EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-PH-EP-2014-206LHCb-PAPER-2014-040

4 September 2014

Measurement of the χb(3P ) massand of the relative rate of χb1(1P )

and χb2(1P ) production

The LHCb collaboration†

Abstract

The production of χb mesons in proton-proton collisions is studied using a datasample collected by the LHCb detector, at centre-of-mass energies of

√s = 7 and

8 TeV and corresponding to an integrated luminosity of 3.0 fb−1. The χb mesons areidentified through their decays to Υ (1S)γ and Υ (2S)γ using photons that convertedto e+e− pairs in the detector. The χb(3P ) meson mass, and the relative promptproduction rate of χb1(1P ) and χb2(1P ) mesons as a function of the Υ (1S) transversemomentum in the χb rapidity range 2.0 < y < 4.5, are measured. Assuming a masssplitting between the χb1(3P ) and the χb2(3P ) states of 10.5 MeV/c2, the mass ofthe χb1(3P ) meson is

m(χb1(3P )) = 10515.7+2.2−3.9(stat)+1.5

−2.1(syst) MeV/c2.

Submitted to JHEP

c© CERN on behalf of the LHCb collaboration, license CC-BY-4.0.

†Authors are listed at the end of this paper.

arX

iv:1

409.

1408

v1 [

hep-

ex]

4 S

ep 2

014

ii

1 Introduction

The study of production and properties of heavy quark-antiquark bound states (quarkonia)provides an important test of the underlying mechanisms described by quantum chro-modynamics (QCD). The quarkonium (cc and bb) states in which quarks have parallelspins include the S-wave (J/ψ , Υ ) and the P -wave (χc, χb) states, where each of the lattercomprises a closely spaced triplet of J = 0, 1, 2 spin states (χcJ , χbJ). In high-energyproton-proton collisions at the LHC, qq pairs (q = c, b) are expected to be producedpredominantly via a hard gluon-gluon interaction followed by the formation of boundquarkonium states. The production of the qq pair is described by perturbative QCD, whilenon-perturbative QCD is needed for the description of the evolution of the qq pair tothe bound state. Several models have been developed for this non-perturbative part suchas the colour singlet model [1–3] and the non-relativistic QCD (NRQCD) model [4, 5],which also includes the production of quarkonium via the colour octet mechanism. Recentstudies support the leading role of the colour singlet mechanism [6, 7]. Measurementsof the relative rate of J = 1 and J = 2 states provide information on the colour octetcontribution. This relative rate is also predicted to have the same dependence on themeson transverse momentum (pT) in χb and χc states, once the pT of the χb meson isscaled by the ratio of χc and χb masses [8].

Measurements of χc production and the ratio of the χc1 and χc2 production cross-sections have been made previously using various particle beams and energies [9–13]. Allthe χb states are below the BB threshold (where B stands for b mesons) and thereforecan be studied through their radiative decays to the Υ mesons, in the same way as the χcstates were studied through their radiative decays to the J/ψ meson [13].

In this paper we report a measurement of the ratio of χb2(1P ) to χb1(1P ) productioncross-sections σ(pp→ χb2(1P )X)/σ(pp→ χb1(1P )X) at centre-of-mass energies of

√s = 7

and 8 TeV in the rapidity range 2.0 < y < 4.5 as a function of the Υ (1S) transversemomentum from 5 to 25 GeV/c. The full LHCb sample is used, corresponding to anintegrated luminosity of 3.0 fb−1. The observation in LHCb data of the recently observedχb(3P ) state [14, 15] is also presented. The measurement of its mass and of the masssplitting between the χbJ(1P ) states (J = 1 and J = 2) provide useful information fortesting QCD models [16–18].

The kinematically allowed transitions χb(1P )→ Υ (1S)γ, χb(2P )→ Υ (1S)γ, χb(3P )→Υ (1S)γ and χb(3P )→ Υ (2S)γ are studied. The Υ (mS) (m = 1, 2) meson is reconstructedin the dimuon final state and only photons that convert in the detector material are used.The converted photons are reconstructed using e+ and e− tracks, allowing a separation ofthe χb1 and χb2 mass peaks, due to the improved energy resolution of converted photonswith respect to that of photons identified with the calorimeter. Any contribution from theχb0 mesons decays is neglected, as their radiative decay rate is expected to be suppressedby an order of magnitude compared to that of the χb2 meson [17,19].

