be combined in order to get a singleconstraint on the ∆D′ versus ∆C plane. Due to the fact that single measurements allow


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Figure 8.9: Constraint on ∆D′ from the B → K∗γ BR. The dark (light) area shows the 68%(95%) probability region.

to exclude a large part of the ranges used for ∆C and ∆D′, we reduce here both ranges to[−5, 5].

The combined constraints can be found in Fig. 8.10. Due to the computational complexityof the calculations, when combining all measurements a long time is needed in order toperform each iteration. Hence, it has not been possible to collect a statistics large enoughto define both a reliable 68% and a 95% area. Hence, only a 95% area is shown. The SMvalue (∆C = ∆D = 0) is at the limit of the 95% area. Such a deviation is not enough toclaim a failure of the SM prediction, hence no conclusive statement can be drawn at thislevel. Anyway, our result shows how the experimental errors are already able to put to thetest the theoretical predictions.

8.2.5 Prospects at SuperB

The phenomenological analysis illustrated in this chapter can be used in order to evaluate thephysics reach of a SuperB factory in the sector of the exclusive b→ s transitions. In general,we assume to observe values consistent with the SM predictions, with errors estimated asfollows:

• For B → K∗νν, we assume to observe this decay with an error similar to the theoreticalone. According to the results of Chapter 7, this is maybe optimistic for the chargedchannel but it is quite conservative for the neutral one.

• The two first points of Fig. 7.6 are used as the expected experimental results for theforward-backward asymmetry.

8.3 CONSTRAINTS ON NEW SOURCES OF MISSING ENERGY 149

C∆-4 -2 0 2 4

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C∆-4 -2 0 2 4

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Figure 8.10: Combined constraint on ∆D′ vs. ∆C. The hatched area shows the 95% proba-bility region.

• The BR measurements for B → K (∗)`+`− and B → K∗γ will be probably dominatedby the systematic uncertainties, which are much higher than the expected statisticalerrors at 50 ab−1. Hence, we assume these BRs to be measured with a total error ofthe same order of the current systematics.

In the MFV scenario considered in our work, the expected constraints on the ∆D′ vs.∆C plane can be found in Fig. 8.11.

The results presented in the previous sections shows the possibility of constraining theWilson coefficients of the effective hamiltonian, using informations coming form rare B de-cays. This is an important point since the discovery of new particles at hadronic machineswould allow to set the mass scale of the NP, but it would be hard to constraint the corre-sponding couplings. Conversly, flavour physics experiments would be able to constraint theeffective lagrangian, from which one can extract informations on the couplings. This is themeaning of the complementary between hadronic machine experiments and flavour physicsexperiments.

8.3 Constraints on new sources of missing energy

We already highlighted many times that the B → K (∗) + invisible channels can be used inorder to constraint models that predict exotic sources of missing energy. In this section wetry to extract some constraint on the parameters of the light dark matter model presented


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Figure 8.11: Constraint on ∆D′ vs. ∆C expected from SuperB, assuming to observe valuesconsistent with the SM prediction. The dark (light) area shows the 68% (95%) probabilityregion.

in Sec. 1.4.1.

Notice that only the BABAR measurements for B → K∗νν presented in this thesis canbe used in this phenomenological analysis In fact, in this case the impact of the NP in thekinematics of the decays can be strong, and the other Belle and BABAR measurements hasbeen performed assuming a SM kinematics, without assessing the impact of this assumptionin the case of a different underlying physics.

8.3.1 Light Dark Matter

We use the equations presented in Sec. 1.4.1 in order to set a constraint on the mass of alight scalar Dark Matter candidate S coupling to the SM Higgs according to Eq. 1.53.

Three unknown parameters are present in this case: the mass of S (mS), its coupling tothe Higgs (λ) and the Higgs mass (mh). On the other hand, Eq. 1.62 makes evident that wecan only be sensitive to mS and the parameter κ ∝ λ/m2

h, which should be ∼ O(1) in orderto satisfy the cosmological constraints on Dark Matter. Hence, in our analysis we assumea flat prior on κ ∈ [0, 2] and mS ∈ [0, (mB −mK∗)/2], this latter range being fixed by thekinematics of the B → K∗SS decay 2.

2Formally, form a Bayesian point of view, we could set a larger range, with a flat likelihood in the regionmS > (mB − mK∗)/2 where our experiment is not sensitive. Having a different range would modify thenormalization and hence any probabilistic assertions (since the likelihood does not go to zero outside theoriginal range). Anyway, since we will set a lower limit for mS , the range [0, (mB −mK∗)/2] is the mostconservative, due to the fact that assuming larger ranges would push the limit upward.

8.3 CONSTRAINTS ON NEW SOURCES OF MISSING ENERGY 151

κ0 0.5 1 1.5 2 2.5 3

[GeV

]S

m

00.20.40.60.8

11.21.41.61.8

2

Figure 8.12: Constraint on mS vs. κ from the BABAR B → K∗νν results. The area betweenthe continuous lines is the 68% probability region. The area above the dashed line is the 95%probability region.

