EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP-2019-121LHCb-PAPER-2019-019

23 July 2019

Measurement of CP violation in theB0s→ φφ decay and search for the

B0 → φφ decay

LHCb collaboration†

AbstractA measurement of the time-dependent CP -violating asymmetry in B0s → φφ decaysis presented. Using a sample of proton-proton collision data corresponding to anintegrated luminosity of 5.0 fb−1 collected by the LHCb experiment at centre-of-massenergies

√s = 7 TeV in 2011, 8 TeV in 2012 and 13 TeV in 2015 and 2016, a signal

yield of around 9000 B0s → φφ decays is obtained. The CP -violating phase φss̄ssis measured to be −0.073 ± 0.115 (stat) ± 0.027 (syst) rad, under the assumptionit is independent of the helicity of the φφ decay. In addition, the CP -violatingphases of the transverse polarisations under the assumption of CP conservation ofthe longitudinal phase are measured. The helicity-independent direct CP -violationparameter is also measured, and is found to be |λ| = 0.99± 0.05 (stat)± 0.01 (syst).In addition, T -odd triple-product asymmetries are measured. The results obtainedare consistent with the hypothesis of CP conservation in b → sss transitions.Finally, a limit on the branching fraction of the B0 → φφ decay is determined to beB(B0 → φφ) < 2.7× 10−8 at 90 % confidence level.

Published in JHEP 12 (2019) 155

c© 2020 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

†Authors are listed at the end of this paper.

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1 Introduction

In the Standard Model (SM) the B0s → φφ decay, where the φ(1020) is implied throughoutthis paper, is forbidden at tree level and proceeds predominantly via a gluonic b→ sssloop (penguin) process. Hence, this channel provides an excellent probe of new heavyparticles entering the penguin quantum loops [1–3]. In the SM, CP violation is governed bya single phase in the Cabibbo–Kobayashi–Maskawa quark mixing matrix [4]. Interferencecaused by the resulting weak phase difference between the B0s -B

0s oscillation and decay

amplitudes leads to a CP asymmetry in the decay-time distributions of B0s and B0s mesons.

For B0s → J/ψK+K− and B0s → J/ψπ+π− decays, which proceed via b→ scc transitions,the SM prediction of the weak phase is −2 arg (−VtsV ∗tb/VcsV ∗cb) = −0.0369+0.0010−0.0007 radaccording to the CKMfitter group [5], and −2 arg (−VtsV ∗tb/VcsV ∗cb) = −0.0370±0.0010 radaccording to the UTfit collaboration [6]. The LHCb collaboration has measured the weakphase in several decay processes: B0s → J/ψK+K−, B0s → J/ψπ+π−, B0s → J/ψK+K−for the K+K− invariant mass region above 1.05 GeV/c, B0s → ψ(2S)φ and B0s → D+s D−s ,corresponding to the combined result of −0.041 ± 0.025 rad [7]. These measurementsare consistent with the SM prediction and place stringent constraints on CP violation inB0s -B

0s oscillations [8]. The CP -violating phase, φ

ssss , in the B

0s→ φφ decay is expected to

be small in the SM. Calculations using quantum chromodynamics factorisation (QCDf)provide an upper limit of 0.02 rad for its absolute value [1–3]. The previous most accuratemeasurement is φssss = −0.17± 0.15 (stat)± 0.03 (syst) rad [9].

CP violation can also be probed by time-integrated triple-product asymmetries. Theseare formed from T -odd combinations of the momenta of the final-state particles. Theseasymmetries complement the decay-time-dependent measurement [10] and are expected tobe close to zero in the SM [11]. Previous measurements of the triple-product asymmetriesin B0s decays from the LHCb and CDF collaborations [9, 12] have shown no significantdeviations from zero.

The B0s→ φφ decay is a P → V V decay, where P denotes a pseudoscalar and V avector meson. This gives rise to longitudinal and transverse polarisation of the final stateswith respect to their direction of flight in the B0s reference frame, the fractions of whichare denoted by fL and fT , respectively. In the heavy quark limit, fL is expected to beclose to unity at tree level due to the vector-axial structure of charged weak currents [2].This is found to be the case for tree-level B decays measured at the B Factories [13–18].However, the dynamics of penguin transitions are more complicated. Previously LHCbreported a value of fL ≡ |A0|2 = 0.364± 0.012 in B0s→ φφ decays [9]. The measurementis in agreement with predictions from QCD factorisation [2, 3]. The observed value of fLis significantly larger than that seen in the B0s → K∗0K∗0 decay [19,20].

In addition to the study of the B0s→ φφ decay, a search for the as yet unobserveddecay B0 → φφ is made. In the SM this is an OZI suppressed decay [21], with anexpected branching fraction in the range (0.1 − 3.0) × 10−8 [1, 2, 22, 23]. However, thebranching fraction can be enhanced, up to the 10−7 level, in extensions to the SM suchas supersymmetry with R-parity violation [23]. The most recent experimental limit wasdetermined to be 2.8× 10−8 at 90 % confidence level [24].

Measurements presented in this paper are based on pp collision data corresponding toan integrated luminosity of 5.0 fb−1, collected with the LHCb experiment at centre-of-massenergies

√s = 7 TeV in 2011, 8 TeV in 2012, and 13 TeV from 2015 to 2016. This paper

reports a time-dependent analysis of B0s→ φφ decays, where the φ meson is reconstructed

1

in the K+K− final state, that measures the CP -violating phase, φss̄ss , and the parameter|λ|, that is related to the direct CP violation. Results on helicity-dependent weak phasesare also presented, along with helicity amplitudes describing the P → V V transition andstrong phases of the amplitudes. In addition, triple-product asymmetries for this decay arepresented. The analysis also includes a search for the decay B0 → φφ. Results presentedhere supersede the previous measurements based on data collected in 2011 and 2012 [9].

2 Detector description

The LHCb detector [25, 26] is a single-arm forward spectrometer covering thepseudorapidity range 2 < η < 5, designed for the study of particles containing b orc quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region [27], a large-area silicon-stripdetector located upstream of a dipole magnet with a bending power of about 4 Tm, andthree stations of silicon-strip detectors and straw drift tubes [28] placed downstreamof the magnet. The tracking system provides a measurement of the momentum, p, ofcharged particles with a relative uncertainty that varies from 0.5% at low momentumto 1.0% at 200 GeV/c. The minimum distance of a track to a primary vertex (PV), theimpact parameter (IP), is measured with a resolution of (15 + 29/pT)µm, where pT isthe component of the momentum transverse to the beam, in GeV/c. Different types ofcharged hadrons are distinguished using information from two ring-imaging Cherenkovdetectors [29]. Photons, electrons and hadrons are identified by a calorimeter systemconsisting of scintillating-pad and preshower detectors, an electromagnetic and a hadroniccalorimeter. Muons are identified by a system composed of alternating layers of iron andmultiwire proportional chambers [25].

The online event selection is performed by a trigger, which consists of a hardware stage,based on information from the calorimeter and muon systems, followed by a softwarestage, which applies a full event reconstruction. At the hardware trigger stage, eventsare required to contain a muon with high pT or a hadron, photon or electron with hightransverse energy in the calorimeters. In the software trigger, B0s→ φφ candidates areselected either by identifying events containing a pair of oppositely charged kaons with aninvariant mass within 30 MeV/c2 of the known φ meson mass, mφ = 1019.5 MeV/c

2 [30],or by using a topological b-hadron trigger. This topological trigger requires a three-tracksecondary vertex with a large sum of the pT of the charged particles and significantdisplacement from the PV. At least one charged particle should have pT > 1.7 GeV/cand χ2IP with respect to any primary vertex greater than 16, where χ

2IP is defined as the

difference in χ2 of a given PV fitted with and without the considered track. A multivariatealgorithm [31] is used for the identification of secondary vertices consistent with the decayof a b hadron.

Simulation samples are used to optimise the signal candidate selection, to derive theangular acceptance and the correction to the decay-time acceptance. In the simulation,pp collisions are generated using Pythia [32] with a specific LHCb configuration [33].Decays of hadronic particles are described by EvtGen [34], in which final-state radiationis generated using Photos [35]. The interaction of the generated particles with thedetector and its response are implemented using the Geant4 toolkit [36], as described inRef. [33].

2

3 Selection and mass model

For decay-time-dependent measurements and the T -odd asymmetries presented in thispaper, the previously analysed data collected in 2011 and 2012 [9] is supplemented withthe additional data taken in 2015 and 2016, to which the selection described below isapplied. For the case of the B0 → φφ search, a wider invariant-mass window is required,along with more stringent background rejection requirements.

Events passing the trigger are required to satisfy loose criteria on the fit quality ofthe four-kaon vertex, the χ2IP of each track, the transverse momentum of each particle,and the product of the transverse momenta of the two φ candidates. In addition, thereconstructed mass of the φ candidates is required to be within 25 MeV/c2 of the known φmass [30].

In order to separate further the B0s → φφ signal candidates from the background,a multilayer perceptron (MLP) [37] is used. To train the MLP, simulated B0s → φφcandidates satisfying the same requirements as the data candidates are used as a proxyfor signal, whereas the four-kaon invariant-mass sidebands from data are used as aproxy for background. The invariant-mass sidebands are defined to be inside the region120 < |mK+K−K+K− −mB0s | < 180 MeV/c

2, where mK+K−K+K− is the four-kaon invariantmass. Separate MLP classifiers are trained for each data taking period. The variablesused in the MLP comprise the minimum and the maximum pT and η of the kaon andφ candidates, the pT and η of the B

0s candidate, the quality of the four-kaon vertex

fit, and the cosine of the angle between the momentum of the B0s and the direction offlight from the PV to the B0s decay vertex, where the PV is chosen as that with thesmallest impact parameter χ2 with respect to the B0s candidate. For measurements ofCP violation, the requirement on each MLP is chosen to maximise NS/

√NS +NB, where

NS (NB) represents the expected signal and background yields in the signal region, definedas mB0s ± 3σ, where mB0s is the known B

0s mass [30]. The signal yield is estimated using

simulation, whereas the number of background candidates is estimated from the datasidebands. For the search of the B0 → φφ decay, the figure of merit is chosen to maximiseε/(a/2 +

√NB) [38], where a = 3 corresponds to the desired significance, and ε is the

signal efficiency, determined from simulation. This figure of merit does not depend on theunknown B0 → φφ decay rate.