1

2 Detector and data samples

The LHCb detector [20] is a single-arm forward spectrometer covering the pseudorapidityrange 2 < η < 5, designed for the study of particles containing b or c quarks. Thedetector includes a high-precision tracking system consisting of a silicon-strip vertexdetector (VELO) surrounding the pp interaction region, a large-area silicon-strip detectorstation located upstream of a dipole magnet with a bending power of about 4 Tm, andthree stations of silicon-strip detectors and straw drift tubes placed downstream of themagnet. The tracking system provides a measurement of momentum, p, with a relativeuncertainty that varies from 0.4% at low momentum to 0.6% at 100 GeV/c. The totalmaterial before the first tracking station corresponds to about 25% of a radiation length.The minimum distance of a track to a primary vertex, the impact parameter, is measuredwith a resolution of (15 + 29/pT)µm, where pT is in GeV/c. Different types of chargedhadrons are distinguished using information from two ring-imaging Cherenkov detectors.Photon, electron and hadron candidates are identified by a calorimeter system consistingof scintillating-pad and preshower detectors, an electromagnetic calorimeter (ECAL) anda hadronic calorimeter. The reconstruction of converted photons is described in Sec. 3.Muons are identified by a system composed of alternating layers of iron and multiwireproportional chambers.

The LHCb coordinate system is right-handed with its origin at the nominal interactionpoint, the z axis aligned along the beam line towards the magnet and the y axis pointingupwards. The magnetic field is oriented along the y axis.

The trigger consists of a hardware stage, based on information from the calorimeterand muon systems, followed by a software stage, which applies a full event reconstruction.Events used in this analysis are first required to pass a hardware trigger that selects muoncandidates with pT > 1.76 GeV/c or dimuon candidates with a product of their pT largerthan (1.6 GeV/c)2. In the software trigger both muons are required to have pT > 0.5 GeV/c,total momentum p > 6 GeV/c, and dimuon invariant mass greater than 4.7 GeV/c2.

In the simulation, pp collisions are generated using Pythia [21] with a specific LHCbconfiguration [22]. Decays of hadronic particles are described by EvtGen [23], in whichfinal state radiation is generated using Photos [24]. The interaction of the generatedparticles with the detector and its response are implemented using the Geant4 toolkit [25]as described in Ref. [26]. The simulated samples consist of events containing at least oneΥ meson that is forced to decay to two muons. In a sample used for background studies,no restriction on the Υ meson production mechanism is imposed. This sample is referredto as inclusive Υ in the following. In another sample, used for the estimation of signalefficiencies and parametrisation, the Υ is required to originate from a χb meson.

3 Event reconstruction and selection

The reconstruction and selection of χb candidates closely follows Ref. [13]. Photons thatconvert in the detector material are reconstructed from pairs of oppositely charged electroncandidates. Since the acceptance is lower for photons that convert in the VELO and the

2

energy resolution is worse, only γ → e+e− candidates without VELO hits are considered.This selection strongly favours conversions that occur between the downstream end of theVELO and the first tracking station upstream of the magnet. The e+e− candidates arerequired to be within the ECAL acceptance and to produce electromagnetic clusters thathave compatible coordinates in the non bending plane. A bremsstrahlung correction isapplied to each electron track: any photon whose position in the ECAL is compatible witha straight line extrapolation of the electron track from the first tracking station is selectedand its energy is added to the electron energy from the reconstructed track. If the samebremsstrahlung candidate is found for both the e+ and the e−, the photon energy is addedrandomly to one of the tracks. The e+ and e− tracks (corrected for bremsstrahlung) arethen extrapolated backwards in order to determine the conversion point and a vertex fit isperformed to reconstruct the photon momentum. The transverse momentum of the photoncandidate (pγT) is required to be larger than 600 MeV/c and the invariant mass of thee+e− pair is required to be less than 50 MeV/c2, which removes most of the combinatorialbackground. The resulting purity of the photon sample is determined from simulation tobe about 99%.

The Υ candidate is reconstructed in its decay to the µ+µ− final state. Each track mustbe identified as a muon with pT > 2 GeV/c and p > 8 GeV/c. The two muons must originatefrom a common vertex with vertex fit χ2/ndf smaller than 25. Only Υ candidates withtransverse momentum (pΥT) greater than 4 GeV/c are kept. Figure 1 shows the invariantmass of Υ candidates. The mass resolution is about 43 MeV/c2. The accepted mass rangesfor the Υ (1S) and for the Υ (2S) candidates are given in Table 1.

The Υ and γ candidates are each associated with the primary vertex (PV) relativeto which they have the smallest impact parameter χ2, defined as the difference betweenthe χ2 of the PV reconstructed with and without the considered tracks. They are thencombined to form a χb candidate. The χb decay time has to be smaller than 0.1 ps.Loose requirements are applied in order to reject combinatorial background and poorlyreconstructed candidates using the following variables: the difference in z-positions of theprimary vertices associated with the Υ and γ candidates, the χ2 of the χb candidate vertexfit and the difference between the χ2 of the PV fitted with and without the χb candidate.These requirements remove about 30% of the background and 8% of the signal. The cosineof the angle between the photon momentum in the χb rest frame and the χb momentum isrequired to be positive. This requirement halves the background while preserving 92% ofthe signal. The χb candidates are selected in the rapidity range 2.0 < y < 4.5.

