University of TurinDEPARTMENT OF PHYSICS

Master’s Degree in Nuclear and Subnuclear Physics

Measurement of the relative phase between EM and strongamplitudes in ψ(2s)→ pp

Candidate:

Barbara Passalacqua

Supervisor:

Prof. Marco Maggiora

Co-Supervisor:

Prof. Marco Giovanni Maria Destefanis

Reviewer:

Prof. Margherita Obertino

Academic Year 2018-2019

Alle notti insonni superate grazie al

sostegno dei miei professori, della mia

famiglia e dei miei amici.

Enthusiasm is followed by disappoint-

ment and even depression, and then by

renewed enthusiasm.

Murray Gell-Man

Abstract

The investigation of the measurement of the relative phase between strong and electro-

magnetic resonant and non-resonant amplitudes could shed new light on many different

open questions for Charmonia. Recently a relative phase of |∆φ| = 90 for J/ψ has been

observed by BESIII Collaboration, and the relation suggests the hypothesis that the J/ψ

and ψ(2S) could be a combination of two resonances, one decaying solely through EM

processes and another one decaying strongly; in this work the process ψ(2s) → pp is

investigated.

After an initial focus on the related theoretical issues, the experimental scenario, the

BESIII spectrometer and BOSS, the official software framework adopted for reconstruc-

tion and event selection, will be described in detail. After the reconstruction and the

event selection are performed, the number of the pp pairs are evaluated by means of p

and p simultaneous fit of momenta distributions. The pp pairs produced in the investi-

gated channel should be emitted back-to-back in the center of mass frame, once taken

into account possible misalignments, detector resolution and contribution of Initial State

Radiation, which was naively implemented by mean of a custom algorithm. The com-

plete procedure to extract the cross section and the branching fraction for the inclusive

process will be reported, from the event selection to the final result. Finally the relative

phase between the strong and electromagnetic (resonant and non-resonant) amplitudes,

has been extracted considering the pp final state. This analysis has been performed on

the full set of events collected in 2018, to perform both the ψ(2S) lineshape scan and a

detailed investigation of the off-resonance interference pattern.

5

Contents

1 Introduction 1

1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Quantum ChromoDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Running Coupling Constant and Confinement . . . . . . . . . . . . . . . . 2

1.4 Charmonium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 Initial State Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.7 Phase Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.8 A Different Theoretical Approach . . . . . . . . . . . . . . . . . . . . . . . 8

2 The BESIII Experiment 9

2.1 The BEPCII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 The BESIII Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 The Superconductor Solenoid Magnet . . . . . . . . . . . . . . . . . 11

2.2.2 Multilayer Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.3 The Time-Of-Flight System . . . . . . . . . . . . . . . . . . . . . . 12

2.2.4 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . 14

2.2.5 Muon Identifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.6 Triggers and Data Acquisition . . . . . . . . . . . . . . . . . . . . . 15

2.3 The BESIII Offline Software System . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Simulation, Reconstruction and Analysis . . . . . . . . . . . . . . . 16

2.3.2 Event Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.3 Particle Transport and Digitalization . . . . . . . . . . . . . . . . . 17

2.3.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4 BESIII Physics Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1 Charmonium Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.2 Open Charm Decays . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.3 Light Hadron Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 18

2.4.4 τ , R, and QCD Studies . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.5 New Physics beyond the Standard Model . . . . . . . . . . . . . . . 19

3 Data Analysis 21

3.1 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Simulations Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

7

3.4 ISR Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5 Background Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.6 Simultaneous Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.7 Systematic Uncertanties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.8 Inclusive Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4 Results 43

4.1 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 Relative Phase Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5 Conclusions 47

List of Figures 49

List of Tables 51

Bibliography 53

Chapter 1

Introduction

Elementary particle physics is trying to address the question, “What is matter made of?”

on the most fundamental level. There are just three fundamental forces in nature: the

strong force, carried by gluons, the electroweak force, carried by photons and W and

Z bosons, and the gravitational force, dominant at macroscopic scale. Each of these

forces is described by a (sometimes unfortunately different) physical theory. According

to the Standard Model, the strong interaction acts on particles carrying color charge e.g.

quarks and gluons. Together the elementary quarks and gluons form hadrons, a class of

composite particles that interact via the strong force. In this work, the strong interaction is

investigated by observing decays into hadrons of quarkonium states, produced in electron-

positron collision provided by the Beijing Electron-Positron Collider II (BEPCII), and

observed by mean of the Beijing Electromagnetic Spectrometer III (BESIII).

1.1 The Standard Model

The Standard Model of fundamental interactions is a theoretical model that led to the uni-

fication of Quantum Electro-Dynamics (QED) and Quantum Chromodynamics (QCD).

QED describes both electromagnetic and weak forces, while QCD the strong force (for

more details see Section 1.2) [1–3]. The Standard Model is mathematically formulated

in terms of renormalizable gauge theories. A gauge theory is a quantum field theory

(QFT) where gauge fields emerge as a consequence of the internal symmetries [4]. In the

Standard Model, these gauge fields are the force mediators.

The basic Lagrangian may be expressed as:

L = Lvct + LHiggs + Llep + Lquark,

where Lvct corresponds to gauge bosons, LHiggs to Higgs scalar, Llep to leptonic

fermions and Lquark to hadronic fermions, respectively.

The total gauge group of the Standard Model is:

SU(3)C × SU(2)L × U(1)Y (1.1)

The symmetry group of the electroweak interaction is SU(2)L × U(1)Y , while the gauge

symmetry of the strong interaction is SU(3)C .

1

The theory is commonly viewed as containing the fundamental set of particles: the

leptons, quarks, gauge bosons and the Higgs particle.

The fermions, spin 1/2 particles which follow the Fermi-Dirac statistics, are divided

into quarks and leptons. Leptons l can be subdivided in three families, each one composed

of one of the three electrically charged leptons — the electron (e), the muon (µ) and the

tauon (τ) — and of one of the three electrically neutral leptons — the electron-neutrino

(νe), the muon-neutrino (νµ) and the tau-neutrino (ντ ). All the charged leptons have

electric charge −e while their antiparticles have charge +e. All leptons interact via the

weak interaction while only the charged ones interact also electromagnetically. None of

the leptons interact via the strong interaction.

Quarks q come in six flavours: down (d), up (u), strange (s), charm (c), bottom (b)

and top (t). In contrast to the charged leptons, the quarks carry fractional electric charge:

−13e for d, s and b, and +2

3e for u, c and t. In addition to the electric charge, quarks also

carry color charge, a further degree of freedom. While electric charge is either positive or

negative, color charge comes in three varieties. The color charges are commonly referred

to as red (r), green (g) and blue (b). For each color charge there is also an anticolor

charge. Combining all three colors, or anticolors, the color neutral states can be obtained

[3].

1.2 Quantum ChromoDynamics

QCD is a gauge field theory that describes the strong interaction by means of the color-

charged gluons and quarks and represents the SU(3) component of the Standard Model.

QCD Lagrangian is given by

L(x) = −1

4F aµν F

aµν +∑q

qq,a (iD −mq) q (1.2)

where repeated indices are summed over. The term F aµν encodes the dynamics of the

gluon fields, D is the gauge covariant derivative [5–7]. The qq,a are quark field spinors for

a quark of flavor q and mass mq. The color-index a runs from 1 to Nc = 3, where Nc is

the number of colors. This degree of freedom is called color, in analogy with the three

color (R,G,B) with which one can build images. Each quark can appear in one of the

three colors that is the same degree of freedom predicted by Han and Nambu [7].

Indication of the nature of the constituent masses can be found considering sponta-

neous and explicit breaking of the chiral symmetry of the QCD Lagrangian. This feature

influences also an important characteristic of the QCD: the confinement. There is no

experimental evidence of free colored quarks or gluons: as observed so far, they bound

together to form color-singlet (hadrons).

1.3 Running Coupling Constant and Confinement

Similarly to QED, in the pure QCD [5, 8] Lagrangian description loops lead to divergent

contributions. They appear in vertices and in the boson propagator. The issue of the

2

infinite contributions by the loops was solved by a mechanism that is now addressed as

renormalization: the coupling constant becomes function of a nonphysical parameter [2]:

αs(|q2|) =12π

21ln(|q2|/Λ2), (1.3)

where Λ is the renormalization scale, and q is the energy scale. In this way the

divergent contribution can be cut-off from the calculations. The introduction of a scale

results in a modification of the coupling strength at different values of this scale, while the

QED coupling constant is αQED ∼ 1/137. The coupling strenght changes according to

the energy scale. In QCD, the possible contributions to the gluon propagator are two: the

first one is the analogous of the QED term, while the second one is due to the gluon-gluon

interaction.

The coupling strength (αs = g2s4π

) is a function of the energy scale (µR):

the coupling strength in QCD decreases at higher energies (e.g. αs = 0.1185 at the

energy of the Z0 and αs ≈ 0.4 at the 1 GeV scale). This feature is called asymptotic

freedom: in high energy processes quarks and gluons can be considered as free particles

during the interaction, thus the rules of the perturbation theory, well tested in QED, can

be applied for QCD as well. This is the core concept of the so-called perturbative QCD

(pQCD) [7].

On the other hand, for very low energies, the coupling constant becomes so large that

any perturbative approach becomes unfeasible. This effect is called confinement and it is

the origin of the binding of quarks and gluons inside the hadrons.

The mathematical expression of QCD potential takes into account both confinement

and asymptotic freedom, and it is usually defined as:

V (r) = −4αs3r

+ σr, (1.4)

where αs is the QCD coupling constant, 43

is a color factor, r is the distance between

the cc pair, and σ is the factor which takes into account the confinement effect.

1.4 Charmonium

Charmonium is a flavorless meson whose constituents are a heavy quark pair: a charm

quark and its own antiquark [8]. The Charmonium system was discovered in Novem-

ber 1974, when two experimental groups at Brookhaven and SLAC announced almost

simultaneously the discovery of a new, narrow resonance, later addressed as J/ψ [8]. The

resonance was characterized by a mass ∼ 3100 MeV/c2 and an extremely narrow width.