The presence of peaking backgrounds is studied using simulation. The decay modesconsidered include B0 → φK∗0, Λ0b → φpK−, B0 → φπ+π− and B+ → φK+, where thelast decay mode could contribute if an extra kaon track is added. The B0 → φπ+π−and B+ → φK+ decays do not contribute significantly. The B0 → φK∗0 decay, resultingfrom a misidentification of a pion as a kaon, is vetoed by rejecting candidates whichsimultaneously have K+π−(K+K−K+π−) invariant masses within 50 (30) MeV/c2 of theknown K∗0 (B0) masses. The K+π− and K+K−K+π− invariant masses are computedby taking the kaon with the highest probability of being misidentified as a pion andassigning it the pion mass. These vetoes reduce the number of B0 → φK∗0 candidatesto a negligible level. Similarly, the number of Λ0b → φpK− decays, resulting from amisidentification of a proton as a kaon, is estimated from data by assigning the protonmass to the final-state particle that has the largest probability to be a misidentified protonbased on the particle-identification information. This method yields 241± 30 Λ0b → φpK−decays in the total data set.

In order to determine the B0s → φφ yield in the final data sample, the four-kaon

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Figure 1: A fit to the four-kaon mass for the (top left) 2011, (top right) 2012, (bottom left) 2015and (bottom right) 2016 data sets, which are represented by the black points. Also shown arethe results of the total fit (blue solid line), with the B0s→ φφ (red dashed), the Λ0b → φpK−(magenta long dashed), and the combinatorial (blue short dashed) fit components.

invariant-mass distributions are fitted with the sum of the following components: aB0s→ φφ signal model, which comprises the sum of a Crystal Ball [39] and a Student’st-function; the peaking background contribution modelled by a Crystal Ball function,with the shape parameters fixed to the values obtained from a fit to simulated events,and the combinatorial background component, described using an exponential function.The yield of the Λ0b → φpK− peaking background contribution is fixed to the numberpreviously stated. Once the MLP requirements are imposed, an unbinned extendedmaximum-likelihood fit to the four-kaon invariant mass gives a total yield of 8843± 102B0s→ φφ decays and 2813± 67 combinatorial background candidates in the total data set.The fits to the four-kaon invariant-mass distributions, after the selection optimised for theCP -violation measurement, separately for each data taking year, are shown in Fig. 1.

4 Formalism

The final state of the B0s→ φφ decay comprises a mixture of CP eigenstates, which aredisentangled by means of an angular analysis in the helicity basis. In this basis, the decayis described by three angles, θ1, θ2 and φ, defined in Fig. 2.

4.1 Decay-time-dependent model

As discussed in Sec. 1, the B0s → φφ decay is a P → V V decay. However, due tothe proximity of the φ resonance to the scalar f0(980) resonance, there are irreducible

4

n̂V1 n̂V2

B0s

Φ

θ2θ1

K−

K+

K−

K+

φ1 φ2

Figure 2: Decay angles for the B0s → φφ decay, where θ1,2 is the angle between the K+ momentumin the φ1,2 meson rest frame and the φ1,2 momentum in the B

0s rest frame, Φ is the angle between

the two φ meson decay planes and n̂V1,2 is the unit vector normal to the decay plane of the φ1,2meson.

contributions to the four-kaon mass spectrum from P → VS (S-wave) and P → SS(double S-wave) processes, where S denotes a scalar meson, or a nonresonant pair of kaons.Thus, the total amplitude is a coherent sum of P -, S-, and double S-wave processes, andis modelled by making use of the different dependence on the helicity angles associatedwith these terms, where the helicity angles are defined in Fig. 2. A randomised choice ismade for which φ meson is used to determine θ1 and which is used to determine θ2. Thetotal amplitude (A) containing the P -, S-, and double S-wave components as a functionof time, t, can be written as [40]

A(t, θ1, θ2,Φ) = A0(t) cos θ1 cos θ2 +A‖(t)√

2sin θ1 sin θ2 cos Φ

+ iA⊥(t)√

2sin θ1 sin θ2 sin Φ +

AS(t)√3

(cos θ1 + cos θ2) +ASS(t)

3, (1)

where A0, A‖, and A⊥ are the CP -even longitudinal, CP -even parallel, and CP -oddperpendicular polarisations of the B0s→ φφ decay. The P → VS and P → SS processesare described by the AS and ASS amplitudes, respectively, where P → VS is CP -odd andP → SS is CP -even. The resulting differential decay rate is proportional to the square ofthe total amplitude and consists of 15 terms [40]

dΓ

dt d cos θ1 d cos θ2 dΦ∝ |A(t, θ1, θ2,Φ)|2 =

1

4

15∑i=1

Ki(t)fi(θ1, θ2,Φ), (2)

where the fi terms are functions of the angular variables and the time-dependence iscontained in

Ki(t) = Nie−Γst

[ai cosh

(1

2∆Γst

)+ bi sinh

(1

2∆Γst

)+ ci cos(∆mst) + di sin(∆mst)

].

(3)

5

The coefficients Ni, ai, bi, ci and di, which are functions of the CP observables, are definedin Appendix A. ∆Γs ≡ ΓL − ΓH is the decay-width difference between the light and heavyB0s mass eigenstates, Γs ≡ (ΓL + ΓH)/2 is the average decay width, and ∆ms is the B0s -B0soscillation frequency. The differential decay rate for a B0s meson produced at t = 0 isobtained by changing the sign of the ci and di coefficients. The amplitudes of helicitystate k are expressed as

Ak(t) = |Ak|eiδk(g+(t) + ηk|λk|e−iφs,kg−(t)

), (4)

where g+(t) and g−(t) describe the time evolution of B0s and B

0s mesons, respectively. CP

violation is parameterised through

q

p

ĀkAk

= ηk|λk|e−iφs,k . (5)

where, q and p relate the light and heavy mass eigenstates to the flavour eigenstates andηk is the CP eigenvalue of the polarisation being considered. Defining the amplitude inthis way leads to the forms of Ni, ai, bi, ci and di, listed in Table 7 (Appendix A). TheCP -violating asymmetry in B0s mixing, which can be characterised by the semileptonicasymmetry, assl is small [41]. Thus, to good approximation |q/p| = 1, and |λk| quantifiesthe level of CP violation in the decay. Two different fit configurations are performed,one in which the CP -violation parameters are assumed to be helicity independent andthe other in which CP -violation parameters are allowed to differ as a function of helicity.The helicity independent fit assumes one CP -violating phase, φssss , which takes the placeof all φs,k contained in the coefficients of Appendix A, and likewise one parameter thatdescribes direct CP violation, |λ|, which takes the place of all λk coefficients. Due tothe small sample size, the number of degrees of freedom is reduced for the case of thehelicity-dependent CP -violation fit. This involves assuming CP conservation for the caseof the direct CP -violation parameters, λ = 1, and also for the phase of the longitudinalpolarisation, φss̄ss,0 = 0. The longitudinal polarisation has been theoretically calculated asclose to zero in the B0s→ φφ decay [1].

The φssss and |λ| parameters are measured with respect to contributions with the sameflavour content as the φ meson, i.e. ss. Regarding the S-wave and double S-wave terms,the impact of the non-ss component of the φ wavefunction is negligible in this analysis.

4.2 Triple-product asymmetries

Scalar triple products of three-momentum or spin vectors are odd under time reversal,T . Nonzero asymmetries for these observables can either be due to a CP-violating phaseor from CP-conserving strong final-state interactions. Four-body final states give rise tothree independent momentum vectors in the rest frame of the decaying B0s meson. For adetailed review of the phenomenology the reader is referred to Ref. [10].

Two triple products can be defined:

sin Φ = (n̂V1 × n̂V2) · p̂V1 , (6)sin 2Φ = 2(n̂V1 · n̂V2)(n̂V1 × n̂V2) · p̂V1 , (7)

where n̂Vi (i = 1, 2) is a unit vector perpendicular to the vector meson (Vi) decay planeand p̂V1 is a unit vector in the direction of V1 in the B

0s rest frame, defined in Fig. 2. This

6

then provides a method of probing CP violation without the need to measure the decaytime or the initial flavour of the B0s meson. It should be noted, that while the observationof nonzero triple-product asymmetries implies CP violation or final-state interactions (inthe case of B0s meson decays), measurements of triple-product asymmetries consistentwith zero do not rule out the presence of CP -violating effects, as the size of the asymmetryalso depends on the differences between the strong phases [10].

In the B0s → φφ decay, two triple products are defined as U ≡ sin Φ cos Φ andV ≡ sin(±Φ) where the positive sign is taken if cos θ1 cos θ2 ≥ 0 and the negative signotherwise [10]. The T -odd asymmetry corresponding to the U observable, AU , is definedas the normalised difference between the number of decays with positive and negativevalues of sin Φ cos Φ,

AU ≡Γ(U > 0)− Γ(U < 0)Γ(U > 0) + Γ(U < 0)

∝∫ ∞

0

=(A⊥(t)A

∗‖(t) + Ā⊥(t)Ā

∗‖(t))

dt. (8)

Similarly, AV is defined as

AV ≡Γ(V > 0)− Γ(V < 0)Γ(V > 0) + Γ(V < 0)

∝∫ ∞

0

=(A⊥(t)A

∗0(t) + Ā⊥(t)Ā

∗0(t))

dt. (9)

Here, A⊥, A‖ and A0 correspond to the three transversity amplitudes. The determinationof the triple-product asymmetries is then reduced to a simple counting experiment.Comparing these formulae with Eq. 3 and Appendix A it can be seen that the tripleproducts are related to the K4(t) and K6(t) terms in the decay amplitude.