The χb candidates’ mass is defined as m∗(µ+µ−γ) ≡ m(µ+µ−γ)−m(µ+µ−) +m(Υ ),where m(Υ (1S)) = 9460.3± 0.3 MeV/c2 and m(Υ (2S)) = 10023.3± 0.3 MeV/c2 are theknown Υ mass values [19]. This allows a nearly exact cancellation of the uncertainty dueto the Υ mass resolution and any possible bias on the Υ candidates mass. The χb massresolution is therefore dominated by the resolution on the photon energy. The requirementson pΥT and pγT and the Υ signal mass ranges used for each χb(nP )→ Υ (mS)γ decay modeare given in Table 1.

3

Table 1: Selection criteria for each χb(nP )→ Υ(mS)γ transition. SB indicates sideband.

(n,m) (1,1) (2,1) (3,1) (3,2)

pΥT ( GeV/c) > 4.0 > 4.0 > 5.0 > 6.0

pγT ( GeV/c) > 0.6 > 0.9 > 1.3 > 0.7

Υ mass range ( MeV/c2) 9360 < m(µ+µ−) < 9560 9960 < m(µ+µ−) < 10100

Low mass SB range ( MeV/c2) 9000 < m(µ+µ−) < 9200 9650 < m(µ+µ−) < 9850

High mass SB range ( MeV/c2) 9650 < m(µ+µ−) < 9850 10150 < m(µ+µ−) < 10250

]2c) [MeV/-µ+µ(m9000 9500 10000 10500 11000

)2 cC

andi

date

s / (

10 M

eV/

0

500

1000

1500

2000LHCb

Figure 1: Invariant dimuon mass of the Υ candidates after the event selection requirements andbefore the Υ mass range requirement. The distribution is fitted with the sum (blue line) of adouble-sided Crystal Ball function for each Υ state (dashed red line for Υ (1S), dotted pink linefor Υ (2S), dash-dotted green line for Υ (3S)) and a second-order polynomial for the background(not shown). The hatched red vertical bands show the signal regions and the hatched blue verticalbands show the mass sidebands used for background studies.

4 Sample composition and fit model

Two background sources are considered in the sample of χb candidates. One source is thenon-Υ background originating mainly from the Drell-Yan process where the dimuon pairis combined with a photon. The second source is the combinatorial background wherea genuine Υ is combined with a random photon. The functions used for the fits are thesums of a background and signal functions.

The χb1 and χb2 peaks are each parametrised with a double sided Crystal Ball (CB)

4

function [27]:

CBi(m∗) ∝ exp(−1

2(m

∗−mi

σi)2) if − αL <

m∗ −mi

σi< αR

CBi(m∗) ∝ (nL/αL)

nLexp(− 12α2L)

(nL/αL−αL−(m∗−mi)/σi)nL

ifm∗ −mi

σi< −αL (1)

CBi(m∗) ∝ (nR/αR)nRexp(− 1

2α2R)

(nR/αR−αR+(m∗−mi)/σi)nR

ifm∗ −mi

σi> αR,

where the index i = 1(2) refers to the χb1 (χb2) CB function. The CB left tail accounts forevents with unreconstructed bremsstrahlung, while the right tail accounts for events withovercorrected bremsstrahlung. Simulation shows that the same tail parameters αR andnL,R can be used for all the χbi(nP ) states, nL = nR = 2.5 and αR = 1.0, while differentvalues of αL have to be used: αL = 0.20, 0.25 and 0.30, for the χbi(1P ), χbi(2P ) andχbi(3P ) shapes, respectively. Since in the study of χc states it was found that the CBtail parameters were similar in data and simulation [13], the values found with simulationare used for the χb. The CB width, σ, increases with the mass difference between theconsidered χb and Υ states. Fits to the mass distributions of χb(1P ) → Υ (1S)γ andχb(2P )→ Υ (1S)γ candidates indicate that the width is 10%− 20% larger in data than insimulation. Therefore, the CB width is fixed to the value found with simulated eventsincreased by 10% and it is varied by ±10% for studies of the systematic effects.

The shape of the non-Υ background and its amplitude are estimated using the Υ masssidebands shown in Fig. 1 and given in Table 1. The mass distribution of these candidatesis fitted with an empirical function

fbkg(m∗) ∝ arctan

(m∗ −m0

c

)+ b

(m∗

m0

− 1

)+ a , (2)

where m0, a, b and c are free parameters. This function is then used to parametrise thenon-Υ background contribution with all parameters fixed to the fitted values. The shapeof the combinatorial background is estimated using the inclusive Υ simulated sample andparametrised with Eq. (2). All parameters are fixed to the values found with simulationexcept for the normalisation. In the case of the χb(3P )→ Υ (2S)γ transition, this shapedoes not reproduce the data properly and the value of the m0 parameter is therefore leftfree in the fit. This discrepancy is due to mismodeling of the pΥT spectrum in simulationand is accounted for in the systematic uncertainties.