Its current values from PDG are [9]:

MJ/ψ = (3096.916± 0.011) MeV/c2,

Γ = (92.9± 2.8) keV.

Another narrow state was soon discovered at SLAC [8], later addressed as ψ(2S). Its

resonance parameters from PDG are [9]:

3

Mψ(2S) = (3686.093± 0.034) MeV/c2,

Γ = (294± 8) keV.

The J/ψ and the ψ(2S) can be formed directly in e+e− annihilations, therefore they have

the same quantum numbers of the photon Jpc = 1−− (Figure 1.1).

Figure 1.1: The J/ψ and the ψ(2S) formation diagram.

Their extremely narrow widths discourage an interpretation of these new states in

terms of the light u, d, s quarks. They were interpreted as bound states of a new quark

(c) and its antiquark (c), whose existence had been predicted in 1970 to account for the

non existence of Strangeness Changing Neutral Currents [6, 10].

Charmonium is a powerful tool for the understanding of the strong interaction. The

high mass of the c quark (mc ≈ 1.5 GeV/c2) allows to attempt a description of the

dynamical properties of the cc system in terms of non-relativistic potential models, in

which the functional form of the potential is chosen to reproduce the known asymptotic

properties of the strong interaction, as explained in Sections 1.2 and 1.3, and in Equation

1.4.

One of the decay features of the Charmonium states below DD threshold is the narrow

width. These states decay violating the OZI rule. According to the OZI rule, branching

fractions related to diagrams with unconnected quark lines are suppressed. States above

threshold can generally decay to open charm (see Section 2.4.2), except when forbidden

by some conservation rule (and in such cases these states are narrow as well). These

strong decays are described within QCD, and hence when the value of αs becomes larger,

they cannot always be described within a perturbative approach.

1.5 Cross Section

Resonant cross sections are generally described by the Breit-Wigner formula [1]:

σ(E) =2J + 1

(2S1 + 1)(2S2 + 1)

4π

k2

[Γ2/4

(E − E0)2 + Γ2/4

]BinBout

where E is the center of mass (CM) energy, J is the spin of the resonance, the number

of polarization states of the two incident particles are 2S1 + 1 and 2S2 + 1, k is the CM

momentum in the initial state, E0 is in the resonance peak CM energy, Γ is the full width at

half maximum height of the resonance, Bin is the branching fraction for the resonance into

4

the initial-state channel and Bout is the one into the final-state channel. The differential

production cross section of point-like, spin 1/2 fermions in e+e− annihilation through a

virtual photon, e+e− → γ∗ → ff , at CM energy squared s is given by [3]:

dσ

dΩ= Nc

α2

4sβ[1 + cos2θ] + (1− β2)[sin2θ]Q2

f , (1.5)

where β is v/c for the produced fermions in the CM frame, θ is the CM scattering angle,

Qf is the charge of the fermion, and the factor Nc is 1 for charged leptons. In the ultra-

relativistic limit β → 1, the cross section integrated over the solid angle is:

σ = NcQ2f

4πα2

3s= NcQ

2f

86.8nb

s(GeV 2)(1.6)

This formula is useful in Section 3.5 for the investigation of the background. The total

cross section for a squared CM energy√s can be expressed as:

σ =N

Lε(1 + δ), (1.7)

where N is the number of events, L is the integrated luminosity, ε is the efficiency, and

(1+δ) is the ISR correction factor, as explained in Section 1.6.

The resonance mass MR, the total width ΓR and the product of branching ratios into

the initial and final state Bin and Bout can be extracted by measuring the formation rate

for that resonance as a function of the CM energy E.

1.6 Initial State Radiation

In an e+e− collision each one of the inciding leptons e+ or e−, or both, can radiate one

or more photons. This process is known as Initial State Radiation (ISR) [11, 12]. The

radiated energy reduces the effective CM energy of the e+e− annihilation. The ISR process

is shown in Figure 1.2.

Figure 1.2: An electron radiating a ISR photon γISR.

Let’s consider a process e+e− → X at a CM energy E0 and its cross section as a

function of the CM energy σ(E). The integrated luminosity is L0, and the data sample

are collected at the nominal CM energy E0. Because of the ISR process, the collisions

actually occur at lower CM energies E < E0. The probability of radiating an ISR photon

is described by the radiator function W (x) [12], where x is the fraction of the beam energy

carried by the ISR photon.

5

The two kinematic paramenters x and E are related by:

x = 1− E2

E20

. (1.8)

We can consider W (x) as a probability distribution function, hence∫ 1

0W (x)dx = 1,

and express the cross section as a function of x: σ0 ≡ σ(E = E0) = σ(x = 0). The

experimental efficiency to detect the process e+e− → X at a CM energy E0 is a function

of x: ε(x). In the no ISR case, we can define ε0 ≡ ε(0).

The number of observed events is then:

N = L′∫ 1

0

ε(x)σ(x)W (x)dx, (1.9)

where L′ is the luminosity for the case of no ISR.

The cross section σ0 can be determined in two steps.

First, one can define an effective efficiency ε′:

ε′ ≡ Nreconstructed

Ngenerated

=LMC

∫ 1

0ε(x)σ(x)W (x)dx

LMC

∫ 1

0σ(x)W (x)dx

, (1.10)

where LMC is the luminosity of the MonteCarlo. To account for the ISR we need then

a correction factor 1 + δ defined as:

1 + δ ≡∫ 1

0

σ(x)

σ0

W (x)dx, (1.11)

that can be evaluated exploiting MonteCarlo simulations.

The cross section is hence:

σ0 =N

L0ε′(1 + δ). (1.12)

Taking into account Eq. 1.10 and 1.11 one can evaluate the product:

ε′(1 + δ) =1

σ0

∫ 1

0

ε(x)σ(x)W (x)dx, (1.13)

where the integral can be limited to any value of x where either ε(x) or σ(x) become

negligible and compatible with zero. The actual values for ε′ and (1 + δ) might depend

on the cut-off, but their product, and hence the final value of σ0, does not.

If one considers the process near the threshold, the integrals in Eq. 1.10 and 1.11 can

be cut off at small x, corresponding to a threshold xT << 1. Assuming ε(x) ≡ ε0 and

σ(x) ∼ σ0 in the small region between x = 0 and x = xT , it is possible to rewrite the

effective efficiency as:

ε′ ≡ Nreconstructed

Ngenerated

=LMC

∫ 1

0ε(x)σ(x)W (x)dx

LMC

∫ 1

0σ(x)W (x)dx

=

∫ xT0

ε(x)σ(x)W (x)dx∫ xT0

σ(x)W (x)dx=ε0σ0

∫ xT0

W (x)dx

σ0

∫ xT0

W (x)dx= ε0.

Thus, effects due to ISR can be neglected in the calculation of the effective efficiency, but

6

they still need to be accounted for in the calculation of 1 + δ:

1 + δ ≡∫ 1

0

σ(x)

σ0

W (x)dx =σ0

σ0

∫ xT

0

W (x)dx. =

∫ xT

0

W (x)dx

The role of the ISR is particularly relevant for the cross section evaluation, as explained

in Section 1.5.

1.7 Phase Measurement

An interference pattern between the J/ψ decay and non-resonant amplitudes was observed

in e+e− → µ+µ− final states [13–15]. Close to resonance, the annihilation of e+e− into

hadronic final states may proceed via three processes: strong and EM decays and the

continuum process, respectively mediated by gluons or virtual photon for the resonant

diagrams, and by a virtual photon for the non-resonant one, as shown in Figure 1.3.

Figure 1.3: The Feynman diagrams for the process e+e− → hadrons (a) strong A3g, (b)

electromagnetic Aγ and (c) Acont continuum.

In a perturbative QCD approach all amplitudes are expected to be almost real, and,

with these assumptions, maximal interference should occur between the above mentioned

amplitudes corresponding to a 0/180 relative phase. On the contrary experimental data

suggest a phase ∼ 90. Such a behaviour has been previously explained by means of

SU(3) symmetry breaking and subsequent restoration [16].

The relative phase could be extracted investigating the interference pattern of e+e−

reaction cross section as a function of CM energy (W) near the resonance [17]. The full

Born cross section for processes including the strong and EM amplitudes can be expressed

as:

σ0 ∝ |Ag(W )eiφg,EM + Aγ(W ) + Acont(W )|2, (1.14)

where φg,EM is the phase between the strong and the full EM amplitudes. The total cross

section becomes hence:

σ[nb] = 12πBinBout

[ cW

]2

· 107 ·

[C1 + C2e

iφ

Wris −W − iΓ2

+ C3eiφ

]2

, (1.15)

where C1, C2 and C3 are proportional to the strong, the electromagnetic and the non-

resonant amplitudes respectivetely, φ is the relative phase and Bout is the branching ratio

of the final states [16].

7

1.8 A Different Theoretical Approach

A possible explanation by Freund and Nambu is that Quarkonium violates the OZI Rule in

its decay [8, 18]. One can interpret quarkonium as a superposition of a narrow resonance

ν, not directly decaying into hadrons, and a wide resonance (a glueball O), not coupled

to leptons but strongly coupled to hadrons, as shown by the diagrams in Figure 1.4.

Figure 1.4: The scheme suggested by Freund and Nambu [8], the process being iterated

in f .

In this scenario f is the coupling constant between ν and O. In this model, assuming

Γ >> ΓJ/ψ and f 2 ∼ Γo(ΓJ/ψ − Γν), the strong and electromagnetic amplitudes can be

expressed as:

Astrong ∼i√BeeMνf

√Bh

M2J/ψ −W 2 − iMJ/ψΓJΨ

(1.16)

Aem =

√BeeMνΓJ/ψ

√Bem

M2J/ψ −W 2 − iMJ/ψΓJψ

(1.17)

where Bee, Bh and Bem are the branching fractions related to electron-positron pairs,

to hadrons and to the continuum respectivetely, Mν and MJ/ψ are the masses of the narrow

ν and J/ψ, W is the energy in the CM frame, and the factor i in the strong amplitude

makes it imaginary. The J/ψ shape can be properly reproduced when |f | ∼ 0.012 GeV ,

Mo ∼ MJ/ψ, and Γo ∼ 0.5 GeV , where Mo and Γo are the mass and the width of the

glueball.