5 Decay-time resolution

The sensitivity to φssss is affected by the accuracy of the measured decay time. In order toresolve the fast B0s -B

0s oscillations, it is necessary to have a decay-time resolution that is

much smaller than the oscillation period. To account for the resolution of the measureddecay-time distribution, all decay-time-dependent terms are convolved with a Gaussianfunction, with width σti that is estimated for each candidate, i, based upon the uncertaintyobtained from the vertex and kinematic fit [42].

In order to apply a candidate-dependent resolution model during fitting, the estimatedper-event decay time uncertainty is needed. This is calibrated using the fact the decaytime resolution for the B0s→ φφ mode is dominated by the secondary vertex resolution.A sample of good-quality tracks, which originate from the primary interaction vertex isselected. Due to the small opening angle of the kaons in the decay of a φ meson, it issufficient to use a single prompt track and assign it the mass of a φ meson. When combiningthis with another pair of tracks, the invariant mass of the three-body combination isrequired to be within 250 MeV/c2 of the known B0s mass. That the decay-time resolutionof the signal B0s decays can be described well using three tracks has been validated usingsimulation.

A linear function is then fitted to the distribution of σti versus σttrue, with parameters

q0 and q1. Here, σttrue denotes the difference between reconstructed decay time and the

exact decay time of simulated signal. The per-event decay-time uncertainty used in thedecay-time-dependent fit is then calculated as σcali = q0 + q1σ

ti . Gaussian constraints are

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Figure 3: Angular acceptance normalised to the average obtained using simulated B0s → φφdecays (top-left) integrated over cos θ2 and Φ as a function of cos θ1, (top-right) integrated overcos θ1 and Φ as a function of cos θ2, and (bottom) integrated over cos θ1 and cos θ2 as a functionof Φ. Each figure includes the resulting fit curve.

used to account for the uncertainties on the calibration parameters in the decay-time-dependent fit. The effective single-Gaussian decay-time resolution is found to be between41 and 44 fs, depending on the data-taking year, in agreement with the expectation fromthe simulation.

6 Acceptances

The B0s→ φφ differential decay rate depends on the decay time and three helicity anglesas shown in Eq. 2. Good understanding of the efficiencies in these variables is required.The decay-time and angular acceptances are assumed to factorise. Control channels showthis assumption has a negligible systematic uncertainty on the physics parameters.

6.1 Angular acceptance

The geometry of the LHCb detector and the momentum requirements imposed on thefinal-state particles introduce distortions of the helicity angles, giving rise to acceptanceeffects. Simulated signal events, selected with the same criteria as those applied to dataare used to determine these efficiency corrections. The angular acceptances as a functionof the three helicity angles are shown in Fig. 3.

The efficiency is parameterised in terms of the decay angles as

8

�(Ω) =∑i,j,k

cijkPi(cos θ1)Yjk(cos θ2,Φ), (10)

where Ω depends on the decay angles, cos θ1, cos θ2 and φ, the cijk are coefficients, Pi(cos θ1)are Legendre polynomials, and Yjk(cos θ2,Φ) are spherical harmonics. The procedurefollowed to calculate the coefficients is described in detail in Ref. [43] and exploits theorthogonality of Legendre polynomials. The coefficients are given by

cijk ≡ (j + 1/2)∫dΩPi(cos θ1)Yjk(cos θ2,Φ)�(Ω). (11)

This integral is calculated by means of a Monte Carlo technique, which reduces the integralto a sum over the number of accepted simulated events (Nobs)

cijk ∝ (j + 1/2)1

Nobs

Nobs∑e=1

Pi(cos θ1,e)Yjk(cos θ2,e,Φe)

P gen(Ωe|te), (12)

where P gen is the probability density function (PDF) without acceptance where theparameters are set to values used in the Monte Carlo generation. In order to easilyincorporate the angular acceptance, it is convenient to write angular functions of Eq. 2 inthe same basis as the efficiency parameterisation, i.e.

fa(cos θ1, cos θ2,Φ) =∑ijkl

κijkl,aPij(cos θ1)Ykl(cos θ2,Φ), (13)

where Pij(cos θ1) are the associated Legendre polynomials, κijkl,a are coefficients and anumerates the 15 terms outlined earlier. The parameterisation for each angular functionis given in Table 1.

The normalisation of the angular component in the decay-time dependent fit occursthrough the 15 integrals ζk =

∫�(Ω)fk(Ω)dΩ, where �(Ω) is the efficiency as a function of

the helicity angles as shown in Eq. 10 and fk(Ω) are the angular functions as defined inEq. 13.

The angular acceptance is calculated correcting for the differences in kinematic variablesbetween data and simulation. This includes differences in the MLP training variables thatcan affect acceptance corrections through correlations with the helicity angles.

The fit to determine the triple-product asymmetries assumes that the U and Vobservables are symmetric in the acceptance corrections. Simulation is used to assign asystematic uncertainty related to this assumption.

6.2 Decay-time acceptance

The impact-parameter requirements on the final-state particles efficiently suppress thebackground from the numerous pions and kaons originating from the PV, but introduce adecay-time dependence in the selection efficiency.

The efficiency as a function of the decay time is taken from theB0s → D−s (→ K+K−π−)π+ decay, in the case of data taken between 2011 and2012, and from the B0 → J/ψ (→ µ+µ−)K∗0(→ K+π−) decay in the case of data takenbetween 2015 and 2016. The reason for the change in control channel is related to changes

9

Table 1: Angular coefficients, written in the same basis as the efficiency parameterisation.

i fi inPi jYk l basis fi1 8/9P00Y00 + 16/9/

√5P00Y20 + 16/9P20Y00 + 32/(9

√5)P20Y20 4 cos2 θ1 cos2 θ2

2 8/9P00Y00 − 8/9P00Y20 − 8/9√

5P20Y00 + 8/(9√

5)P20Y20 + (2/9)√

12/5P22Y22 sin2 θ1 sin

2 θ2(1+ cos 2Φ)

3 8/9P00Y00 − 8/9P00Y20 − 8/9√

5P20Y00 + 8/(9√

5)P20Y20 − (2/9)√

12/5P22Y22 sin2 θ1 sin

2 θ2(1− cos 2Φ)4 −8/9

√3/5P2,2Y2,−2 −2 sin2 θ1 sin2 θ2 sin 2Φ

5 8/9√

6/5P2,1Y2,1√

2 sin 2θ1 sin 2θ2 cos Φ

6 −8/9√

6/5P2,1Y2,1 −√

2 sin 2θ1 sin 2θ2 sin Φ

7 (8/9)P00Y0049

8 16/9P00Y00 + 16/9/√

5P00Y20 + 16/9P20Y 00 + 16√

3/9P10Y1043

(cos θ1 + cos θ2)2

9 16√

3/2P10Y00 + 16/9P00Y108

3√3

(cos θ1 + cos θ2)

10 16/(3√

3)P10Y1083

cos θ1 cos θ2

11 (8/9)√

6P11Y114√2

3sin θ1 sin θ2 cos Φ

12 (8/9)√

6P11Y1−1 − 4√2

3sin θ1 sin θ2 sin Φ

13 16√

3/9P10Y00 + 16/9P00Y10 + 32/9P20Y 10 + 32/(9√

5)P20Y208√3

cos θ1 cos θ2

×(cos θ1 + cos θ2)

14 (8/9)√

2/3P21Y11 + (24/9)√

2/15P11Y214√2√3

sin θ1 sin θ2

×(cos θ1 + cos θ2) cos Φ

15 −(8/9)√

2/3P21Y1−1 − (24/9)√

2/15P11Y2−1− 4√2

3sin θ1 sin θ2

×(cos θ1 + cos θ2) sin Φ

1 2 3 4 5 6 7 8 9 10Time [ps]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Acc

epta

nce

LHCb

+π−sD →0sB

1 2 3 4 5 6 7 8 9 10Time [ps]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Acc

epta

nce

LHCb

*K ψJ/ →0B

Figure 4: Decay-time acceptances calculated from (left) B0s → D−s π+ decays to match Run 1data and (right) B0 → J/ψK∗0 decays to match Run 2 data. Superimposed is a parameterisationusing cubic splines..

to the software-trigger selection between the two data-taking periods. The decay-timeacceptances of the control modes are weighted by a multivariate algorithm based onsimulated kinematic and topological information, in order to match more closely those ofthe signal B0s→ φφ decay.

Cubic splines are used to model the acceptance as a function of decay time in thePDF. The PDF can then be computed analytically with the inclusion of the decay-timeacceptance following Ref. [44]. Example decay-time acceptances are shown for the case ofthe B0s → D−s π+ and B0 → J/ψK∗0 decays in Fig. 4.

To simplify the measurement of the triple-product asymmetries, the decay-time ac-ceptance is not applied in the fit to determine the triple-product asymmetries. The time

10

Table 2: Tagging performance of the opposite-side (OS) and same-side kaon (SSK) flavourtaggers for the B0s→ φφ decay.