The fits have at most five free parameters: the mean mass value for the χb1 peak m1,the mass difference between the χb2 and χb1 peaks ∆m12, the normalisation of the χb1CB function, the ratio of the χb2 to χb1 CB amplitudes r12, and the normalisation of thecombinatorial background.

5

5 χb meson masses

5.1 Mass measurements

The masses of the χb mesons are determined using unbinned maximum likelihood fits tothe χb mass distributions as described in Sec. 4. Figures 2 (a) and (b) show the massdistributions for the χb(1P )→ Υ (1S)γ and χb(2P )→ Υ (1S)γ decays with the fit resultsoverlaid. Table 2 reports the resulting mass determinations for these states compared to theworld average values [19]. A small bias is expected on the measured masses, attributed tounreconstructed bremsstrahlung of the e+e− pair. This bias is proportional to the Q-valueof the transition and is expected, from simulation, to be about −0.5 and −1.5 MeV/c2

for the χb(1P )→ Υ (1S)γ and χb(2P )→ Υ (1S)γ decays, respectively. The measurementsgiven in Table 2 are not corrected for this bias and are consistent with such a bias. Theχb(3P ) mass measured using the χb(3P )→ Υ (mS)γ transitions is therefore corrected forthe bias estimated with simulation, −3.0± 2.0 MeV/c2 and −0.5± 0.5 MeV/c2 for m = 1and m = 2, respectively, where the uncertainties cover possible discrepancies between dataand simulation.

In the case of the χb(3P ) meson, the mass splitting and the relative yields are alsofixed, as the spin-1 and spin-2 peaks cannot be separated. Theory predictions vary from 9to 12 MeV/c2 [16, 17] for ∆m12 and this parameter is fixed to 10.5 MeV/c2. The value ofr12 is fixed based on theoretical predictions [17] and our experimental measurement. Itcan be expressed as the product of the ratio of branching fractions to Υγ and of the ratioof production cross-sections of the χb2(3P ) and χb1(3P ) states. Predictions for branchingfractions are found in Refs. [17, 18]. The predictions from Ref. [17] agree well with theexperimental measurements for the χb(1P ) and the χb(2P ) mesons. The model of Ref. [17]predicts similar values for the two transitions, B(χb2(3P ) → Υ (mS)γ))/B(χb1(3P ) →Υ (mS)γ) ≈ 0.47 (m = 1, 2). According to Ref. [8] the ratio of production cross-sections isexpected to be the same for the χb(3P ) and χb(1P ) mesons and thus, using the measurementdetailed in Sec. 6, we obtain σ(χb2(nP ))/σ(χb1(nP )) = 0.9± 0.2.

To summarise, the value r12 = 0.47 × 0.9 = 0.42 is used in the fits to the massdistributions associated with the transitions of the χb(3P ) meson to Υ (1S) and Υ (2S)mesons. Table 3 gives the result of the fits to the mass distributions for the χb(3P ) →Υ (1S)γ and χb(3P )→ Υ (2S)γ transitions. A simultaneous fit to these two distributions isalso performed and the result is reported in the last column of Table 3. Figure 2 shows theresults of these fits. The χb(3P )→ Υ (1S)γ and χb(3P )→ Υ (2S)γ decays are seen with astatistical significance, determined from the likelihood ratio of the fits with backgroundonly and with signal plus background hypotheses, of 6.0σ and 3.6σ respectively. Thetotal statistical significance determined with the simultaneous fit is 7σ. No systematicuncertainty is included in the estimate of the significance.