8

Chapter 2

The BESIII Experiment

The experimental data analyzed in this work were collected by the Beijing Spectrometer

III (BESIII) [19]. BESIII is a multipurpose particle spectrometer hosted on the Beijing

Electron-Positron Collider II (BEPCII) at the Institute for High Energy Physics (IHEP)

in Beijing, China. The BESIII Collaboration is an international collaboration which

involves more than 500 members from 72 institutions from 15 countries, including IHEP

and INFN.

2.1 The BEPCII

The Beijing Electron Positron Collider II (BEPCII) is a double-ring e+e− collider with

two interaction points (IPs). BEPCII is also exploited for synchrotron radiation, taking

advance of photons emitted in a direction tangential to the particle trajectory. The

upgrade of BEPC to BEPCII increased the design peak luminosity by two orders of

magnitude from L ≈ 1031fb−1 to L ≈ 1033fb−1, where L was evaluated in both cases at

the optimal beam energies of 1.89 GeV.

The luminosity for a circular e+e− collider is given by:

L0[fb−1] = 2.17 · 1010(1 + r)ξyeE0(GeV )NbNe

T0(s)β∗y(cm)Fh,

where E0 is the nominal energy, Ne is the e+e− bunch population, Nb is the bunch num-

ber, T0 is the revolution time, β∗y is the vertical betatron function at the interaction point,

r is the interaction point (IP) beam size ratio σ∗y/σ∗x, and ξy is the vertical beam-beam

tune shift. Fh is the luminosity reduction factor due to the hourglass effect. The values of

beam-beam tune shifts and the luminosity reduction factor are calculated by beam-beam

simulations. The storage rings of BEPCII are 237.5 m long and are installed in the tun-

nels that previously hosted BEPC. In BEPCII, electrons and positrons are accelerated

from 1.0 GeV up to maximum energy of 2.3 GeV in the linear accelerator Linac, that is

1.2 km long, before they are injected into the storage rings. The electrons and positron

circulate in separate vacuum tubes and are therefore brought to collide at a small angle

of 22 mrad at the interaction point inside the BESIII detector, as shown in Figure 2.1.

9

Figure 2.1: Schematic layout of the Beijing Electron Positron Collider II.

Both storage rings hold 93 electron/positron bunches each with a bunch spacing of

8 ns, giving a total beam current of 2× 910 mA (see [20–22]).

2.2 The BESIII Spectrometer

The purpose of the BESIII spectrometer, shown schematically in Figure 2.2, is to detect

particles created in e+e− interactions and their charged and neutral decay products. It is

composed of different detectors, each one with its peculiar capabilities.

Figure 2.2: Schematic layout of the BESIII Spectrometer.

As particles traverse the different BESIII subsystem, signals are collected and used to

reconstruct the tracks and to perform particle identification (PID). The spectrometer,

cylindrically symmetric, is mainly hosted inside the 1 T superconducting solenoid, pro-

viding a geometrical acceptance ∆Ω/4π = 0.93. The main characteristics of each detector

system will be briefly addressed in the following Sections (see [23–25]).

10

2.2.1 The Superconductor Solenoid Magnet

The 1 T magnetic field provided by the superconductor solenoid magnet (SSM) [23] bends

the trajectories of charged particles inside the detector volume via the Lorentz force.

The magnetic field enables the determination of momenta of charged particles by

means of the measurement of curvatures of the trajectories in the MDC. Typically the

momentum of the particle is given by:

p = 0.3Bρ,

where ρ is the radius of the curved paths and B is the magnetic field. In order to

establish the γ or β factors together with the particle momenta, the other components of

the spectrometer are used to identify the particles and their masses.

2.2.2 Multilayer Drift Chamber

The Multilayer Drift Chamber (MDC) [21, 23] is situated in the central region of BESIII

surrounding the beam pipe, as shown in Figure 2.3.

Figure 2.3: Scheme of BESIII MDC.

The inner radius of the MDC is 60 mm and the outer radius is 810 mm, with a polar

angle acceptance of |cosθ| < 0.93. The MDC consists of an inner tracker and an outer

chamber filled with a gas mixture of 60% He and 40% C3H8. The multilayer drift chamber

is a gaseous detector used to track the paths of charged particles in the magnetic field

provided by the SSM. The MDC also provides information of particle energy loss due to

ionization of the gas (dEdx

). The evaluated dEdx

can be used as input for particle identification

(PID), since each different kind of particle shows a characteristic correlation among its dEdx

11

and momentum. The basic operating principle of a drift chamber is the following: when a

charged particle passes through a suitable gas, some of the gas molecules become ionized

and the charged particle loses parts of its energy.

Drift chambers, developed in the early ’70s, can be used as well to estimate the lon-

gitudinal position of a track by exploiting the arrival time of electrons at the anodes if

the interaction time is known. A drift cell, the basic unit of the drift chamber, consists

of a sense wire (anode) with a large positive voltage, surrounded by grounded field wires

(cathodes). As the passage of a charged particle in a drift cell ionizes the gas, electrons

will start to drift towards the anode. Electrons are collected at the sense wire and thereby

cause an electric pulse which is amplified by the front-end electronics. After amplifica-

tion, the signal is branched for timing, charge measurement and for the first level (L1)

trigger. Signals from different drift cells are combined by pattern matching algorithms to

form track candidates. Momentum and energy loss per distance traveled in the detector

(dEdx

) are determined for each track. In total, there are 6796 sense wires in the BESIII

MDC. The BESIII drifts cells consist of a gold-plated tungsten sense wire surrounded by 8

aluminum field wires. The position resolution, measured at the interaction vertex, in the

rφ-plane of the MDC is better than 120 µm, and in the z-axis is ∼ 2 mm. The momentum

resolution is better than 5% for a particle with transverse momentum of 1 GeV/c. The

transverse momentum resolution can be expressed as:

σptpt

=

√(σwirept

pt

)2

+

(σmsptpt

)2

,

where σwirept is the momentum resolution provided by each individual wire spatial resolu-

tion, and σmspt is the momentum resolution due to multiple scattering. The factors which

contribute to the dEdx

resolution are the fluctuation of the number of primary ionizations

along the track, the recombination loss of electron-ion pair, and the fluctuations in the

avalanche process.

2.2.3 The Time-Of-Flight System

The Time Of Flight System (TOF) [21–23] is located outside the MDC: its barrel section

covers |cosθ| < 0.83 and its end-cap section 0.85 < |cosθ| < 0.95. The TOF system

consists of a two staggered-layer barrel sections and two one-layer end-cap sections. The

two barrel layers are composed of 88 plastic scintillators each and the end-caps of 48

scintillators. The total lenght of the TOF system is 2.3 m, with a radius of 0.81 m.

The purpose of the time-of-flight system (TOF) is to provide flight-time measurements

of charged particles, to be exploited for particle identification (PID). The basic component

of the TOF system is the scintillation counter. There are two main types of scintillator

materials, inorganic crystals and organic materials. Common inorganic crystals used

in scintillation detectors are CsI(T l) and CsI(Na). As a charged particle crosses the

scintillation material, molecules in the material are excited. Scintillation light is hence

emitted when the molecules de-excite. As the scintillation light hits the base cathode

of the photo-multiplier tubes (PMT), electrons are knocked out via the photoelectric

effect. The electrons are then accelerated in a 2000 V potential over about 5 cm in

12

Figure 2.4: Scheme of BESIII TOF

the Hamamatsu R5924-70 PMTs, used in the TOF. As electrons hit the dynodes in the

PMT, additional electrons are knocked out. The subsequent knock-out and acceleration

of electrons result in a cascade of electrons reaching the anode, producing an electric pulse

with the charge proportional to the light collected at the photocathode. Each scintillation

counter consists of a block of plastic scintillator material with two PMTs attached directly

at the two end faces of the block. Signals from the PMTs are amplified and fed to the

Front End Electronics (FEE) which splits the signal for timing and charge measurements.

The time resolution of the TOF system depends on several variables, the single layer

resolution being in the range 100−110 ps. The main contribution to the uncertainty in the

time measurement comes from the intrinsic time resolution of the scintillation counters.

Other major contributions to the resolution come from uncertainty in vertex position of

colliding 15 mm bunches, from the time resolution of the readout electronics, and from

the error propagation to the expected time of flight from flight path length and momen-

tum measurements. The overall time resolution σ of the spectrometer can be expressed as:

σ =√σ2i + σ2

b + σ2l + σ2

z + σ2e + σ2

t + σ2w

where the value of each term is reported in Table 2.1.

σ Barrel[ps] EndCap[ps]]

σi: counter intrinsic time resolution 80 ∼ 90 80

σl: uncertainty from 15 mm bunch length 35 35

σb: uncertainty from clock system ∼20 ∼ 20

σθ: uncertainty from θ-angle 25 50

σe: uncertainty from electronics 25 25

σt: uncertainty in expected flight time 30 30

σw: uncertainty from time walk 10 10

σ1: total time resolution, one layer 100-110 110

combined time resolution, two layers 80-90 -

Table 2.1: TOF time resolution performance for 1 GeV/c particles.

13

2.2.4 Electromagnetic Calorimeter

The main purpose of the electromagnetic calorimeter (EMC) [21] is to precisely measure

the energy and position of electrons, positrons and photons. It also provides input to the

L1 trigger. The EMC is similar to the TOF in terms of operationg principles. However, it

differs in the choice of scintillator material and light-readout from the scintillator. Since

one of the main purposes of the EMC is to detect photons, the scintillator needs to be

composed of a material with large atomic number (Z). This is because the total cross

section of photons with matter scales with Z. In the typical energy range of photons at

BESIII, from 25 MeV to 2000 MeV , the main interaction mechanisms with the detector

material are Compton scattering and pair production.