Category ε (%) D2 εD2 (%)OS-only 12.5 0.10 1.24± 0.10SSK-only 41.0 0.04 1.74± 0.36OS&SSK 23.3 0.12 2.76± 0.20Total 76.8 0.08 5.74± 0.43

acceptance correction has an impact on the asymmetry of 0.3% and is treated as a sourceof systematic uncertainty, as further described in Sec. 9.3.

7 Flavour tagging

To obtain sensitivity to φssss , the flavour of the B0s meson at production must be determined.

At LHCb, tagging is achieved through the use of various algorithms described in Refs.[45, 46]. With these algorithms, the flavour-tagging power, defined as �tagD2 can beevaluated. Here, �tag is the flavour-tagging efficiency defined as the fraction of candidateswith a flavour tag with respect to the total, and D ≡ (1− 2ω) is the dilution, where ωis the average fraction of candidates with an incorrect flavour assignment. This analysisuses opposite-side (OS) and same-side kaon (SSK) flavour taggers.

The OS flavour-tagging algorithm [45] makes use of the b (b) hadron produced inassociation with the signal b (b) hadron. In this analysis, the predicted probability of anincorrect flavour assignment, ω, is determined for each candidate by a neural network thatis calibrated using B+ → J/ψK+, B+ → D0π+, B0 → J/ψK∗0, B0 → D∗−µ+νµ, andB0s → D−s π+ data as control modes. Details of the calibration procedure can be found inRef. [47].

When a signal B0s meson is formed, there is an associated s quark formed in the firstbranches of the fragmentation that about 50 % of the time forms a charged kaon, whichis likely to originate close to the B0s meson production point. The kaon charge thereforeallows for the identification of the flavour of the signal B0s meson. This principle is exploitedby the SSK flavour-tagging algorithm [46], which is calibrated with the B0s → D−s π+decay mode. A neural network is used to select fragmentation particles, improving theflavour-tagging power quoted in the previous decay-time-dependent measurement [9].

Table 2 shows the tagging power for the candidates tagged by only one of the algorithmsand those tagged by both. Uncertainties due to the calibration of the flavour taggingalgorithms are applied as Gaussian constraints in the decay-time-dependent fit. The initialflavour of the B0s meson established from flavour tagging is accounted for during fitting.

11

8 Decay-time-dependent measurement

8.1 Likelihood fit

The fit parameters in the polarisation-independent fit are the CP violation parameters,φssss and |λ|, the squared amplitudes, |A0|2, |A⊥|2, |AS|2, and |ASS|2, and the strongphases, δ⊥, δ‖, δ0, δS, and δSS, as defined in Sec. 4.1. The P -wave amplitudes are definedsuch that |A0|2 + |A⊥|2 + |A‖|2 = 1, hence only two of the three amplitudes are freeparameters. This normalisation effectively means the S and SS components are measuredrelative to the P -wave. The polarisation-dependent fit allows for a perpendicular, paralleland longitudinal component of φssss and |λ|.

The measurement of the parameters of interest is performed through an unbinned nega-tive log likelihood minimisation. The log-likelihood, L, of each candidate is weighted usingthe sPlot method [48,49], to remove partly reconstructed and combinatorial background.The negative log-likelihood then takes the form

− lnL = −α∑

e∈candidates

We ln(SeTD), (14)

where We are the signal sPlot weights calculated using the four-kaon invariant massas the discriminating variable. The correlations between the angular and decay-timevariables used in the fit with the four-kaon mass are small enough for this technique tobe appropriate. The factor α =

∑eWe/

∑eW

2e accounts for the sPlot weights in the

determination of the statistical uncertainties. The parameter SeTD is the differential decayrate of Eq. 2, modified to the effects of decay-time and angular acceptance, in addition tothe probability of an incorrect flavour tag. Explicitly, this can be written as

SeTD =

∑i sei (te)fi(Ωe)�(te)∑

k ζk∫sk(t)fk(Ω)�(t)dt dΩ

, (15)

where ζk are the normalisation integrals used to describe the angular acceptance describedin Sec. 6.1 and

sei (t) = Nie−Γste [ciqe(1− 2ωe) cos(∆mste) + diqe(1− 2ωe) sin(∆mste)

+ai cosh

(1

2∆Γste

)+ bi sinh

(1

2∆Γste

)]⊗R(σcale , te). (16)

The calibrated probability of an incorrect flavour assignment is given by ωe, R denotesthe Gaussian time-resolution function, and the ⊗ denotes a convolution operation. InEq. 16, qe = 1 (−1) for a B0s (B0s) meson at t = 0 or qe = 0 where no flavour-tagginginformation is assigned. The data samples corresponding to the different years of datataking are assigned independent signal weights, decay-time and angular acceptances, andseparate Gaussian constraints are applied to the decay-time resolution parameters, asdefined in Sec. 5. The B0s -B

0s oscillation frequency is constrained to the value measured

by LHCb of ∆ms = 17.768 ± 0.023 (stat) ± 0.006 (syst) ps−1 [50], with the assumptionthat the systematic uncertainties are uncorrelated with those of the current measurement.The values of the decay width and decay-width difference are constrained to the currentbest known values of Γs = 0.6646± 0.0020 ps−1 and ∆Γs = 0.086± 0.006 ps−1 [51].

Correction factors must be applied to each of the S-wave and double S-wave interferenceterms in the differential decay width. These factors modulate the sizes of the contributions

12

of the interference terms in the angular PDF due to the different line-shapes of kaon pairsoriginating from spin-1 and spin-0 configurations. This takes the form of a multiplicativefactor for each time a S-wave pair of kaons interferes with a P -wave pair. Their K+K−

invariant-mass parameterisations are denoted by g(mK+K−) and h(mK+K−), respectively.The P -wave configuration is described by a Breit–Wigner function and the S-waveconfiguration is assumed to be uniform. The correction factors, denoted by CSP , aredefined in Ref. [47]

CSP =

∫ mhml

g∗(mK+K−)h(mK+K−)dmK+K− , (17)

where mh and ml are the upper and lower edges of the mK+K− window and the phase ofCSP is absorbed in the measurements of δS−δ⊥. The factor |CSP |, is calculated to be 0.36.In order to determine systematic uncertainties due to the model dependence of the S-wave,CSP factors are recalculated based on the S-wave originating from an f0(980) resonanceand incorporating the effects of the mK+K− resolution. These alternative assumptions onthe P -wave and S-wave lineshapes yield a |CSP | value of 0.34, which is found to have anegligible effect on the parameter estimation.

8.2 Results

The resulting parameters are given in Table 3. A polarisation-independent fit is performedto calculate values for φssss and |λ|. A negligible fraction of S-wave and double S-wave isobserved.

In addition, the CP -violating phases are also determined in a polarisation-dependentmanner. Due to limited size of data samples, the phases φs,‖ and φs,⊥ are measured underthe assumptions that the longitudinal weak phase is CP -conserving and that there is nodirect CP violation. In addition, all S-wave and double S-wave components of the fit areset to zero. The results of the polarisation dependent fit are shown in Table 4. The resultsfor |A0|2, |A⊥|2, δ⊥ and δ‖ are not shown but are in agreement with the results reportedin Table 3.

The correlation matrices for the two fit configurations are provided in Appendix B.Correlations with such decay-time-dependent measurements depend on the central valuesof the parameters. No large correlation is expected between the CP -violating parameterswhen the central values are consistent with CP conservation. The largest correlationsare found to be between the different decay amplitudes. Cross-checks are performed on

Table 3: Results of the decay-time-dependent, polarisation-independent fit for the CP -violationfit. Uncertainties shown do not include systematic contributions.

Parameter Fit resultφssss [rad] −0.073± 0.115|λ| 0.99± 0.05|A0|2 0.381± 0.007|A⊥|2 0.290± 0.008δ⊥ [rad] 2.82± 0.18δ‖ [rad] 2.56± 0.05

13

Table 4: Results of the polarisation-dependent fit for the CP violation fit. Uncertainties showndo not include systematic contributions.

Parameter Fit resultφs,‖ [rad] 0.014± 0.055φs,⊥ [rad] 0.044± 0.059

Decay time [ps]2 4 6 8 10

Can

dida

tes

/ (0.

4850

ps)

1−10

1

10

210

310LHCb

[rad]Φ2− 0 2

Can

dida

tes

/ (0.

314

rad)

0

100

200

300

400

500

LHCb

1θcos1− 0.5− 0 0.5 1

Can

dida

tes

/ 0.1

050

100150200250300350400450 LHCb

2θcos1− 0.5− 0 0.5 1

Can

dida

tes

/ 0.1

0

100

200

300

400

500

LHCb

Figure 5: One-dimensional projections of the B0s → φφ fit for (top-left) decay time with binnedacceptance, (top-right) helicity angle Φ and (bottom-left and bottom-right) cosine of the helicityangles θ1 and θ2. The background-subtracted data are marked as black points, while the bluesolid lines represent the projections of the fit. The CP -even P -wave, the CP -odd P -wave andthe combined S-wave and double S-wave components are shown by the red long dashed, greenshort dashed and purple dot-dashed lines, respectively. Fitted components are plotted takinginto account efficiencies in the time and angular observables.

simulated data sets generated with the same yield as observed in data, and with the samephysics parameters, to establish that the generated values are recovered without biases.

Figure 5 shows the distributions of the B0s decay time and the three helicity angles.Superimposed are the projections of the fit result. The projections include correctionsfor acceptance effects. Pseudoexperiments were used to confirm that the deviation of thedata around cos θ2 = ±0.5 from the resulting distribution of the fit is compatible with astatistical fluctuation.

14

8.3 Systematic uncertainties

Various sources of systematic uncertainty are considered in addition to those applied asGaussian constraints in the fit. These arise from the angular and decay-time acceptances,the mass model used to describe the mass distribution, the determination of the timeresolution calibration, and the fit bias. A summary of the systematic uncertainties isgiven in Table 5.