6

]2c)) [MeV/1S(Υ(m)+µµ(m)-γµµ(m9750 9800 9850 9900 9950

)2 cC

andi

date

s / (

3.0

MeV

/

0

20

40

60

80

100

120

(a) γ)1S(Υ→)1P(b

χ LHCb

]2c)) [MeV/1S(Υ(m)+µµ(m)-γµµ(m10100 10200 10300 10400

)2 cC

andi

date

s / (

5.0

MeV

/

0

10

20

30

40

50

60

70

80

90

(b) γ)1S(Υ→)2P(b

χ LHCb

]2c)) [MeV/1S(Υ(m)+µµ(m)-γµµ(m10400 10500 10600 10700 10800

)2 cC

andi

date

s / (

6.0

MeV

/

0

5

10

15

20

25

30

35

40

(c) γ)1S(Υ→)3P(b

χ LHCb

]2c)) [MeV/2S(Υ(m)+µµ(m)-γµµ(m10400 10500 10600 10700 10800

)2 cC

andi

date

s / (

6.0

MeV

/

0

5

10

15

20

25

(d) γ)2S(Υ→)3P(b

χLHCb

]2c)) [MeV/1S(Υ(m)+µµ(m)-γµµ(m10400 10500 10600 10700 10800

)2 cC

andi

date

s / (

6.0

MeV

/

0

5

10

15

20

25

30

35

40

(e) γ)1S(Υ→)3P(b

χ LHCb

]2c)) [MeV/2S(Υ(m)+µµ(m)-γµµ(m10400 10500 10600 10700 10800

)2 cC

andi

date

s / (

6.0

MeV

/

0

5

10

15

20

25

(f) γ)2S(Υ→)3P(b

χLHCb

Figure 2: Distribution of m∗(µ+µ−γ) ≡ m(µ+µ−γ)−m(µ+µ−) +m(Υ ) for χb candidates withfit projections overlaid for (a) χb(1P )→ Υ (1S)γ, (b) χb(2P )→ Υ (1S)γ, (c,e) χb(3P )→ Υ (1S)γand (d,f) χb(3P )→ Υ (2S)γ channels. The result of the simultaneous fit to the χb(3P )→ Υ (1S)γand χb(3P )→ Υ (2S)γ mass distributions is shown in (e) and (f). The cyan dotted line showsthe non-Υ background, the magenta dashed line shows the combinatorial background, the reddashed line the χb1 contribution, the green dash-dotted line the χb2 contribution, and the bluefull line the sum of all these contributions. 7

Table 2: Fitted values of the χb(nP ) (n = 1, 2) masses (in MeV/c2) from the χb(nP )→ Υ (1S)γtransitions, compared to the world average values. The uncertainties are statistical only.

(n,m) (1,1) (2,1)

m1 9892.3± 0.5 10254.7± 1.3

m1 world average 9892.8± 0.4 10255.5± 0.6

∆m12 19.81± 0.65 12.3± 2.6

∆m12 world average 19.43± 0.37 13.5± 0.6

Table 3: Fitted values of the χb(3P ) mass (in MeV/c2) for the χb(3P ) → Υ (mS)γ (m = 1, 2)transitions. The last column gives the result of the simultaneous fit to the two transitions. Thevalues are corrected for the mass bias (−3 MeV/c2 and −0.5 MeV/c2 for the Υ (1S) and Υ (2S)transitions, respectively). The last row gives the total χb yields. The uncertainties are statisticalonly.

(n,m) (3,1) (3,2) (3,1)+(3,2)

m1 10509.0+5.0−2.6 10518.5+1.9

−1.3 10515.7+2.2−3.9

∆m12 10.5 (fixed) 10.5 (fixed) 10.5 (fixed)

N(χb) 107± 19 41± 12 169± 25

5.2 Systematic uncertainties

The systematic uncertainties on the measurement of the χb(nP ) (n = 1, 2) mass splittingand of the χb(3P ) mass are detailed as follows.

First the systematic uncertainties related to the signal parametrisation are considered.The χb0 contribution is expected to be small because its branching fraction to Υ (1S)γis less than 2% for χb(1P ) and χb(2P ) mesons [19]. In order to estimate the systematicuncertainty due to the presence of a χb0 or another unknown state, a third CB function isadded to the fit, with a peak position fixed to the world average value for the χb(nP ) forn = 1, 2 and left free for the χb(3P ). The resulting yield of χb0 mesons is compatible withzero. The Gaussian width of the CB function is varied within ±10% to cover possibledifferences between data and simulation. For these two fit variations, the differencesbetween results of the nominal and alternative fits are taken as systematic uncertainties,added in quadrature and referred to as signal uncertainty in Table 4.

Imperfect modelling of the background is also considered as a possible source ofsystematic uncertainty. The normalisation of the non-Υ background is varied within theuncertainty of the estimated number of background events under the Υ peak (typically 10%).Negligible variations are observed when the shape of this background is determined usingonly the low or the high mass sideband. Therefore no systematic uncertainty is assigned

8

Table 4: Summary of the systematic uncertainties on the χb(nP ) (n = 1, 2) mass splitting andon the χb1(3P ) mass in MeV/c2. The last column refers to the simultaneous fit to the twotransitions.

∆m12(1P) ∆m12(2P) m(χb1(3P)) m(χb1(3P)) m(χb1(3P))

from Υ (1S) from Υ (2S) combined

Signal ±0.16 ±0.5 ±0.3 ±0.1 ±0.6

Background ±0.08 ±0.3 ±0.2 ±0.1 ±0.2

Bias ±0.10 ±0.1 ±2.0 ±0.5 +1.2−1.6

r12 - - +0.7−0.4

+0.1−0.2

+0.6−1.1

∆m12 - - ±1.2 ±0.1 ±0.3

m(Υ ) - - ±0.3 ±0.3 ±0.3

Total ±0.20 ±0.6 +2.5−2.4 ±0.6 +1.5

−2.1

from the non-Υ background modelling. The shape of the combinatorial background isparticularly sensitive to the m0 value, therefore this parameter is varied within twice itsuncertainty. In the case of the χb(3P ) → Υ (2S)γ transition, where the value of m0 isleft free in the fit, the value found in simulation is used in an alternative fit, leading to achange of 0.1 MeV/c2 on the χb(3P ) mass. The fit range is also varied by ±100 MeV/c2 onboth sides. The differences between results of the nominal fit and these two alternative fitsare taken as systematic uncertainties and added in quadrature. The resulting systematicuncertainty is referred to as background uncertainty.