As photons or charged particles interact with a scintillator crystal they initialize elec-

tromagnetic showers. An electromagnetic shower is a process that occurs when highly

energetic (> a few MeV ) particle give away its energy in the form of e.g. pair production

(if a photon) or bremsstrahlung (if a charged particle). This initilizes a cascade of events

where the highly energetic particles undergo bremsstrahlung and pair production, hence

creating a shower-like process. The electromagnetic shower starting in a seed crystal

can spread to adjacent crystals, creating a cluster. Each kind of particle have different

shower pattern characteristics and can therefore be used as input for PID. By the end

of the process, all the energy of the initial high-energetic particle has been converted

into a large number of low-energetic photons i.e. into visible light. The light from the

crystals is converted to electrical signals by photodiodes attached to the back faces of the

crystals. Photodiodes are compact semiconductor detectors. Like the TOF, the EMC in

BESIII consists of a barrel section covering |cosθ| < 0.83 and the two end-cap sections

covering 0.85 < |cosθ| < 0.93. The EMC consists of 6240 CsI(T l) scintillating crystals,

each crystal covers approximately 3 in the φ direction and 1.5 ÷ 3 in the θ direction.

The crystals are 28 cm long, with a pyramidal shape. The front and back faces of the

crystals are square shaped with side lengths of 5.2 cm and 6.4 cm, respectively. The

main contributions to the energy resolution are imperfections in the crystals and light

leakage. The design range for photon energy measurement is approximately in the range

20÷ 2000 MeV , with an energy resolution of 2.5% at 1 GeV and a position resolution of

σxy ≤ 6mm/√E(GeV ).

2.2.5 Muon Identifier

Since muons and pions have similar masses, 105 MeV/c2 and 139MeV/c2 respectivetely,

they are difficult to be resolved exploting to perform the PID the TOF and MDC systems

only. However, muons interact only electromagnetically and weakly.

Muons can therefore penetrate large amounts of matter without being heavily dis-

torted. This allows to single them out from the strongly interacting pions. Most pions

are in fact stopped in either the EMC or in the SSC coil. By placing specialized detec-

tors inside the SSC coil, in this case resistive plate chambers (RPC), one can combine

information from the muon chambers (MUC), which is shown in Figure 2.5, the MDC,

the EMC and the TOF system to tag muons[26].

RPCs are gaseous detectors where high voltage is applied between two electrodes of

14

Figure 2.5: BESIII Muon Chamber.

highly resistive bakelite slabs, separated by a compartment filled with a gas mixture con-

sisting of 50% Ar, 42% C2F4H2 and 8% C4HC10. As muons pass through the gas, they

ionize the molecules of the gas along their trajectories. The electrons start to drift towards

the anode (+HV ) in the strong electric field. However, since the electrodes are highly

resistive, they are essentially ”invisible” to the electrons which are collected by readout

strips. The readout strips have a width of about 4 cm. In total, there are 9 layers of RPC

units in the barrel and 8 layers in the end-caps, each layer alternating the direction of the

readout strips to allow for 2D position measurement.

2.2.6 Triggers and Data Acquisition

The goal of the BESIII trigger system [21] is to select relevant Physics events and to

suppress background from sources other than the e+e− annihilation process. Background

from cosmic rays, Bhabha scattering (e+e− → e+e−) and beam interactions are expected

to contribute with more than 100 kHz to the total event rate. To suppress the total

event rate and to keep as many of the Physics events as possible, a two-level trigger

system is employed. This system consist of the L1 hardware trigger system, and the

L3 software trigger system. The L1 trigger system is ”online”, i.e. it performs event

filtering in real time using fast electronics and fast algorithms. The L3 trigger is ”offline”

and uses more sophisticated algorithms whose computational load is heavier and hence

require more time. An L1 trigger decision, based on signals from the trigger sub-systems

of the detector modules’ FEE, is performed every clock cycle. The L1 trigger frequency

is 41.65 MHz, i.e. the cycle is 24 ns long. The reference time for the L1 timing is

the accelerator radio frequency (RF) clock with a frequency of 499.8 MHz (2 ns). The

subsystems that provide input for the L1 trigger are the TOF, the MDC, the EMC and

the MUC. The final trigger decision is handled with the Global Trigger Logic (GLT).

Once the L3 trigger filtering has been applied, background events are reduced to below

1 Hz, while keeping the signal event rate basically constant.

15

2.3 The BESIII Offline Software System

The BESIII Offline Software System (BOSS) [27] is a software framework that integrates

full custom algorithms developed for the BESIII experiment with external algorithms.

BOSS aims to streamline the analysis chain from interactions in the detector to recon-

struction and selection of data. BOSS is coded in C++ and builds upon the GAUDI

framework, originally developed by the LHCb collaboration. The ROOT scientific soft-

ware framework from CERN, also coded in C++, is heavily exploited in the BOSS frame-

work. ROOT is also used for visualization, selection and fitting of data. Depending on

the release, BOSS runs on Scientific Linux versions SLC5 for older versions (< 6.6.4.p01)

and SLC6 for newer releases. The main tools integrated into BOSS used in the analy-

ses performed within my thesis are described in the following sections. This work was

performed within BOSS version 7.0.4.

2.3.1 Simulation, Reconstruction and Analysis

Monte Carlo simulations are used to estimate detection efficiency and background, as well

as to optimize selection criteria. The simulation-to-analysis chain consists of five main

stages:

• event generation;

• transport through detector materials;

• digitization to simulate detector and trigger response;

• reconstruction;

• analysis.

Reconstruction and analysis of simulated and real data is performed by the same

algorithms. The only difference is that in the simulations the un-digitized MonteCarlo

information is retained in parallel to the digitized simulated events [27, 28].

2.3.2 Event Generation

The EvtGen framework, coded in C++ as well [21], models all decay distributions cor-

rectly, and allows at the same time the implementation of new physical models.

There are approximately 70 models implemented that simulate a large variety of phys-

ical processes. The modularity of the code allows for easy implementation of additional

models and all particles property are contained. The decay table contained in the EvtGen

package provides an extensive list of decays for resonances, and the table is updated with

the available experimental and theoretical information on a regular basis. There are three

main components needed to specify a decay channel: the branching ratio, the list of final

state particles, and the model used to simulate the decay. In this work, the J1BB1 model

is used, and it is explained in detail in Section 3.1.

16

2.3.3 Particle Transport and Digitalization

The particles generated in the previous step are propagated through the BESIII detector

model implemented in Geant4 [27, 29]. The propagation through the detector material

takes into account energy loss (ionization), multiple scattering, and magnetic field effects.

When a particle enters on active detector material, where it interacts, a hit point with

a perfect resolution is registered. The output from the particle transport is a collection

of hit points containing information about hit location, time and energy deposit. After

the particle transport, the collection of hits is digitized. The task of the digitization code

is to simulate output signals from the readout electronics corresponding to the hits posi-

tion, smearing hence the initially simulated resolution. Here, energy losses are converted

into pulse heights and the hit points are converted into hits, whose spatial resolution

corresponds to the granularity of the detector. The digitized output from the simulated

detector sub-systems is then feeded to a trigger simulation. After the trigger simulation,

the events firing the trigger condition are saved as raw data, containing all the information

output from the detector sub-systems that gave signals during the event. At this stage,

the simulated data should provide the same information as the real data. During the final

reconstruction, simulated data and real data are treated by the same algorithms. The

representation of the BESIIII detector geometry and materials used by Geant4 is stored

using the Geometry Markup Design Language (GDML) [27]. GMDL is an application-

independent persistent data format based on XML for describing geometries and materials

involved in Physics experiments.

2.3.4 Reconstruction

The reconstruction algorithm takes as inout the raw data and processes them in order

to construct more accessible objects for Physics analysis. Such objects are MDC tracks,

EMC clusters and MUC hits.

For charged tracks, track reconstruction is performed in two stages. Tracks in the MDC

are reconstructed by fast pattern recognition algorithms together with TOF information

for the L1 trigger decisions. Track matching is also performed on the L1 trigger level,

i.e. information from all detector sub-systems is combined to find matching hits and

tracks. Information about drift times is taken into account already at trigger level. Then,

a Kalman track fit is performed by iterating over the hits in the MDC by solving the

equations of motions. After each step of the fit the track parameters and their covariance

matrix as well as the χ2 of the fit are updated. Two iterative processes are applied:

one starting from the interaction vertex of the e+e− as pivot in a forward fit, and the

other from the last hit in a backward fit, the procedure being performed for the particle

hypotheses. After the Kalman track fit is completed, a track object is created and stored.

The track object is used in higher level track selection and as an input to kinematic and

vertex fits and PID algorithms. The TOF timing is determined by extrapolating tracks

from the MDC and matching with hits in the TOF.

17

2.4 BESIII Physics Program

The BESIII physics program is quite wide and it can be roughly subdived into five topics:

Charmonium spectroscopy, open Charm decay, light hadron spectroscopy, τ −R−QCDstudies, and new Physics searches. For a more detailed description of the BESIII physics,

please refer to the BESIII Physics Book [21].

2.4.1 Charmonium Spectroscopy

Firstly predicted by the Glashow-Iliopoulos-Maiani (GIM) mechanism [3], the existence

of the charm quark was confirmed by the J/ψ discovery in the early 70s [8]. Very soon

its first radial exctitation as well, the ψ(2S), was identified. The discovery of the two

resonances in the Charmonium spectrum confirmed the possibility to describe these states

in a spectroscopic approach, as for the atomic structure. Other excited states where hence

soon predicted. This very simplified model worked properly until the beginning of the

XXI Century, leading even to the suspect that all the missing states had not yet been

detected just due to the limited statistics available in literature. In 2003, the discovery

by the BELLE Collaboration of a very narrow resonance above the open charm threshold

decaying mostly in π+π−J/ψ changed completely the picture [19]. The X(3872), as it is

called nowadays, was only the first of several new states unpredicted by the simple Quark

Model. Most of these states show exotic features (charged Charmonia decay preferentially

in other Charmonia, rather than into charmed mesons) and nowadays they are usually

addressed as XY Z states [30].