An uncertainty due to the angular acceptance arises from the choice of weightingscheme described in Sec. 6. This is accounted for by performing multiple alternativeweighting schemes for the weighting procedure, based on different kinematic variables inthe decay. The largest variation is then assigned as the uncertainty. Further checks areperformed to verify that the angular acceptance does not depend on the way in which theevent was triggered.

Two sources of systematic uncertainty are considered concerning the decay-timeacceptance. These are the statistical uncertainty from the spline coefficients, and also theresidual disagreement between the weighted control mode and the signal decay acceptances(see Sec. 6.2). The former is evaluated through fitting the signal data set with 30 differentspline functions, whose coefficients are varied according to the corresponding uncertainties.This study is performed with the three different choices of the knot points. The RMSof the fitted parameters is then assigned as the uncertainty. The residual disagreementbetween the control mode and the signal mode is accounted for with a simulation-basedcorrection. Simplified simulation is used with the corrected acceptance and then fittedwith the nominal acceptance. This process is repeated and the resulting bias on the fittedparameters is used as an estimate of the systematic uncertainty.

The uncertainty on the mass model is found by refitting the data with variousalternative signal models, consisting of the sum of two Crystal Ball models, the sum of adouble-sided Crystal Ball and a Gaussian model. In addition, a Chebyshev polynomial isused to describe the combinatorial background. The signal weights are recalculated andthe largest deviation from the nominal fit results is used as the corresponding uncertainty.

Fit biases can arise in maximum-likelihood fits where the number of candidates issmall compared to the number of free parameters. The effect of such a bias is taken as asystematic uncertainty which is evaluated by generating and fitting simulated data setsand taking the resulting bias as the uncertainty.

The uncertainties of the effective flavour-tagging power are included in the statisticaluncertainty through Gaussian constraints on the calibration parameters, and amount to10 % of the statistical uncertainty on the CP -violating phases.

9 Triple-product asymmetries

9.1 Likelihood

To determine the triple-product asymmetries, the data sets are divided according tothe sign of the observables U and V . Simultaneous likelihood fits to the four-kaonmass distributions are preformed for the U and V variables separately. The set of freeparameters in the fits to determine the U and V observables consists of their total yieldsand the asymmetries AU(V ). The mass model is the same as that described in Sec. 3. The

15

Table 5: Summary of systematic uncertainties (in units of 10−2) for parameters of interest inthe decay-time-dependent measurement.

Parameter Mass Angular Decay-time Time Fit Totalmodel acceptance acceptance resolution bias

|A0|2 0.4 1.1 0.1 - 0.2 1.2|A⊥|2 - 0.5 - - 0.1 0.5δ‖ [rad] 2.7 0.2 0.5 0.1 1.7 3.3δ⊥ [rad] 3.8 0.3 0.8 1.4 6.0 7.3φssss [rad] 1.2 0.5 0.6 2.0 1.1 2.7

λ 0.5 0.5 0.2 0.3 0.9 1.2φs,‖ [rad] 0.2 0.2 0.4 0.2 1.0 1.1φs,⊥ [rad] 1.4 0.3 0.4 0.3 0.4 1.9

total PDF, DTP, is then of the form

DTP =∑

i∈{+,−}

(fSi G

S(mK+K−K+K−) +∑k

fki Pk(mK+K−K+K−)

), (18)

where k indicates the sum over the background components with corresponding PDFs,P j , and GS is the signal PDF, as described in Sec. 3. The parameters fSi found in Eq. 18are related to the asymmetry, ASU(V ), through

fSU(V ),+ =1

2(1 + ASU(V )), (19)

fSU(V ),− =1

2(1− ASU(V )), (20)

where S denotes the signal component of the four-kaon mass fit, as described in Sec. 3.Peaking backgrounds are assumed to be symmetric in U and V .

9.2 Results

The triple-product asymmetries found from the simultaneous fit described in Sec. 9.1 aremeasured separately for the 2015 and 2016 data. The results are combined by performinglikelihood scans of the asymmetry parameters and summing the two years. This gives

AU = −0.003 ± 0.015 ,AV = −0.012 ± 0.015 ,

where the uncertainties are statistical only.

9.3 Systematic uncertainties

As for the case of the decay-time-dependent fit, significant contributions to the systematicuncertainty arise from the decay-time and angular acceptances. Minor uncertainties alsoresult from the knowledge of the mass model of the signal and the composition of peakingbackgrounds.

16

Table 6: Summary of systematic uncertainties on AU and AV .

Source UncertaintyTime acceptance 0.003Angular acceptance 0.003Mass model 0.001Combinatorial background 0.001Peaking background 0.001Total 0.005

The effect of the decay-time acceptance is determined through the generation ofsimulated samples including the decay-time acceptance and fitted with the methoddescribed in Sec. 9.1. The resulting deviation from the nominal fit results is used toassign a systematic uncertainty. The effect of the angular acceptance is evaluated bygenerating simulated data sets with and without the inclusion of the angular acceptance.The difference between the nominal fit results and the results obtained using the simulatedsamples including the decay-time acceptance is then used as a systematic uncertainty.

Uncertainties related to the mass model are evaluated using a similar approach tothat described in Sec. 8.3. Additional uncertainties arise from the assumption that thepeaking background is symmetric in U and V . The deviation observed without thisassumption is then added as a systematic uncertainty. Similarly, the assumption thatthe combinatorial background has no asymmetry yields an identical uncertainty. Thesystematic uncertainties are summarised in Table 6.

9.4 Combination of Run 1 and Run 2 results

The Run 2 (2015–2016) values for the triple product asymmetries are

AU = −0.003 ± 0.015 (stat) ± 0.005 (syst),AV = −0.012 ± 0.015 (stat) ± 0.005 (syst),

whilst the Run 1 (2011–2012) values from Ref. [9] are

AU = −0.003 ± 0.017 (stat) ± 0.006 (syst),AV = −0.017 ± 0.017 (stat) ± 0.006 (syst).

The Run 1 and Run 2 results are combined by calculating a weighted average. In thisprocedure the decay-time and angular acceptance systematic uncertainties and peakingbackgrounds are assumed to be fully correlated. All other systematic uncertainties areassumed to be uncorrelated. This gives a final result of

AU = −0.003 ± 0.011 (stat) ± 0.004 (syst),AV = −0.014 ± 0.011 (stat) ± 0.004 (syst).

The Run 1 and Run 2 results are compatible with each other, and the asymmetriesare consistent with zero. No evidence for CP violation is found.

17

5200 5300 5400 5500 5600]2c) [MeV/−K+K−K+KM(

2−10

1−10

1

10

210

310

)2 cC

andi

date

s / 9

(M

eV/

LHCb 2011-2016

Figure 6: Fit to the four-kaon invariant mass. The total PDF as described in the text isshown as a blue solid line, B0s→ φφ as a red dashed line, B0 → φφ as a green dotted line, theΛ0b → φpK contribution as a magenta long-dashed line and the combinatorial background as ablue short-dashed line.

10 Search for the B0 → φφ decayThe selection criteria for the B0 → φφ mode are based on the B0s→ φφ selection, with somemodifications. The Punzi figure of merit [38] is used for the B0 → φφ search, resulting ina more stringent MLP requirement. Furthermore, the uncertainty on the four-kaon massis required to be less than 25 MeV/c2, corresponding to roughly 3σ separation betweenthe B0s and B

0 mass peaks. The B0s→ φφ decay is used as normalisation decay mode.The signal PDF for the mass of the B0 meson is assumed to be the same as that of theB0s decay, with the modification of the resolution according to a scaling factor, which isdefined as

α =mB0 − 4mKmB0s − 4mK

= 0.974, (21)

where mK is the known K+ mass.

Figure 6 shows the fit to the full data set. The Λ0b → φpK contribution is fixed to109 candidates, following the same method described in Sec. 3. The fit returns a yield of4.9± 9.2 B0 → φφ decays.

The Confidence Levels (CLs) method [52] is used to set a limit on the B0 → φφ

branching fraction. A total of 10,000 pseudoexperiments are used to calculate each pointof the scan. Figure 7 shows the results of the CLs scan. At 90 % CL, NB0 < 23.7. Theselimits are converted to a branching fraction using

B(B0 → φφ) = NB0 ×�B0→φφ�B0s→φφ

× B(B0s → φφ)× fs/fdNB0s→φφ

, (22)

where NB0 is the limit on the B0 → φφ yield, and NB0s→φφ is the B

0s yield from the fit

displayed in Fig. 6. The relative reconstruction and selection efficiency of the B0s →φφ and B0 → φφ decays, �B0→φφ/�B0s→φφ, is determined to be 0.986 using simulation.The ratio of the fragmentation functions has been measured at 7 and 8 TeV to be

18

10 20 30

9−10×

)φφ→0BBF(

3−10

2−10

1−10

1sC

L

LHCb

Figure 7: Results of the CLs scan as a function of the B0 → φφ yield. The solid black line shows

the observed CLs distribution, while the dotted black line indicates the expected distribution.The green (yellow) band marks the 1σ (2σ) confidence region on the expected CLs. The 90 %CL limit is shown as a red line.

fs/fd = 0.259 ± 0.015 within the LHCb acceptance [53]. The production fraction at13 TeV has been shown to be consistent with that of the 7 and 8 TeV data [54]. TheB(B0s→ φφ) = (1.84±0.05 (stat)±0.07 (syst)±0.11(fs/fd)±0.12 (norm))×10−5 branchingfraction is an external input taken from Ref. [24]. To set the limit, the uncertainties onthe B0s→ φφ branching fraction are propagated to the limit, where the uncertainty on theB0s→ φφ branching fraction arising from fs/fd is already included in the uncertainty onthe normalisation mode, B0 → φK∗. The maximum value of B(B0s→ φφ) including thesystematic contribution is found to be 1.99× 10−5 and is used in Eq. 22. This thereforetranslates to a limit of

B(B0 → φφ) < 2.7 (3.0)× 10−8 at 90 % (95 %) CL,

which supersedes the previous best limit.