The uncertainty on the mass bias (2.0 and 0.5 MeV/c2 for the χb(3P ) mass measurementbased on the transition to Υ (1S) and Υ (2S) respectively) is assigned as systematicuncertainty. For the simultaneous fit to the two χb(3P ) mass distributions, the two biasesare varied independently within their uncertainties and the largest variation is taken assystematic uncertainty. A small bias is expected on the χb(1P ) mass splitting and isestimated to be at most 0.10 MeV/c2, which is added as a systematic uncertainty. Nosignificant bias on the χb(nP ) mass splitting is expected from the fit procedure.

For the determination of the χb(3P ) mass, the ∆m12 and r12 parameters are fixed inthe nominal fit. They are varied independently within their expected uncertainties inorder to evaluate the associated systematic uncertainties. The mass splitting, ∆m12, isvaried between 9 and 12 MeV/c2 and the r12 parameter is varied by ±30%, which includestheoretical uncertainties and the precision on the χb(1P ) production ratio measured inthis work and used to estimate r12.

Finally, the 0.3 MeV/c2 uncertainty on the world-average values of the Υ (1S) and Υ (2S)masses is added as a systematic uncertainty to the χb(3P ) mass.

Table 4 lists the individual systematic uncertainties. The total systematic uncertaintyis the quadratic sum of all individual uncertainties.

9

Table 5: Relative rate of χb1(1P ) and χb2(1P ) production and ratio of total efficiency (in thethree pΥT ranges). Uncertainties only refer to the statistical contributions.

pΥT bin ( GeV/c) 5–10 10–15 15–25

N(χb2)/N(χb1) 0.61± 0.15 0.57± 0.15 0.52± 0.15

ε(χb1)/ε(χb2) 1.01± 0.03 0.90± 0.05 1.18± 0.11

6 Relative rate of χb2(1P ) and χb1(1P ) production

6.1 Measurement of the relative rates

The production cross-section ratio of the χb2(1P ) and χb1(1P ) mesons is measured in threepΥT ranges of different size (the bin limits are given in Table 5) using

σ(χb2)

σ(χb1)=Nχb2

Nχb1

εχb1

εχb2

B(χb1 → Υ (1S)γ)

B(χb2 → Υ (1S)γ), (3)

where σ(χbJ) (J = 1, 2) is the χbJ(1P ) meson production cross-section; NχbJis the

χbJ(1P ) yield; εχbJis the efficiency to trigger, detect, reconstruct and select a χbJ meson

including the contribution from the approximately 20% probability for a photon to convertupstream of the first tracking station; and B(χb1(1P ) → Υ (1S)γ) = (33.9 ± 2.2)% andB(χb2(1P )→ Υ (1S)γ) = (19.1± 1.2)% are the known branching fractions [19] .

The inefficiency is dominated by the converted photon acceptance and reconstruction:low-energy photons produce low-energy electrons, which have a high chance to escape thedetector due to the magnetic field. The efficiency of converted photon reconstruction andselection relative to non-converted photons is measured in Ref. [13] and ranges from about1% at pγT of 600 MeV/c to 3% at pγT of 2000 MeV/c. These numbers include the conversionprobability. Due to the correlation between the pT of the photon and that of the Υ meson,the efficiency is lower for low pΥT. The ratio of efficiencies is given in Table 5. This ratiodiffers from unity because the pΥT spectrum is different for χb1 and χb2 in Pythia 8, asexpected [8]. The ratio of efficiencies is also calculated assuming equal pT spectra. It isstill slightly different from unity due to the small difference in the χb1 and χb2 masses.

The mass distribution of χb candidates in each pΥT bin is fitted using the signal andbackground functions described in Sec. 4. In these fits the mass of the χb1 state and themass splitting are fixed to the values found from the fit to the whole data set (see Table 2)and then varied within their uncertainties for systematic studies. The result of the fit isshown in Fig. 3 and the ratio of yields is given in Table 5 for each pΥT range.

6.2 Systematic uncertainties

The same sources of systematic uncertainties as for the mass measurements (see Sec. 5.2)are investigated and reported in Table 6. Additional systematic checks relevant only forthe relative rates of χb2(1P ) and χb1(1P ) are detailed as follows.