Also in this case we adopt the iterative procedure described in Sec. 8.1, without NPcontributions to C(υ) and D′(υ). Instead, for each iteration mS and κ are generated ran-domly according to their priors and a B → K∗SS BR is extracted. It is added to the SMB → K(∗)νν BR and the weight is extracted from the experimental measurements throughthe likelihoods defined in Sec. 8.2.1. The resulting two-dimensional posterior for mS versusκ is showed in Fig. 8.12. In general, for a given value of κ, we can exclude low values of mS,up to a certain limit, since they would give a too large branching ratio (due to the largeravailable phase space). Obviously, for low values of κ it is not possible to exclude any rangefor mS, since the decay would be suppressed by the coupling also in presence of a very lowmass. On the other hand, such low values of κ are disfavored by the cosmological constraints.

Conclusions

The theoretical limits of the Standard Model and its inability to give a satisfactory answer tosome important questions arising from cosmology and astrophysics are the main reasons forlooking for a new phenomenology emerging at higher energy scales than the ones exploredup to now.

Beside the recent improvements of high energy astrophysics, two classes of experimentscan be performed in order to explore the new scales: high energy (∼ O(TeV)) experimentsaiming at the on-shell production of new particles and high intensisty experiments lookingfor the virtual effects of off-shell states, modifing the low energy phenomenology. Far frombeing alternative, the two options are complemetary and are both needed in order to builda new particle physics in the next decades.

The physics of the B meson decays provide a wide range of observables that are able toconstraint several new physics scenarios and potentially produce the observation of significantdeviations from the SM.

In this thesis we described a search for the rare decays B → K∗νν in the data samplecollected by the BABAR experiment. We highlighted that these processes, suppressed in theSM due to the absence of Flavour-changing neutral currents at tree level, allow to constraintNP scenarios whose contribution could be competitive with the SM. Moreover, due to theimpossibility of detecting the two neutrinos, the signature of the decay is given by a K∗

and a significant amount of missing energy. Therefore, this search is also sensitive to exoticsources of missing like light dark matter and Unparticles.

For the first time, the search for B → K∗νν has been performed in such a way thatits result can be rigorously interpreted in any NP scenario. In particular, it required theanalysis strategy to be independent on the kinematical properties of the decay, since theycan be strongly modified by the NP. In this sence. our analysis provided the first modelindependent constraint on the BR of B → K∗ + invisible.

This analysis has been performed by exploiting a recoil technique: one of the B mesonsproduced at BABAR in the decay of the Υ (4S) resonance is reconstructed in a B → D(∗)`νfinal state, then a K∗ is looked for in the rest of the event. A selection strategy to be appliedto the two B’s has been developed, and optimized in order to maximize the sensitivity tothe branching ratio.

The experimental informations have been collected in a likelihood function, which weused in order to extract a probabilistic interpretation of our results. No significant signalhas been observed, and we used a Bayesian approach to set the following limits:

BR(B0 → K∗0νν) < 18× 10−5 , (8.16)

153

BR(B± → K∗±νν) < 9× 10−5 , (8.17)

which improve significantly the previous results by the Belle collaboration [15] and have beenaccepted by Physical Review D for publication [43].

In this thesis, we also considered the improvement that could be reached, in the searchfor these decays and other similar processes, by building a new generation of B-Factories,which would be able to collect up to 100 times the BB statistics available at present. Weconcluded that the B → K∗νν decays would be observed, at least in the neutral channel,also in a very conservative scenario that does not envisage any improvement of detector andanalysis technique.

Finally, we extracted some phenomenological constraints from B → K (∗)νν and otherb → s exclusive decays measured by the BABAR and Belle collaborations. At first, weconsidered a Minimal Flavour Violation scenario, in which the flavour structure of the SMis not modified by the NP. Our ability of constraining the effective lagrangian shows thepossibility of constraining the couplings of the new particles, if they would be discovered atLHC. Second, we considered a scenario with a light scalar dark matter candidate and wehave been able to constrain its mass and its coupling to the SM Higgs. In this specific case,the unprecetented model independence of our analysis makes our results the only ones thatcan be used for extracting a reliable constraint.

In conclusion, we clarified by a few examples the ability of a B-Factory experiment onexploring new physics scenarios that would arise manifestly only at very high energy scales,and the potentialities of a new generation of machines whose results would be fundamentalalso in the LHC era.

154

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Acknowledgments

The work presented in this thesis is the result of my activity inside the BABAR group ofUniversity of Rome “La Sapienza” and INFN Rome. I would like to thank the present andpast coordinators of this group for their support and the opportunities they gave me forimproving my education and training.

Special thanks go to Riccardo Faccini and Gianluca Cavoto, which acted as tutors formy thesis; to Paul Jackson that coordinated the activity of the B → K∗νν group; to ElisaManoni and other colleagues from Perugia, that worked in close synergy with us in order toextract combined limits from the semileptonic and hadronic recoil techniques.

I would also like to thank my office friends in Rome (the “Baita” guests) and all thefriends I met at SLAC. Thanks to the warm atmosphere they always contributed to create,it has been a pleasure to work and share such an important part of my life with them.

Finally, my thanks go to all my friends and relatives, that supported me and alwaysdemonstrated me their appreciation, affection and friendship.

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