2.4.2 Open Charm Decays

In the past, the interest in the investigation of open charm mesons was limited, since most

of the more interesting phenomena that can be observed in B meson Physics (Cabibbo-

Kobayashi-Maskawa transitions, CP violation, D0 − D0 oscillation) are weak or very

small in D spectrum. However, the interest in these processes increased significantly in

the recent years. On one side, the discovery of the Dsj states revived the interest in

the charmed meson spectroscopy. On the other side, being the weak forces well-known

in the SM, it is possible to reach unprecedented precision in the investigation of the

interplay between strong and weak interaction. Moreover, the tools previously developed

for the B physics can be tuned and employed in an environment with less background. In

addition, thanks to the high luminosity of the e+e− colliders, it is possible to be sensitive

to discrepancies between the SM predictions and experimental data, eventually gaining

access to New Physics [31].

2.4.3 Light Hadron Spectroscopy

Light hadron spectroscopy is a broad sector which includes the search for glueballs (full

gluonic states), the characterization of η/η′, the search for new resonances of conven-

tional baryons and mesons. The common issue among all these different branches is the

18

interpretation of the strong interaction in the low energy regime, where the perturbative

approach cannot be extended [32].

2.4.4 τ , R, and QCD Studies

The main Physics goal is the precise measurement of different key parameters of the Stan-

dard Model (τ properties, muon anomalous magnetic moment), and the investigation of

the QCD perturbative (determination of the R value) and non-perturbative regime. Even

though the QCD is a well tested theory, a better knowledge of several parameters requires

extremely precise measurements, far more precise w.r.t. those available in literature: BE-

SIII can measure with unprecedented precision hadronic contribution to the muon anoma-

lous magnetic moment. A working group is dedicated to such precise studies in both the

perturbative and non-perturbative sections of the QCD spectrum. While electrons and

muons properties are well understood, τ leptons are yet less known. Such measurements

are quite challenging, since τ can decay hadronically into a large number of different final

states, being heavier than many hadrons (Mτ = (1776.86 ± 0.12) MeV/c2). The main

challenge in such studies arises from the presence of at least one neutrino in each decay

(ντ , for lepton number conservation), so the kinematic variables of the event can not be

completely determined, leading to a lower precision in the experimental measurement.

BESIII took advantage of the possibility to produce the τ pairs at or near the threshold,

and to scan the line-shape to precisely measure the mass opening providing the most

precise single measurement of the τ lepton mass. The last data taking was scheduled in

the data taking period 2017-2018, in order to further improve this measurement.

In the early years of the investigation of the strong interaction, a key measurement was

the ratio between the e+e− → hadrons and the e+e− → µ+µ−, addressed R− value. By

determining such a ratio, physicist confirmed the existence of a further degree of freedom

[2], the color, and thus provided the first confirmation of the theory nowadays known

as Quantum Chromodynamics. After more than 40 years, the precise measurement of

this ratio it is still an important parameter to be determined when investigating QCD,

as previously explained in Section 1.2, and to eventually spot any possible discrepancy

means to gain access to New Physics beyond the Standard Model.

2.4.5 New Physics beyond the Standard Model

Although the Standard Model represents the most complete theory to understand the

world at quantum level, there are several experimental evidences suggesting that there are

still some open questions and that there are issues not yet fully understood, e.g. neutrino

masses, naturalness, dark matter, dark energy completeness. The typical energy regime

in which such issues can be addressed is usually extimated to be in the range between

∼ 1 TeV and ∼ 100 TeV . Such high energy ranges leaves most of these searches to the

higher energy accelerators, as LHC [33], and in the future to the possibly-forthcoming

Circular Electron Positron Collider(CEPC) [22] in China, International Linear Collider

(ILC)[34] in Japan and Future Circular Collider (FCC) at CERN [19].

However, in recent years, thanks to the high luminosity delivered by the e+e− colliders,

19

tests for new Physics became available also in the lower energy regime. Among the

different theories, one foresees the existence of a massive partner of the photon, called

Dark Photon. This new vector boson behaves as a portal between standard and dark

particles, it couples directly to the SM photon, and it can decay both in SM electron or in

supersymmetric partners, like the neutralino of the WIMPs (Weakly Interacting Massive

Particles) [21].

20

Chapter 3

Data Analysis

3.1 Experimental Data

The process investigated in this work is e+e− → X → pp, in the ψ(2S) energy regime. The

data collected during the 2018 run were analysed using BOSS version 7.0.4, considering

the data collected at CM energies in the 3.4÷3.8 GeV range by the BESIII Collaboration

close to the ψ(2S) resonance (Mψ(2S) = 3.686 GeV ). These data were collected to perform

a ψ(2s) lineshape scan and will be also used to evaluate the relative phase between strong

and electromagnetic decay amplitudes [16, 35]. The nominal energies, the real energies

with their spread and the integrated luminosities of each collected CM energy data sample

are shown in Table 3.1

Nominal E[MeV ] E σE L[pb−1]

3580.0 3581.543 0.060 85.7

3670.0 3670.158 0.063 84.7

3681.0 3680.144 0.061 84.8

3683.0 3682.752 0.115 28.7

3684.0 3684.224 0.119 28.7

3685.5 3685.264 0.105 26.0

3686.6 3686.496 0.120 25.1

3690.0 3691.363 0.075 69.4

3710.0 3709.755 0.074 70.3

Table 3.1: Data set collected by BESIII during the 2018 data taking.

MonteCarlo simulations are used to define proper selection criteria and to estimate

the reconstruction efficiency. ROOT version 5.34 was used for the analysis. To perform

efficiency corrections, I have also used the 400M MonteCarlo ψ(2S) inclusive samples,

provided by the Collaboration and analysed with the BOSS version 7.0.4.

In this inclusive samples, all the ψ(2S) decays are simulated with their respective

branching ratios (BR). To generate Charmonium decay events produced from the e+e−

annihilation, the KKMC+BesEvtGen event generators were used, following the scheme de-

picted in Figure 3.1.

21

Figure 3.1: Scheme of e+e− annihilation into Charmonia.

The KKMC [27] was used to simulate the e+e− annihilation into a Charmonium including

ISR effects, as previously explained in Section 1.6, together with the beam energy spread.

Then the Charmonium decays have been generated with BesEvtGen, adopting in this work

the J1BB1 model to simulate the final states. The J1BB1 model distributes the final states

particle according to the theoretical model described in [2], with an angular distribution

1 + αcos2θ, where α = 0.68 is a value specific for Charmonium, and assumed to be same

both at the peak and at the continuum. Events were generated in the e+e− CM [36].

In total 104 events were generated for each energy value and for each e+e− → γ∗ → pp

process.

3.2 Event Selection

In order to reconstruct Charmonia from the pp final state, the event selection must identify

events with two good charged tracks reconstructed in the MDC and zero net charge. To

increase the signal over backround ratio, the following kinematic cuts are required for the

proton tracks:

• the point of closest approach to the Interaction Point must be inside a cylinder of

radius 1 cm and longitudinally 10 cm long;

• proton momentum p ≤ 2 GeV/c, so to have a total event momentum not larger

than Mψ(2S);

• proton polar angle |cosθ| < 0.8 in the LAB frame, in order to select the barrel region

of the spectrometer, where the sample is more clean;

• Ep

p< 0.5, where Ep is the energy deposited in the EMC.

Moreover the following cuts are applied to both the proton and the antiproton tracks:

• 178 < θ < 180, where theta is the angle among the two p and p tracks, in order

to select back-to-back tracks;

22

• PID tags selecting proton and antiproton;

• specific momentum p cuts, for both proton and antiproton, tuned considering the

MonteCarlo simulations.

In detail, PID information allows to identify the tracks exploiting the probability den-

sity function method. To be identified as a proton a track candidate: must be associated

with a probability > 0.001 to be a proton; and this probability must be larger than the

one to be a kaon or a pion.

Figures 3.2, 3.3, 3.4, and 3.5 show the MonteCarlo pp pairs angular distributions,

Eshow/p proton spectra, and 3-momenta distribution of the tracks, respectively, plotted

for the 9 investigated CM energies listed in Table 3.1.

166 168 170 172 174 176 178 180

ang [deg]pp

1

10

210

310

410

Cou

nts

166 168 170 172 174 176 178 180

ang [deg]pp

1

10

210

310

410

Cou

nts

166 168 170 172 174 176 178 180

ang [deg]pp

1

10

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410

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nts

166 168 170 172 174 176 178 180

ang [deg]pp

1

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410

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nts

166 168 170 172 174 176 178 180

ang [deg]pp

1

10

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nts

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ang [deg]pp

1

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nts

166 168 170 172 174 176 178 180

ang [deg]pp

1

10

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166 168 170 172 174 176 178 180

ang [deg]pp

1

10

210

310

410

Cou

nts

166 168 170 172 174 176 178 180

ang [deg]pp

1

10

210

310

410

Cou

nts

Figure 3.2: pp pairs angular distributions for the 165÷180 region for each CM energy.

23

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

0

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Figure 3.3: Eshow/p proton spectra for each CM energy.

24

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

pE

0

200

400

600

800

1000

Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

pE

0

200

400

600

800

1000Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

pE

0

200

400

600

800

1000

1200

Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

0

200

400

600

800

1000

1200

Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

pE

0

200

400

600

800

1000

1200

Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

pE

0

200

400

600

800

1000

1200

Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

pE

0

200

400

600

800

1000

1200

Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

pE

0

200

400

600

800

1000

1200

Co

un

ts

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

0

200

400

600

800

1000

1200

Co

un

ts

Figure 3.4: Eshow/p antiproton spectra for each CM energy.

25

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

1.2 1.3 1.4 1.5 1.6 1.7

Mom p [Gev/c]

1

10

210

310

Co

un

ts

Figure 3.5: Proton momentum spectra for each CM energy; antiproton momentum spectra

are analogous.