10

]2c)) [MeV/1S(Υ(m)+µµ(m)-γµµ(m9750 9800 9850 9900 9950

)2 cC

andi

date

s / (

4.0

MeV

/

0

10

20

30

40

50

60

70

80

γ)1S(Υ→)1P(b

χ

c< 10 GeV/ΥT

p(a) 5 < LHCb

]2c)) [MeV/1S(Υ(m)+µµ(m)-γµµ(m9750 9800 9850 9900 9950

)2 cC

andi

date

s / (

4.0

MeV

/

0

10

20

30

40

50

γ)1S(Υ→)1P(b

χ

c< 15 GeV/ΥT

p(b) 10 < LHCb

]2c)) [MeV/1S(Υ(m)+µµ(m)-γµµ(m9750 9800 9850 9900 9950

)2 cC

andi

date

s / (

4.0

MeV

/

0

5

10

15

20

25

30

35

γ)1S(Υ→)1P(b

χ

c< 25 GeV/ΥT

p(c) 15 < LHCb

Figure 3: Distribution of m∗(µ+µ−γ) ≡ m(µ+µ−γ)−m(µ+µ−) +m(Υ ) for χb(1P ) candidateswith fit projections overlaid for each of the three ranges in pΥT: (a) 5–10 GeV/c, (b) 10–15 GeV/cand (c) 15–25 GeV/c. The cyan dotted line show the non-Υ background, the magenta dashedline shows the combinatorial background, the red dashed line the χb1 contribution, the greendash-dotted line the χb2 contribution and the blue full line the sum of all these contributions.

The dominant uncertainty on the ratio of efficiencies is due to the limited knowledge ofthe efficiency for reconstructing converted photons, which is estimated following Ref. [13]and amounts to 4% on the relative rates. This uncertainty is added in quadrature to theuncertainty due to the limited size of the simulated sample.

Due to the large size of the pT bins, the efficiency depends on the choice of the pTspectrum of χb production as discussed in Sec. 6.1. In order to assess the uncertaintydue to the shape of the pT spectrum, the simulated χb2 (χb1) spectrum is changed tobe identical to the simulated χb1 (χb2) spectrum. The relative difference in the ratio ofefficiencies is taken as a systematic uncertainty.

The fit is also performed on simulated data and a mean bias of (−4± 4)% is observed

11

Table 6: Summary of the systematic uncertainties on the χb(1P ) relative rates, expressed asfractions of the relative rate.

pΥT bin ( GeV/c) 5–10 10–15 15–25

Signal ±0.05 ±0.08 ±0.08

Background ±0.06 ±0.04 ±0.03

Fit bias ±0.04 ±0.04 ±0.04

Efficiency ±0.05 ±0.06 ±0.10

pT model −0.13 −0.05 −0.04

Total +0.10−0.16

+0.12−0.13

+0.13−0.14

on the relative yields. A systematic uncertainty of ±4% is added to take the possible biasinto account. The values of the χb1(1P ) mass m1 and of the mass splitting ∆m12 are alsovaried within their uncertainties from Table 2. The variation of the result is taken assystematic uncertainty and is added in quadrature to the uncertainty referred to as signal.

Table 6 lists the systematic uncertainties on the relative rates. The total systematicuncertainty is the quadratic sum of all individual uncertainties. The ratio of cross-sectionsis also affected by the uncertainties on the branching fraction of χb(1P )→ Υ (1S)γ, leadingto an additional systematic uncertainty of 9.0% [19].

7 Results

The results for the χb(1, 2P ) mass splittings between the J = 1 and J = 2 states

∆m12(1P ) = 19.81± 0.65(stat)± 0.20(syst) MeV/c2

∆m12(2P ) = 12.3± 2.6(stat)± 0.6(syst) MeV/c2

are in agreement with the world average values, ∆m12(1P ) = 19.43 ± 0.37 MeV/c2 and∆m12(2P ) = 13.5± 0.6 MeV/c2 [19]. A measurement of the χb1(3P ) mass,

m(χb1(3P )) = 10509.0+5.0−2.6(stat)+2.5

−2.4(syst) MeV/c2,

is derived from the radiative transition to the Υ (1S) meson, where the χb(3P ) is observedwith a statistical significance of 6.3σ. Another measurement,

m(χb1(3P )) = 10518.5+1.9−1.3(stat)± 0.6(syst) MeV/c2,

is derived from the radiative transition to the Υ (2S) transition, where evidence is foundfor the χb(3P ) with a statistical significance of 4.0σ. The systematic uncertainty relatedto r12 is largely uncorrelated between the Υ (2S) and Υ (1S) channels as the branchingfractions of χbi to final states involving Υ (1S) and to Υ (2S) mesons can be different. By

12

Table 7: Relative production cross section of χb1 to χb2 mesons for the 1P state for each pΥT bin.The first uncertainty is statistical, the second is the systematic uncertainty and the third is dueto the uncertainty on the branching fractions.