11 Summary and conclusions

Measurements of CP violation in the B0s→ φφ decay are presented, based on a sample ofproton-proton collision data corresponding to an integrated luminosity of 5.0 fb−1 collectedwith the LHCb detector. The CP -violating phase, φssss , and CP violation parameter, |λ|,are determined in a helicity-independent manner to be

φssss = −0.073 ± 0.115 (stat) ± 0.027 (syst) rad,|λ| = 0.99 ± 0.05 (stat) ± 0.01 (syst) .

The CP -violating phases are also measured in a polarisation-dependent manner, with theassumption that the longitudinal weak phase is CP -conserving (φs,0 = 0) and that no

19

direct CP violation is present (|λ| = 1). The CP phases corresponding to the parallel,φs,‖, and perpendicular, φs,⊥, polarisations are determined to be

φs,‖ = 0.014 ± 0.055 (stat) ± 0.011 (syst) rad,φs,⊥ = 0.044 ± 0.059 (stat) ± 0.019 (syst) rad.

The results are in agreement with SM predictions [1–3]. The uncertainties have beenvalidated with simulation. When compared with the CP -violating phase measured inB0s → J/ψK+K− and B0s → J/ψπ+π− decays [47], these results show that no significantCP violation is present either in B0s -B

0s mixing or in the b→ sss decay amplitude, though

the increased precision of the measurement presented in Ref. [47] leads to more stringentconstraints on CP violation in B0s -B

0s mixing.

The polarisation amplitudes and strong phases are measured independently of polari-sation to be

|A0|2 = 0.381 ± 0.007 (stat) ± 0.012 (syst) ,|A⊥|2 = 0.290 ± 0.008 (stat) ± 0.007 (syst) ,δ⊥ = 2.818 ± 0.178 (stat) ± 0.073 (syst) rad,δ‖ = 2.559 ± 0.045 (stat) ± 0.033 (syst) rad.

The polarisation amplitudes and strong phases measured in the polarisation-dependentfit are in agreement with the results listed here. In addition, values of the polarisationamplitudes are found to agree well with previous measurements [9, 12, 55, 56] and withpredictions from QCD factorisation [2, 3].

The most precise measurements to date of the triple-product asymmetries are deter-mined from a separate time-integrated fit to be

AU = −0.003 ± 0.011 (stat) ± 0.004 (syst) ,AV = −0.014 ± 0.011 (stat) ± 0.004 (syst) ,

in agreement with previous measurements [9, 12, 55]. The measured values of the CP -violating phase and triple-product asymmetries are consistent with the hypothesis of CPconservation in b→ sss transitions.

In addition, the most stringent limit on the branching fraction of the B0 → φφ decayis presented and it is found to be

B(B0 → φφ) < 2.7× 10−8 at 90 % CL.

Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments for theexcellent performance of the LHC. We thank the technical and administrative staff at theLHCb institutes. We acknowledge support from CERN and from the national agencies:CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3(France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSWand NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MinECo (Spain); SNSF andSER (Switzerland); NASU (Ukraine); STFC (United Kingdom); DOE NP and NSF (USA).We acknowledge the computing resources that are provided by CERN, IN2P3 (France),KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP

20

(United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH(Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted tothe communities behind the multiple open-source software packages on which we depend.Individual groups or members have received support from AvH Foundation (Germany);EPLANET, Marie Sk lodowska-Curie Actions and ERC (European Union); ANR, LabexP2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Programof Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China);RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); theRoyal Society and the Leverhulme Trust (United Kingdom).

A Time-dependent terms

In Table 7, δS and δSS are the strong phases of the P → VS and P → SS processes,respectively. The P -wave strong phases are dependent on δ‖ and δ0.

21

Tab

le7:

Coeffi

cien

tsof

the

tim

e-d

epen

den

tte

rms

and

angu

lar

fun

ctio

ns

use

din

Eq.

2.A

mp

litu

des

are

defi

ned

att

=0.

iNi

ai

b ic i

di

f i1

|A0|2

1+|λ

0|2

−2|λ

0|c

os(φ

)1−|λ

0|2

2|λ

0|s

in(φ

)4

cos2θ 1

cos2θ 2

2|A‖|2

1+|λ‖|2

−2|λ‖|

cos(φs,‖)

1−|λ‖|2

2|λ‖|

sin

(φs,‖)

sin

2θ 1

sin

2θ 2

(1+

cos

2Φ)

3|A⊥|2

1+|λ⊥|2

2|λ⊥|c

os(φ

s,⊥

)1−|λ⊥|2

−2|λ‖|

sin

(φs,⊥

)si

n2θ 1

sin

2θ 2

(1−

cos

2Φ)

4|A‖||A⊥|

2

sin

(δ‖−δ ⊥

)−|λ‖||λ⊥|·

sin

(δ‖−δ ⊥−φs,‖

+φs,⊥

)−|λ‖|

sin

(δ‖−δ ⊥−φs,‖)

+|λ⊥|s

in(δ‖−δ ⊥

+φs,⊥

)si

n(δ‖−δ ⊥

)+|λ‖||λ⊥|·

sin

(δ‖−δ ⊥−φs,‖

+φs,⊥

)|λ‖|

cos(δ ‖−δ ⊥−φs,‖)

+|λ⊥|c

os(δ‖−δ ⊥

+φs,⊥

)−

2si

n2θ 1

sin

2θ 2

sin

2Φ

5|A‖||A

0|

2

cos(δ ‖−δ 0

)+|λ‖||λ

0|·

cos(δ ‖−δ 0−φs,‖

+φ

)−|λ‖|

cos(δ ‖−δ 0−φs,‖)

+|λ

0|c

os(δ‖−δ 0

+φ

)co

s(δ ‖−δ 0

)−|λ‖||λ

0|·

sin

(δ‖−δ 0−φs,‖

+φ

)−|λ‖|

sin

(δ‖−δ 0−φs,‖)

+|λ

0|s

in(δ‖−δ 0

+φ

)

√2

sin

2θ1

sin

2θ2

cos

Φ

6|A

0||A⊥|

2

sin

(δ0−δ ⊥

)−|λ

0||λ⊥|·

sin

(δ0−δ ⊥−φ

+φs,⊥

)−|λ

0|s

in(δ

0−δ ⊥−φ

)+|λ⊥|s

in(δ

0−δ ⊥

+φs,⊥

)si

n(δ

0−δ ⊥

)+|λ

0||λ⊥|·

sin

(δ0−δ ⊥−φ

+φs,⊥

)|λ

0|c

os(δ

0−δ ⊥−φ

)+|λ⊥|c

os(δ

0−δ ⊥

+φs,⊥

)−√

2si

n2θ

1si

n2θ

2si

nΦ

7|A

SS|2

1+|λss|2

−2|λss|c

os(φ

s,ss

)1−|λss|2

2|λss|s

in(φ

s,ss

)4 9

8|A

S|2

1+|λs|2

2|λs|c

os(φ

s,s)

1−|λs|2

−2|λs|s

in(φ

s,s)

4 3(c

osθ 1

+co

sθ 2

)2

9|A

S||A

SS|

2

cos(δ s−δ ss)−|λs||λ

ss|·

cos(δ s−δ ss−φs,s

+φs,ss

)|λs|c

os(δs−δ ss−φs,s)

+|λss|c

os(δs−δ ss

+φs,ss

)co

s(δ s−δ ss)

+|λs||λ

ss|·

sin

(δs−δ ss−φs,s

+φs,ss

)|λs|s

in(δs−δ ss−φs,s)

+|λss|s

in(δs−δ ss

+φs,ss

)8

3√

3(c

osθ 1

+co

sθ 2

)

10|A

0||A

SS|

2

cos(δ 0−δ ss)

+|λ

0||λ

ss|·

cos(δ 0−δ ss−φ

+φs,ss

)−|λ

0|c

os(δ

0−δ ss−φ

)+|λss|c

os(δ

0−δ ss

+φs,ss

)co

s(δ 0−δ ss)−|λ

0||λ

ss|·

sin

(δ0−δ ss−φ

+φs,ss

)−|λ

0|s

in(δ

0−δ ss−φ

)+|λss|s

in(δ

0−δ ss

+φs,ss

)8 3

cosθ 1

cosθ 2

11|A‖||A

SS|

2

cos(δ ‖−δ ss)

+|λ‖||λss|·

cos(δ ‖−δ ss−φs,‖

+φs,ss

)−|λ‖|

cos(δ ‖−δ ss−φs,‖)

+|λss|c

os(δ‖−δ ss

+φs,ss

)co

s(δ ‖−δ ss)−|λ‖||λss|·

sin

(δ‖−δ ss−φs,‖

+φs,ss

)−|λ

0|s

in(δ‖−δ ss−φs,‖)

+|λss|s

in(δ‖−δ ss

+φs,ss

)4√

23

sinθ 1

sinθ 2

cos

Φ

12|A⊥||A

SS|

2

sin

(δ⊥−δ ss)−|λ⊥||λ

ss|·

sin

(δ⊥−δ ss−φs,⊥

+φs,ss

)|λ⊥|s

in(δ⊥−δ ss−φs,⊥

)−|λss|s

in(δ⊥−δ ss

+φs,ss

)si

n(δ⊥−δ ss)