Figure 3.4 shows clearly how different are the antiproton interactions in the EMC

w.r.t. the proton ones. This is the reason why no cut has been applied for the antiproton

26

Eshow/p.

All these cuts were optimized in order to reduce the background in the real dataset

when performing the analysis of 3-momenta distributions, shown in Figure 3.6. For more

details see Section 3.5.

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

210

Cou

nts

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

20

40

60

80

100

120

140

160

180

200

Cou

nts

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

50

100

150

200

250

Cou

nts

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

20

40

60

80

100

120

140

160Cou

nts

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

0

100

200

300

400

500

600

Cou

nts

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

0

200

400

600

800

1000

1200C

ount

s

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

0

200

400

600

800

1000

1200Cou

nts

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

50

100

150

200

250

300

350

Cou

nts

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

40

60

80

100

120

Cou

nts

Figure 3.6: Proton momentum spectra for each CM energy; the cut on momentum is not

applied.

27

3.3 Simulations Efficiency

Signal events may go undetected due to: the not complete geometrical acceptance of

BESIII; inefficiencies in the detection; failed or incorrect event reconstruction or event

selection.

The agreement between the real dataset and the performed MonteCarlo simulations

must be carefully verified, in order to have full control of the acceptance corrections,

which are needed and are crucial to evaluate the cross section. The efficiency is strictly

connected to the choice of the MonteCarlo Generator, that mimics the underlying Physics

as closely as possible to estimate detection efficiency, as explained in the previous sections.

The efficiency is evaluated dividing the number of reconstructed ψ(2S) events by the total

number of the generated ones.

The statistical uncertainty in ε is estimated as binomial:

σεε

=

√1− ε

Ngenerated

(3.1)

The values of reconstructed events obtained from the MonteCarlo simulations for the

different CM energies are reported in Table 3.2.

Nominal Energy [MeV ] Nreconstructed Efficiency Error Efficiency

3580.0 110 0.7025 0.0038

3670.0 180 0.7002 0.0038

3681.0 257 0.6941 0.0038

3683.0 304 0.6981 0.0038

3684.0 1408 0.6959 0.0038

3685.5 3113 0.6944 0.0038

3686.6 2955 0.6998 0.0038

3690.0 622 0.6952 0.0038

3710.0 300 0.6951 0.0038

Table 3.2: Number of reconstructed events from the MonteCarlo simulations and efficiency

for each CM energy.

Figure 3.7 shows as an overall efficiency of 70% can be achieved.

28

3580 3600 3620 3640 3660 3680 3700 3720 E[MeV]

0.6

0.65

0.7

0.75

0.8

0.85

0.9ε

Figure 3.7: Efficiency, the red dashed line is at the fixed value of 0.70.

3.4 ISR Correction

Due to the nature of the ISR correction, an iterative process is needed. A custom algorithm

was implemented, exploiting the Bonneau-Martin formula [11], and evaluating the ISR

correction by mean of the hit-or-miss method. In detail, the nominal energy W of the

process, with its spread (see Table 3.1), is the input for the extraction of the momenta

of the ISR photon and for the evaluation of its effect on the collinearity. The probability

distribution of the ISR photon p(k)dk = βkβ−1 is strictly correlated to the factor β:

β = 4 · α/π · [ln(W1/me)− 0.5], (3.2)

where α = 1/137 is the fine-structure constant, W1 is the energy after the spread, and

me is the electron mass. Generally, the factor β is parametrized as:

β = 2α

π(ln(

Q2

m2)− 1), (3.3)

where Q is the Q-value of the process, and the scale depends on the actual interaction

process. For example, for a central production process, it can be defined as Q2 = s =

4Ecm. According to Touscheck [37] the correction factor can be expressed as:

C =∣∣1− E(1−β)

n + 0.5E(2−β)n

∣∣ , (3.4)

29

900 1000 1100 1200 1300 1400 1500 1600 1700Mom p [GeV/c]

50

100

150

200

250

Cou

nts

Figure 3.8: Proton momenta distributions due to ISR effects for the nominal energy of

E = 3.710 GeV .

where R is the integral of the probability distribution and En = k/R is the energy after

the correction. The correction factor from Equation 3.4 can be simulated by means of

the hit-or-miss method. The hit-or-miss MonteCarlo method generates random points in

a approximately bounded area and counts the number of ”hits” that contribute hence an

estimation of the area one wants to evaluate.

The energy after the ISR (W2) can be calculated as:

W2 =√W 2

1 − 2 · k ·W1. (3.5)

At a given energy W2, the momenta of both proton and antiproton can be finally

determined with a Lorentz transformation assuming, as previously explained in Section

3.1, an angular distribution 1 + αcos2(θ) in the LAB frame. An example of the ISR

momenta distribution is shown in Figure 3.8.

The energy after the ISR, the proton and the antiproton momenta, their collinearity

and the angle of pp pairs in the CM frame can hence be easily determined. Theoretical pre-

dictions suggest an ISR ptohon energy ∼ 50 MeV [12, 37], and its effect on the collinearity

should be hence 4 at most. A statistical approach would be useful for the qualitative

understanding of the obtained results which are in agreement with the observations.

3.5 Background Studies

Due to the clear relevance of the background within the real dataset collected in the

continuum region, an analysis of MonteCarlo simulated data is performed in order to

qualitatively evaluate the impact of misidentified events on the event selection. The

following background processes were investigated:

e+e− → J/ψ → pp, (1)

30

e+e− → e+e−, (2)

e+e− → µ+µ−, (3)

e+e− → K+K−, (4)

e+e− → π+π−.(5)

2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5]2 [GeV/cinvM

0

1

2

3

4

5

Cou

nts

Figure 3.9: Invariant mass for (1) at nominal energy of 3.670 GeV , real dataset.

Background studies aim to verify if the application of the same selection criteria

adopted for the signal, and described in Section 3.2, is enough to clearly remove the back-

ground. The considered channels have a Branching Ratio and a Cross Section greater

by more than one order of magnitude with respect to the process analyzed [9]. More-

over, the processes (2), (3), (4), (5) were selected due to the kinematic reasons. In a two

body-decay, the particle 3-momenta can be obtained as:

|p| =√M2 − 4m2

x

2, (3.6)

where M is the invariant mass in the center of mass frame, and mx is the mass of the

chosen candidate as final states.

The background processes were investigated exploiting 104 simulated events, applying

the same selection adopted for the analysis of the real data. Basically no event passed

such selection in the momentum region relevant for our investigation for the processes

(2) and (3); the processes (4) and (5) were excluded as well, as consequence of the PID

tag, although PID can still sometime fail. Moreover the process (1) was useful for the

optimization of the lower cuts on the 3-momenta. For the first CM energy, in particular,

a lower cut on the momenta (Ppp ≥ 1.2 GeV/c) was chosen, due to the kinematics of the

event. Figures 3.9, 3.10 and 3.11 clearly show how effective are the selection criteria to

reject the considered backround processes both in the real and in the simulated datasets.

An irreducible background is the ppγ final state, which can be considered as the

principal radiative contribution to the background in our sample. But such a background

31

2 2.5 3 3.5 4 4.5 5

Minv (GeV/c^2)

0

20

40

60

80

100

120

140

160

180

200

2 2.5 3 3.5 4 4.5 5

Minv (GeV/c^2)

0

0.2

0.4

0.6

0.8

1

Figure 3.10: Invariant mass for (2) at nominal energy 3.670 GeV , MonteCarlo simulations.

2 2.5 3 3.5 4 4.5 5

Minv (GeV/c^2)

0

20

40

60

80

100

120

140

160

180

200

2 2.5 3 3.5 4 4.5 5

Minv (GeV/c^2)

0

0.2

0.4

0.6

0.8

1

Figure 3.11: Invariant mass for (3) at nominal energy 3.670 GeV , MonteCarlo simulations.

can be accounted for performing a simultaneous fit on the proton and the antiproton, as

explained in Section 3.6.

3.6 Simultaneous Fit

In order to achieve the best signal over background ratio and to extract the number of pp

pairs, a 2-dimensional fit of the pp scatter plot was performed.

32

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

200

400

600

800

1000

1200

1400

Eve

nts

Figure 3.12: Proton momentum spectra for each CM energy, MonteCarlo simulations.

Figures 3.12, 3.13, 3.14 and 3.15 show the p and p momenta spectra for the signal

simulation and for the experimental data, respectively. The distributions were fitted with

a CrystalBall (CB) function [38] plus a flat background for the simulations, and a zero

or first order polynomial for the real dataset (for the first two energies values). The

3-momenta distributions are not symmetric, so the CB function is needed in order to

consider possible ISR contributions. The CrystalBall function is a probability density

33

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

1600

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

200

400

600

800

1000

1200

1400

Eve

nts

Figure 3.13: Antiproton momentum spectra for each CM energy, MonteCarlo simulations.

function, and is the convolution of Gaussian and a power-law low end tail below a certain

threshold:

f(x, α, n, x, σ) = N

exp(− (x−x)2

2σ2

)forx−x

σ> −α

A ·(B − x−x

σ

)−nforx−x

σ≤ −α

(3.7)

34

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

5

10

15

20

25

30

35

40

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

5

10

15

20

25

30

35

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

20

40

60

80

100

120

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

10

20

30

40

50

60

70

80

90

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

50

100

150

200

250

300

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

100

200

300

400

500

600

700

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

100

200

300

400

500

600

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

20

40

60

80

100

120

140

160

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

5

10

15

20

25

30

35

40

45

Eve

nts

Figure 3.14: Proton momentum spectra for each CM energy, real dataset.

where

A =

(n

|α|

)nexp

(−|α|

2

2

),

B =n

|α|− |α|,

35

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

5

10

15

20

25

30

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

5

10

15

20

25

30

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

20

40

60

80

100

120

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

10

20

30

40

50

60

70

80

90

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

50

100

150

200

250

300

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

100

200

300

400

500

600Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

100

200

300

400

500

600

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

20

40

60

80

100

120

140

160

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

(GeV/c)pMom

0

5

10

15

20

25

30

35

40

45

Eve

nts

Figure 3.15: Antiproton momentum spectra for each CM energy, real dataset.

N =1

σ(C +D),

C =n

|α|1

n− 1exp

(−|α|

2

2

),

36

D =

√π

2

(1 + erf(

|α|√2

)

),

where N is a normalization factor, α, n, x and σ are parameters which are fitted with

the data in Figures 3.14 and 3.15. For each plot the blue line represents the fit on the

data, the red dashed line only the signal distribution, and the light blue and brown dashed

lines show the shape of the background on x axis convoluted with the CB shape along y

axis and viceversa.

Such an approach shows a good signal over background ratio at the energies closer

to the resonance, while the contribution from background is comparable to the signal at

lower energies. The fitting procedures always provide reasonable χ2 for each CM energy,

as reported in Tables 3.3 and 3.4.

Nominal Energy [MeV ] Nevents σE χ2x χ2

y

3580.0 6594 81 0.26 0.29

3670.0 6543 81 0.20 0.42

3681.0 6555 81 0.21 0.20

3683.0 6536 81 0.18 0.13

3684.0 6588 81 0.33 0.24

3685.5 6572 81 0.18 0.17

3686.6 6586 81 0.23 0.14

3690.0 6581 81 0.23 0.38

3710.0 6536 81 0.20 0.24

Table 3.3: Number of pp pairs selected at each CM energy for MonteCarlo simulations.

Nominal Energy [MeV ] Nevents σE χ2x χ2

y

3580.0 81 9 0.12 0.08

3670.0 63 8 0.12 0.11

3681.0 537 23 0.18 0.24

3683.0 350 19 0.10 0.10

3684.0 1397 38 0.08 0.10

3685.5 3098 56 0.14 0.12

3686.6 2934 54 0.10 0.09

3690.0 741 27 0.15 0.16

3710.0 236 15 0.10 0.12

Table 3.4: Number of pp pairs selected at each CM energy for the real dataset.

The number of pp pairs is obtained by calculating the integral of each signal distribu-

tion within 3σ from its peak value, as Npp = I ∗ Nsignal, where I is the integral and Npp

is the number of signal events from the fit.

The errors where estimated assuming a poissonian distribution, thus σN =√Npp

[39]. Once determined the number of signal events, the cross section can be evaluated as

explained in Section 1.5.

37

3.7 Systematic Uncertanties

Systematic uncertanties play an important role in the measurement of physical quantities,

as they are often of comparable scale w.r.t. the statistical ones. They arise from different

sources: the value of the parameters used to perform event selection and the specific

values of the fit. In order to be more conservative as possible, a wide variation interval

was chosen. From those variation, the number of pp pairs was again calculated, performing

simultaneous fits. The variations on the selection criteria are summarized in Table 3.5.

Cut Value Variation

Eshow/p 0.5 ± 0.05

θpp 178 < < 180 −0.5 and +1

fit −3σ < < 3σ ± 0.5

PID 0.00 + 0.001

Table 3.5: Parameter values used for the event selection and their variations to evaluate

the systematic errors.

A 1% per track was taken into account for the systematic error coming from tracking.

To obtain an estimation of the systematic errors relative to each cut variation, the weighted

average between the number of events of the analysis and the one with the parameter

change was calculated.

To be more specific the weighted average and its error has been evaluated by:

x =

∑ixiσ2xi∑

i1σ2xi

(3.8)

and

σ2x =

1∑i

1σ2xi

(3.9)

where xi are the measurements and σxi their errors. The total systematic error was

obtained by summing in quadrature each single contribution:

σsyst =

√∑i

σ2i (3.10)

where σi is the weighted average error of the number of events extracted from the simul-

taneous fit. The obtained values are shown in Table 3.6.

In order to investigate the systematic errors due to the fitting function, the sideband

method [40] was used. The sideband method allows to divide a 2-dimensional plot into

areas: one for the signal, and eight for the background estimation. The three regions are

defined, as shown in Figure 3.17.

38

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

5

10

15

20

25

30

35

40

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

5

10

15

20

25

30

35

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

20

40

60

80

100

120

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

10

20

30

40

50

60

70

80

90

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

50

100

150

200

250

300

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

100

200

300

400

500

600

700

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

100

200

300

400

500

600

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

20

40

60

80

100

120

140

160

Eve

nts

1.4 1.45 1.5 1.55 1.6 1.65 1.7

Mom p (GeV/c)

0

5

10

15

20

25

30

35

40

45

Eve

nts

Figure 3.16: Proton momentum spectra for each energy value with a different parameter

of PID.

The number of pp events (N0) was extracted with the sideband method as:

N0 = N − 1

2B +

1

4A, (3.11)

where N is the number of events in the signal region, and A and B are the number of

events in the corresponding regions, shown in Figure 3.17. For this study the 4σ − 10σ

regions were considered, and all the obtained distributions are similar to the one shown

in Figure 3.18.

39

Energy [MeV ] NEshow/p σEshow/p NT σT NPID σPID NF* σF σtot3580.0 80.03 5.19 6.05 0.94 80.55 8.97 93.51 5.36 9.84

3670.0 62.77 4.57 10.94 2.54 62.77 7.92 122.54 5.23 9.28

3681.0 537.38 13.38 27.02 3.29 537.38 23.18 531.39 13.11 25.11

3683.0 349.42 10.80 12.73 2.38 350.28 18.72 349.87 10.71 20.31

3684.0 1381.20 21.54 5.17 1.66 1396.93 37.38 1405.44 21.23 40.20

3685.5 3076.45 32.09 45.88 4.06 3097.80 55.66 3126.30 31.87 60.09

3686.6 2938.12 31.29 31.07 3.83 2094.12 54.17 3125.32 31.58 58.82

3690.0 736.47 15.68 21.02 2.83 740.49 27.21 752.39 15.43 29.37

3710.0 236.59 8.87 53.67 3.44 236.59 15.38 259.07 8.91 16.97

Table 3.6: Number of events and their error for each parameter variation and total sys-

tematic error.

Figure 3.17: Example of sideband definition taken from [41].

3.8 Inclusive Simulations

The BESIII Collaboration provided a 400M events inclusive MonteCarlo sample, pro-

duced for the analysis of the 2012 ψ(2S) data taking. The final states were generated

according to the LUNDCHARM model [42], and the simulated events were reconstructed and

analysed with the BOSS version 6.6.4.p03. The list of the processes considered in the

production of the inclusive ψ(2S) dataset is reported in Table 3.7.

The number of pp in the final state was determined performing the same event selection

procedure described above for the real dataset. Figure 3.19 shows the obtained spectrum.

The advantage of this approach is that the detection efficiency of inclusive ψ(2S)

decays can be extracted directly from the data sample already analyzed [43]. After ap-

plying the same selection criteria as for the real data and using the sideband method,

40

1.4 1.45 1.5 1.55 1.6 1.65 1.7Mom p [GeV/c]

1.4

1.45

1.5

1.55

1.6

1.65

1.7

[GeV

/c]

pM

om

Figure 3.18: Bi-dimensional scatter plot of pp at 3.684 GeV.

Decay Branching Ratio

ppπ0 (1.53± 0.07)x10−4

ηpp (6.0± 0.4)x10−5

ωpp (6.9± 2.1)x10−5

φpp < 2.4x10−5

π+π−pp (6.0± 0.4)x10−4

ρ0pp (5.0± 2.2)x10−5

ppπ+π−π0 (7.3± 0.7)x10−4

γpp (3.9± 0.5)x10−5

Table 3.7: List and BR of the processes included in the production of the inclusive simu-

lations dataset.

Ninc = 73383± 271 candidate events are selected from the ψ(2S) 2012 sample.

Assuming the same detection efficiency at√s = 3.580 GeV as for the ψ(2S) peak, the

number of background events for the ψ(2S) sample is estimated to be [44]:

Nbg = Ninc ·Lψ(2S)

Linc·sψ(2S)

sinc, (3.12)

where Lψ(2S) and Linc are the integrated luminosities for the ψ(2S) data sample taken at

3.580 GeV and for the data sample taken at√s = 3.6866 GeV , and sψ(2S) and sinc are

the corrisponding squares of the CM energies. The values obtained are reported in Table

3.8.

41

1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

0

5000

10000

15000

20000

25000

30000

Cou

nts

Figure 3.19: Proton momentum spectrum, inclusive MonteCarlo; ∼ 75k events were

selected.

Energy [MeV ] Nbg σbg3581.54 22126 82

3670.16 21818 81

3680.14 21817 81

3682.75 64200 237

3684.22 64218 0.24

3685.5 67867 262

3691.36 26506 98

3709.76 26036 0,90

Table 3.8: Number of background events for each energy value.

42

Chapter 4

Results

The results of the evaluation of the relative phase between the strong and electromagnetic

amplitudes, performed considering the inclusive final state pp, are discussed herewith.

Such an investigation is part of a more extended experimental effort in progress at

BESIII and led by the Italian component of the BESIII Collaboration.

4.1 Cross Section

To determine the relative phase among the amplitudes we need to perform a fit of the

experimental cross section at each CM energies. It is hence possible to determine the

cross section as:

σ(e+e− → ψ(2S)→ pp) =Npp

εL, (4.1)

where Npp is the number of the reconstructed pp pairs (see Section 3.6), ε is the

reconstruction efficiency (see Section 3.3), and L is the integrated luminosity, reported in

Table 3.1.

Table 4.1 reports the cross section values determined for each center of mass energy,

and their statistical and systematic errors, determined according to Equations 3.8 and

3.9.