+|λ⊥||λ

ss|·

sin

(δ⊥−δ ss−φs,⊥

+φs,ss

)−|λ⊥|c

os(δ⊥−δ ss−φs,⊥

)−|λss|c

os(δ⊥−δ ss

+φs,ss

)−

4√

23

sinθ 1

sinθ 2

sin

Φ

13|A

0||A

S|

2

cos(δ 0−δ s

)−|λ

0||λ

s|·

cos(δ 0−δ s−φ

+φs,s)

−|λ

0|c

os(δ

0−δ s−φ

)−|λs|c

os(δ

0−δ s

+φs,s)

cos(δ 0−δ s

)+|λ

0||λ

s|·

sin

(δ0−δ s−φ

+φs,s)

−|λ

0|s

in(δ

0−δ s−φ

)−|λs|s

in(δ

0−δ ss

+φs,s)

8 √3

cosθ 1

cosθ 2

×(c

osθ 1

+co

sθ 2

)

14|A‖||A

S|

2

cos(δ ‖−δ s

)−|λ‖||λs|·

cos(δ ‖−δ s−φs,‖

+φs,s)

−|λ‖|

cos(δ ‖−δ s−φs,‖)

−|λs|c

os(δ‖−δ s

+φs,s)

cos(δ ‖−δ s

)+|λ‖||λs|·

sin

(δ‖−δ s−φs,‖

+φs,s)

−|λ‖|

sin

(δ‖−δ s−φs,‖)

−|λs|s

in(δ‖−δ ss

+φs,s)

4√

2√

3si

nθ 1

sinθ 2

×(c

osθ 1

+co

sθ 2

)co

sΦ

15|A⊥||A

S|

2

sin

(δ⊥−δ s

)+|λ⊥||λ

s|·

sin

(δ⊥−δ s−φs,⊥

+φs,s)

|λ⊥|s

in(δ⊥−δ s−φs,⊥

)+|λs|s

in(δ⊥−δ s

+φs,s)

sin

(δ⊥−δ s

)−|λ⊥||λ

s|·

sin

(δ⊥−δ s−φs,⊥

+φs,s)

−|λ⊥|c

os(δ⊥−δ s−φs,⊥

)+|λs|c

os(δ⊥−δ s

+φs,s)

−4√

23

sinθ 1

sinθ 2

×(c

osθ 1

+co

sθ 2

)si

nΦ

22

B Correlation matrices for the time-dependent fits

Table 8: Statistical correlation matrix of the time-dependent fit.

δ‖ |A⊥|2 δ⊥ |A0|2 |λ| φssssδ‖ 1.00 0.14 0.13 −0.03 0.02 0.01|A⊥|2 1.00 0.01 −0.45 0.00 −0.03δ⊥ 1.00 0.00 −0.26 −0.15|A0|2 1.00 −0.01 0.01|λ| 1.00 −0.05φssss 1.00

Table 9: Statistical correlation matrix of the time-dependent fit in which CP violation ispolarisation dependent.

δ‖ |A⊥|2 δ⊥ |A0|2 φs,‖ φs,⊥δ‖ 1.00 0.13 0.13 −0.02 0.58 0.41|A⊥|2 1.00 0.03 −0.45 0.00 0.01δ⊥ 1.00 0.00 0.08 0.13|A0|2 1.00 0.00 0.01|λ| 1.00 0.71φssss 1.00

23

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27

https://doi.org/10.1088/1748-0221/11/05/P05010http://arxiv.org/abs/1602.07252https://doi.org/10.1103/PhysRevLett.114.041801http://arxiv.org/abs/1411.3104https://doi.org/10.1016/j.nima.2005.08.106http://arxiv.org/abs/physics/0402083http://arxiv.org/abs/0905.0724https://doi.org/10.1088/1367-2630/15/5/053021http://arxiv.org/abs/1304.4741https://doi.org/10.1140/epjc/s10052-017-5058-4https://doi.org/10.1140/epjc/s10052-017-5058-4http://arxiv.org/abs/1612.07233https://hflav.web.cern.chhttps://doi.org/10.1088/0954-3899/28/10/313https://doi.org/10.1088/0954-3899/28/10/313https://doi.org/10.1007/JHEP04(2013)001http://arxiv.org/abs/1301.5286https://cds.cern.ch/record/1559262https://doi.org/10.1103/PhysRevLett.118.191801https://doi.org/10.1103/PhysRevLett.118.191801http://arxiv.org/abs/1703.05747https://doi.org/10.1016/j.physletb.2012.06.012http://arxiv.org/abs/1204.2813https://doi.org/10.1103/PhysRevLett.110.241802http://arxiv.org/abs/1303.7125

LHCb collaboration

R. Aaij30, C. Abellán Beteta47, B. Adeva44, M. Adinolfi51, C.A. Aidala78, Z. Ajaltouni8,S. Akar62, P. Albicocco21, J. Albrecht13, F. Alessio45, M. Alexander56, A. Alfonso Albero43,G. Alkhazov36, P. Alvarez Cartelle58, A.A. Alves Jr44, S. Amato2, Y. Amhis10, L. An20,L. Anderlini20, G. Andreassi46, M. Andreotti19, J.E. Andrews63, F. Archilli21, J. Arnau Romeu9,A. Artamonov42, M. Artuso65, K. Arzymatov40, E. Aslanides9, M. Atzeni47, B. Audurier25,S. Bachmann15, J.J. Back53, S. Baker58, V. Balagura10,b, W. Baldini19,45, A. Baranov40,R.J. Barlow59, S. Barsuk10, W. Barter58, M. Bartolini22, F. Baryshnikov74, V. Batozskaya34,B. Batsukh65, A. Battig13, V. Battista46, A. Bay46, F. Bedeschi27, I. Bediaga1, A. Beiter65,L.J. Bel30, V. Belavin40, S. Belin25, N. Beliy4, V. Bellee46, K. Belous42, I. Belyaev37,G. Bencivenni21, E. Ben-Haim11, S. Benson30, S. Beranek12, A. Berezhnoy38, R. Bernet47,D. Berninghoff15, E. Bertholet11, A. Bertolin26, C. Betancourt47, F. Betti18,e, M.O. Bettler52,Ia. Bezshyiko47, S. Bhasin51, J. Bhom32, M.S. Bieker13, S. Bifani50, P. Billoir11, A. Birnkraut13,A. Bizzeti20,u, M. Bjørn60, M.P. Blago45, T. Blake53, F. Blanc46, S. Blusk65, D. Bobulska56,V. Bocci29, O. Boente Garcia44, T. Boettcher61, A. Boldyrev75, A. Bondar41,w, N. Bondar36,S. Borghi59,45, M. Borisyak40, M. Borsato15, M. Boubdir12, T.J.V. Bowcock57, C. Bozzi19,45,S. Braun15, A. Brea Rodriguez44, M. Brodski45, J. Brodzicka32, A. Brossa Gonzalo53,D. Brundu25,45, E. Buchanan51, A. Buonaura47, C. Burr59, A. Bursche25, J.S. Butter30,J. Buytaert45, W. Byczynski45, S. Cadeddu25, H. Cai69, R. Calabrese19,g, S. Cali21,R. Calladine50, M. Calvi23,i, M. Calvo Gomez43,m, A. Camboni43,m, P. Campana21,D.H. Campora Perez45, L. Capriotti18,e, A. Carbone18,e, G. Carboni28, R. Cardinale22,A. Cardini25, P. Carniti23,i, K. Carvalho Akiba2, A. Casais Vidal44, G. Casse57, M. Cattaneo45,G. Cavallero22, R. Cenci27,p, M.G. Chapman51, M. Charles11,45, Ph. Charpentier45,G. Chatzikonstantinidis50, M. Chefdeville7, V. Chekalina40, C. Chen3, S. Chen25, S.-G. Chitic45,V. Chobanova44, M. Chrzaszcz45, A. Chubykin36, P. Ciambrone21, X. Cid Vidal44,G. Ciezarek45, F. Cindolo18, P.E.L. Clarke55, M. Clemencic45, H.V. Cliff52, J. Closier45,J.L. Cobbledick59, V. Coco45, J.A.B. Coelho10, J. Cogan9, E. Cogneras8, L. Cojocariu35,P. Collins45, T. Colombo45, A. Comerma-Montells15, A. Contu25, G. Coombs45, S. Coquereau43,G. Corti45, C.M. Costa Sobral53, B. Couturier45, G.A. Cowan55, D.C. Craik61, A. Crocombe53,M. Cruz Torres1, R. Currie55, C.L. Da Silva64, E. Dall’Occo30, J. Dalseno44,51, C. D’Ambrosio45,A. Danilina37, P. d’Argent15, A. Davis59, O. De Aguiar Francisco45, K. De Bruyn45,S. De Capua59, M. De Cian46, J.M. De Miranda1, L. De Paula2, M. De Serio17,d, P. De Simone21,J.A. de Vries30, C.T. Dean56, W. Dean78, D. Decamp7, L. Del Buono11, B. Delaney52,H.-P. Dembinski14, M. Demmer13, A. Dendek33, D. Derkach75, O. Deschamps8, F. Desse10,F. Dettori25, B. Dey6, A. Di Canto45, P. Di Nezza21, S. Didenko74, H. Dijkstra45, F. Dordei25,M. Dorigo27,x, A.C. dos Reis1, A. Dosil Suárez44, L. Douglas56, A. Dovbnya48, K. Dreimanis57,L. Dufour45, G. Dujany11, P. Durante45, J.M. Durham64, D. Dutta59, R. Dzhelyadin42,†,M. Dziewiecki15, A. Dziurda32, A. Dzyuba36, S. Easo54, U. Egede58, V. Egorychev37,S. Eidelman41,w, S. Eisenhardt55, U. Eitschberger13, R. Ekelhof13, S. Ek-In46, L. Eklund56,S. Ely65, A. Ene35, S. Escher12, S. Esen30, T. Evans62, A. Falabella18, C. Färber45, N. Farley50,S. Farry57, D. Fazzini10, M. Féo45, P. Fernandez Declara45, A. Fernandez Prieto44, F. Ferrari18,e,L. Ferreira Lopes46, F. Ferreira Rodrigues2, S. Ferreres Sole30, M. Ferro-Luzzi45, S. Filippov39,R.A. Fini17, M. Fiorini19,g, M. Firlej33, C. Fitzpatrick45, T. Fiutowski33, F. Fleuret10,b,M. Fontana45, F. Fontanelli22,h, R. Forty45, V. Franco Lima57, M. Franco Sevilla63, M. Frank45,C. Frei45, J. Fu24,q, W. Funk45, E. Gabriel55, A. Gallas Torreira44, D. Galli18,e, S. Gallorini26,S. Gambetta55, Y. Gan3, M. Gandelman2, P. Gandini24, Y. Gao3, L.M. Garcia Martin77,J. Garćıa Pardiñas47, B. Garcia Plana44, J. Garra Tico52, L. Garrido43, D. Gascon43,C. Gaspar45, G. Gazzoni8, D. Gerick15, E. Gersabeck59, M. Gersabeck59, T. Gershon53,D. Gerstel9, Ph. Ghez7, V. Gibson52, A. Gioventù44, O.G. Girard46, P. Gironella Gironell43,

28

L. Giubega35, K. Gizdov55, V.V. Gligorov11, C. Göbel67, D. Golubkov37, A. Golutvin58,74,A. Gomes1,a, I.V. Gorelov38, C. Gotti23,i, E. Govorkova30, J.P. Grabowski15, R. Graciani Diaz43,L.A. Granado Cardoso45, E. Graugés43, E. Graverini46, G. Graziani20, A. Grecu35, R. Greim30,P. Griffith25, L. Grillo59, L. Gruber45, B.R. Gruberg Cazon60, C. Gu3, E. Gushchin39,A. Guth12, Yu. Guz42,45, T. Gys45, T. Hadavizadeh60, C. Hadjivasiliou8, G. Haefeli46,C. Haen45, S.C. Haines52, P.M. Hamilton63, Q. Han6, X. Han15, T.H. Hancock60,S. Hansmann-Menzemer15, N. Harnew60, T. Harrison57, C. Hasse45, M. Hatch45, J. He4,M. Hecker58, K. Heijhoff30, K. Heinicke13, A. Heister13, K. Hennessy57, L. Henry77, M. Heß71,J. Heuel12, A. Hicheur66, R. Hidalgo Charman59, D. Hill60, M. Hilton59, P.H. Hopchev46,J. Hu15, W. Hu6, W. Huang4, Z.C. Huard62, W. Hulsbergen30, T. Humair58, M. Hushchyn75,D. Hutchcroft57, D. Hynds30, P. Ibis13, M. Idzik33, P. Ilten50, A. Inglessi36, A. Inyakin42,K. Ivshin36, R. Jacobsson45, S. Jakobsen45, J. Jalocha60, E. Jans30, B.K. Jashal77,A. Jawahery63, F. Jiang3, M. John60, D. Johnson45, C.R. Jones52, C. Joram45, B. Jost45,N. Jurik60, S. Kandybei48, M. Karacson45, J.M. Kariuki51, S. Karodia56, N. Kazeev75,M. Kecke15, F. Keizer52, M. Kelsey65, M. Kenzie52, T. Ketel31, B. Khanji45, A. Kharisova76,C. Khurewathanakul46, K.E. Kim65, T. Kirn12, V.S. Kirsebom46, S. Klaver21,K. Klimaszewski34, S. Koliiev49, M. Kolpin15, A. Kondybayeva74, A. Konoplyannikov37,P. Kopciewicz33, R. Kopecna15, P. Koppenburg30, I. Kostiuk30,49, O. Kot49, S. Kotriakhova36,M. Kozeiha8, L. Kravchuk39, M. Kreps53, F. Kress58, S. Kretzschmar12, P. Krokovny41,w,W. Krupa33, W. Krzemien34, W. Kucewicz32,l, M. Kucharczyk32, V. Kudryavtsev41,w,G.J. Kunde64, A.K. Kuonen46, T. Kvaratskheliya37, D. Lacarrere45, G. Lafferty59, A. Lai25,D. Lancierini47, G. Lanfranchi21, C. Langenbruch12, T. Latham53, C. Lazzeroni50, R. Le Gac9,R. Lefèvre8, A. Leflat38, F. Lemaitre45, O. Leroy9, T. Lesiak32, B. Leverington15, H. Li68,P.-R. Li4,aa, X. Li64, Y. Li5, Z. Li65, X. Liang65, T. Likhomanenko73, R. Lindner45,F. Lionetto47, V. Lisovskyi10, G. Liu68, X. Liu3, D. Loh53, A. Loi25, J. Lomba Castro44,I. Longstaff56, J.H. Lopes2, G. Loustau47, G.H. Lovell52, D. Lucchesi26,o, M. Lucio Martinez44,Y. Luo3, A. Lupato26, E. Luppi19,g, O. Lupton53, A. Lusiani27, X. Lyu4, F. Machefert10,F. Maciuc35, V. Macko46, P. Mackowiak13, S. Maddrell-Mander51, O. Maev36,45, A. Maevskiy75,K. Maguire59, D. Maisuzenko36, M.W. Majewski33, S. Malde60, B. Malecki45, A. Malinin73,T. Maltsev41,w, H. Malygina15, G. Manca25,f , G. Mancinelli9, D. Marangotto24,q, J. Maratas8,v,J.F. Marchand7, U. Marconi18, C. Marin Benito10, M. Marinangeli46, P. Marino46, J. Marks15,P.J. Marshall57, G. Martellotti29, L. Martinazzoli45, M. Martinelli45,23,i, D. Martinez Santos44,F. Martinez Vidal77, A. Massafferri1, M. Materok12, R. Matev45, A. Mathad47, Z. Mathe45,V. Matiunin37, C. Matteuzzi23, K.R. Mattioli78, A. Mauri47, E. Maurice10,b, B. Maurin46,M. McCann58,45, L. Mcconnell16, A. McNab59, R. McNulty16, J.V. Mead57, B. Meadows62,C. Meaux9, N. Meinert71, D. Melnychuk34, M. Merk30, A. Merli24,q, E. Michielin26,D.A. Milanes70, E. Millard53, M.-N. Minard7, O. Mineev37, L. Minzoni19,g, D.S. Mitzel15,A. Mödden13, A. Mogini11, R.D. Moise58, T. Mombächer13, I.A. Monroy70, S. Monteil8,M. Morandin26, G. Morello21, M.J. Morello27,t, J. Moron33, A.B. Morris9, R. Mountain65,H. Mu3, F. Muheim55, M. Mukherjee6, M. Mulder30, D. Müller45, J. Müller13, K. Müller47,V. Müller13, C.H. Murphy60, D. Murray59, P. Naik51, T. Nakada46, R. Nandakumar54,A. Nandi60, T. Nanut46, I. Nasteva2, M. Needham55, N. Neri24,q, S. Neubert15, N. Neufeld45,R. Newcombe58, T.D. Nguyen46, C. Nguyen-Mau46,n, S. Nieswand12, R. Niet13, N. Nikitin38,N.S. Nolte45, A. Oblakowska-Mucha33, V. Obraztsov42, S. Ogilvy56, D.P. O’Hanlon18,R. Oldeman25,f , C.J.G. Onderwater72, J. D. Osborn78, A. Ossowska32, J.M. Otalora Goicochea2,T. Ovsiannikova37, P. Owen47, A. Oyanguren77, P.R. Pais46, T. Pajero27,t, A. Palano17,M. Palutan21, G. Panshin76, A. Papanestis54, M. Pappagallo55, L.L. Pappalardo19,g,W. Parker63, C. Parkes59,45, G. Passaleva20,45, A. Pastore17, M. Patel58, C. Patrignani18,e,A. Pearce45, A. Pellegrino30, G. Penso29, M. Pepe Altarelli45, S. Perazzini18, D. Pereima37,P. Perret8, L. Pescatore46, K. Petridis51, A. Petrolini22,h, A. Petrov73, S. Petrucci55,

29

M. Petruzzo24,q, B. Pietrzyk7, G. Pietrzyk46, M. Pikies32, M. Pili60, D. Pinci29, J. Pinzino45,F. Pisani45, A. Piucci15, V. Placinta35, S. Playfer55, J. Plews50, M. Plo Casasus44, F. Polci11,M. Poli Lener21, M. Poliakova65, A. Poluektov9, N. Polukhina74,c, I. Polyakov65, E. Polycarpo2,G.J. Pomery51, S. Ponce45, A. Popov42, D. Popov50, S. Poslavskii42, K. Prasanth32, E. Price51,C. Prouve44, V. Pugatch49, A. Puig Navarro47, H. Pullen60, G. Punzi27,p, W. Qian4, J. Qin4,R. Quagliani11, B. Quintana8, N.V. Raab16, B. Rachwal33, J.H. Rademacker51, M. Rama27,M. Ramos Pernas44, M.S. Rangel2, F. Ratnikov40,75, G. Raven31, M. Ravonel Salzgeber45,M. Reboud7, F. Redi46, S. Reichert13, F. Reiss11, C. Remon Alepuz77, Z. Ren3, V. Renaudin60,S. Ricciardi54, S. Richards51, K. Rinnert57, P. Robbe10, A. Robert11, A.B. Rodrigues46,E. Rodrigues62, J.A. Rodriguez Lopez70, M. Roehrken45, S. Roiser45, A. Rollings60,V. Romanovskiy42, A. Ro