Nominal Energy [MeV ] σ[pb−1] σσ[pb−1] σsyst[pb−1]

3580.0 1.43 0.16 0.23

3670.0 1.14 0.14 0.22

3681.0 9.66 0.42 0.58

3683.0 18.68 1.00 1.40

3684.0 74.01 1.98 2.79

3685.5 181.42 3.26 4.59

3686.6 177.80 3.28 4.66

3690.0 16.23 0.59 0.84

3710.0 5.13 0.33 0.47

Table 4.1: Cross sections for each CM energy with their statistical and systematic errors.

43

Figure 4.1: Cross section for the pp final state (y-axis in logarithmic scale). Error bars

include both statistical and systematic uncertainties.

4.2 Relative Phase Evaluation

The cross section values determined above were used to extract the relative phase between

the strong and electromagnetic amplitudes (see Chapter 1). The errors considered for the

cross section values included both the statistical and systematic uncertainties.

As discussed in Section 1.7, the cross section pattern is a direct consequence of the

formalism used in Equation 1.15. Theoretically we should expect a 0 phase, thus a full

interference pattern (φ = 0/180), but the previous experimental evidence [16, 41] in the

J/ψ sector points toward a no-interference pattern (φ ∼ 90).

The fit of the cross section is performed by means of a complex fitting function,

which was already developed in the BESIII-Italy group in order to perform a fit of the

e+e− → J/ψ → pp cross section. Such fitting function exploits a MonteCarlo simulation

for the ISR extraction, determining the cross section as [41]:

σ[nb] =

∣∣∣∣∣√

12πBinBout

[~cW

]2

·107C1 + C2e

iφ

Mψ −W − iΓ2

+ C3eiφ

∣∣∣∣∣2

(4.2)

The Real and the Imaginary part of the cross section, AA and BB respectively, can

be defined as:

44

AA =√C0

(C1 + C2cosφ) · (Mψ −W ) + C2Γ/2sinφ

(Mψ −W )2 + (Γ/2)2+ C3cosφ,

BB =√C0

(C1 + C2cosφ)Γ/2 + C2sinφ

(Mψ −W )2 + (Γ/2)2+ C3sinφ,

For each extraction, the cross section is hence:

σi = AA2 +BB2 (4.3)

The final value of the simulated cross section is then obtained as the average of the

cross section values obtained in each extraction:

σ =1

Nest

∑σi (4.4)

where Next is the number of extractions.

The MonteCarlo simulates at each extractions the radiative corrections at each CM

energy. The estimated value of the theoretical cross section, including the radiative cor-

rections, divided by the number of extractions, provides the functional dependence.

The fit procedure depends then on three variables:

• φ, which is the relative phase between the amplitudes, the main goal of our analysis;

• σ1 which is the cross section at 3.580 GeV and it is an estimation of the cross section

in the non-resonant region;

• Bout, which is an estimation of the BR of the considered process.

Figure 4.2 shows the best fit of the experimental cross sections. .

The fit is in good agreement with the experimental data, but to achieve such a result

(χ2red ∼ 4.90) we had to exclude from the fitted dependence the third energy point.

The exclusion of this energy point is due to the fact that we need a more precise

determination of the beam energies, in particular on the rising of the resonance, where

the sensitity of the fitting procedure is the highest.

The data were in fact collected at a time in which the Beam Energy Measurement

System (BEMS) of the BESIII Spectrometer was not active. We need hence to perform

further analyses on the collected experimental datasets, exploiting benchmark channels,

in order to determine offline more precisely the CM energy of each point, and hence to

improve the input to the fitting procedure.

The fit provides an estimation of the relative phase φ:

φ = (89.05± 14.70), (4.5)

of the Branching Ratio of the investigated process:

Bout = (3.06± 0.07)x10−4, (4.6)

and of the cross section at the continuum:

σc = (7.54± 1.12) pb (4.7)

45

]2Mass [MeV/c3580 3600 3620 3640 3660 3680 3700 3720

[nb]

ppσ

-410

-310

-210

-110

Figure 4.2: Fit of the pp cross section distribution on the CM energy.

The value of the phase determined by this work is in good agreement with the outcome

of the other analyses performed at BESIII for the J/ψ production considering the same

final states [16, 41]. The BR determined by the fitting procedure described above is in

good agreement as well with the value listed by the PDG [18]:

BRPDG(ψ(2S)→ pp) = (2.88± 0.10)× 10−4 (4.8)

Further investigations on the origin of this phase are needed, and few theoretical

proposal have already been published, waiting for an experimental confirmation.

46

Chapter 5

Conclusions

The relative phase between strong and electromagnetic ψ(2S) amplitudes has been de-

termined, in Beijing at IHEP with the BESIII Spectrometer on the BEPCII e+e− col-

lider, by evaluating their Q2 behaviour. The pp pairs produced in the final state of the

e+e− → X → pp process in the ψ(2S) energy regime, have been selected through a set of

cuts tuned on the kinematics of the process and on the structure of the spectrometer.

By selecting only events collected in the Barrel region of the BESIII Spectrometer a

good background rejection have been achieved, leading to a good signal over background

ratio.

MonteCarlo simulations have been used in order to determine the detection and re-

construction efficiencies as well as to tune the selection criteria, for each dataset collected

at the different center of mass energies.

The cross section has been determined at each center of mass energy at which the

separate datasets have been collected. The cross section is strictly connected to the

relative phase, and depends on the number of events that has been extracted by means

of a simultaneous fit on the proton and antiproton tracks, optimizing in such a way the

signal over background ratio.

The number of events depends clearly on the choice both of the selection criteria and

of the fitting method: such dependences have been investigated by mean of the sidebands

method and the corresponding systematic uncertanties evaluated.

The dependence on the center of mass energy of the experimental values determined for

the cross section for the different datasets collected at various center of mass energies in the

ψ(2S) regime, were hence fitted considering both statistical and systematic uncertainties,

in order to determine the relative phase and the branching fraction of the ψ(2S) → pp

process.

The relative phase, obtained for the first time in this energy regime for the pp final

state, is:

φ = (89.05± 14.70). (5.1)

The Branching Ratio:

Bout = (3.06± 0.07)x10−4 (5.2)

has been extracted as well and is in good agreement with the literature.

47

A better determination of the center of mass energies at which the different datasets

have been collected is needed, and will be performed in the near future in order to slightly

increase the precision of the phase measurement.

This work led to a first generation measurement: the relative phase has been evalu-

ated for the first time in the ψ(2S) regime, considering the pp final state. The BESIII

Collaboration plans to soon evaluate the relative phase exploiting different final states, in

the same kinematic regime.

48

List of Figures

1.1 The J/ψ and the ψ(2S) formation diagram. . . . . . . . . . . . . . . . . . 4

1.2 An electron radiating a ISR photon γISR. . . . . . . . . . . . . . . . . . . . 5

1.3 The Feynman diagrams for the process e+e− → hadrons (a) strong A3g,

(b) electromagnetic Aγ and (c) Acont continuum. . . . . . . . . . . . . . . . 7

1.4 The scheme suggested by Freund and Nambu [8], the process being iterated

in f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1 Schematic layout of the Beijing Electron Positron Collider II. . . . . . . . . 10

2.2 Schematic layout of the BESIII Spectrometer. . . . . . . . . . . . . . . . . 10

2.3 Scheme of BESIII MDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Scheme of BESIII TOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 BESIII Muon Chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1 Scheme of e+e− annihilation into Charmonia. . . . . . . . . . . . . . . . . 22

3.2 pp pairs angular distributions for the 165÷180 region for each CM energy. 23

3.3 Eshow/p proton spectra for each CM energy. . . . . . . . . . . . . . . . . . 24

3.4 Eshow/p antiproton spectra for each CM energy. . . . . . . . . . . . . . . . 25

3.5 Proton momentum spectra for each CM energy; antiproton momentum

spectra are analogous. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.6 Proton momentum spectra for each CM energy; the cut on momentum is

not applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.7 Efficiency, the red dashed line is at the fixed value of 0.70. . . . . . . . . . 29

3.8 Proton momenta distributions due to ISR effects for the nominal energy of

E = 3.710 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.9 Invariant mass for (1) at nominal energy of 3.670 GeV , real dataset. . . . . 31

3.10 Invariant mass for (2) at nominal energy 3.670 GeV , MonteCarlo simulations. 32

3.11 Invariant mass for (3) at nominal energy 3.670 GeV , MonteCarlo simulations. 32

3.12 Proton momentum spectra for each CM energy, MonteCarlo simulations. . 33

3.13 Antiproton momentum spectra for each CM energy, MonteCarlo simulations. 34

3.14 Proton momentum spectra for each CM energy, real dataset. . . . . . . . . 35

3.15 Antiproton momentum spectra for each CM energy, real dataset. . . . . . . 36

3.16 Proton momentum spectra for each energy value with a different parameter

of PID. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.17 Example of sideband definition taken from [41]. . . . . . . . . . . . . . . . 40

3.18 Bi-dimensional scatter plot of pp at 3.684 GeV. . . . . . . . . . . . . . . . 41

49

3.19 Proton momentum spectrum, inclusive MonteCarlo; ∼ 75k events were

selected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1 Cross section for the pp final state (y-axis in logarithmic scale). Error bars

include both statistical and systematic uncertainties. . . . . . . . . . . . . 44

4.2 Fit of the pp cross section distribution on the CM energy. . . . . . . . . . . 46

50

List of Tables

2.1 TOF time resolution performance for 1 GeV/c particles. . . . . . . . . . . 13

3.1 Data set collected by BESIII during the 2018 data taking. . . . . . . . . . 21

3.2 Number of reconstructed events from the MonteCarlo simulations and ef-

ficiency for each CM energy. . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Number of pp pairs selected at each CM energy for MonteCarlo simulations. 37

3.4 Number of pp pairs selected at each CM energy for the real dataset. . . . . 37

3.5 Parameter values used for the event selection and their variations to eval-

uate the systematic errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.6 Number of events and their error for each parameter variation and total

systematic error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7 List and BR of the processes included in the production of the inclusive

simulations dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.8 Number of background events for each energy value. . . . . . . . . . . . . . 42

4.1 Cross sections for each CM energy with their statistical and systematic

errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

51

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