pΥT bin ( GeV/c) σ(χb2)/σ(χb1)

5–10 1.09± 0.27(stat)+0.11−0.18(syst)± 0.10 (B)

10–15 0.91± 0.24(stat)+0.10−0.12(syst)± 0.08 (B)

15–25 1.09± 0.31(stat)+0.14−0.15(syst)± 0.10 (B)

treating the systematic uncertainties related to the mass splitting and to the mass bias asfully correlated and all other uncertainties as uncorrelated, the two results for the χb1(3P )mass differ by 9.3+3.2

−5.2(stat)± 2.0(syst) MeV/c2. A combined fit is performed leading to

m(χb1(3P )) = 10515.7+2.2−3.9(stat)+1.5

−2.1(syst) MeV/c2.

In these measurements, the relative rate of χb2 to χb1, is assumed to be r12 = 0.42 for thetwo transitions. The χb1(3P ) mass result exhibits a linear dependence on the assumedfraction of χb1 decays and varies from 10517.6 to 10515.2 when the χb2/χb1 yield ratiochanges from zero to 0.5. This result is compatible with and significantly more precise thanthat reported by the ATLAS experiment, m(χb(3P )) = 10530± 5(stat)± 9(syst) MeV/c2

for r12 = 1 and ∆m12 = 12 MeV/c2, where m(χb(3P )) is the average mass of χb1 and χb2states [14]. The LHCb result is also compatible with the D0 measurement, m(χb(3P )) =10551± 14(stat)± 17(syst) MeV/c2 [15].

The ratio of the χb2 to χb1 production cross-sections is measured in three pΥT rangesusing Eq. (3). The results are given in Table 7. Figure 4 (a) shows a comparison of themeasured values with LO NRQCD predictions from Ref. [8]. The common systematicuncertainty (9.0%) due to the branching fraction of χb → Υ (1S)γ is not shown. Theorypredicts the χc and χb ratio of production cross-section to be the same when the χc pTvalue is scaled by the ratio of the χb and χc masses [8]. As the χb(χc) and Υ (J/ψ ) pT arestrongly correlated, this is assumed to be valid when replacing the χb(χc) by the Υ (J/ψ )pT. The measurement obtained by LHCb for the χc production ratio [13] with the pT axisscaled accordingly is also shown for comparison. The χb results are in good agreement withthe scaled χc results. These results are not precise enough to establish the deviation fromunity predicted by theory at low pT, but the agreement is better with a flat dependence.Our results are also in agreement with the CMS preliminary results [28] as shown on Fig. 4(b).

8 Conclusion

The radiative decays of χb mesons to Υ mesons are reconstructed with photons convertingin the detector material. Owing to the good energy resolution obtained with converted

13

]c [GeV/ΥT

p6 8 10 12 14 16 18 20 22 24

)b1χ(σ

) /

b2χ(σ

0

0.5

1

1.5

2

2.5

3b

χLHCb

scaledc

χLHCb

LO NRQCD

<4.5y2.0<

(a)

]c [GeV/ΥT

p5 10 15 20 25 30 35 40

)b1χ(σ

) /

b2χ(σ

0

0.5

1

1.5

2b

χLHCb

scaledc

χLHCb

bχCMS

unpolarisedb

χ

(b)

Figure 4: Relative production cross-sections of χb1 to χb2 mesons as a function of pΥT. Panel (a)shows the comparison of this measurement (the hatched rectangles show the statistical uncer-tainties and the red crosses the total experimental uncertainty) to the LO NRQCD prediction [8](green band), and to the LHCb χc result (blue crosses), where the pT axis has been scaled bym(χb)/m(χc) = 2.8. Panel (b) compares this measurement (empty squares) to CMS preliminaryresults [28] (filled squares) and to the LHCb χc results (empty circles). The error bars are thetotal experimental uncertainties and do not include the uncertainties on the branching fractions.

photons, the χb(1P ) states are separated and the mass splitting between the χb1(1P ) andχb2(1P ) is measured. The χb(3P ) mass is measured using its radiative decays to the Υ (1S)and Υ (2S) mesons yielding,

m(χb1(3P )) = 10515.7+2.2−3.9(stat)+1.5

−2.1(syst) MeV/c2.

This result is compatible with the measurement performed by LHCb with the radia-tive decays to the Υ (3S) meson that uses non-converted photons [29], m(χb1(3P )) =10511.3 ± 1.7(stat) ± 2.5(syst) MeV/c2. Since the photon reconstruction is based ondifferent subdetectors, the experimental systematic uncertainties are uncorrelated, whilethe uncertainty related to the model used for summing the J = 1 and J = 2 contributions(parametrised with the mass splitting ∆m12 and the relative rates r12) are fully correlated.The combined value is

m(χb1(3P )) = 10512.1± 2.1(exp)± 0.9(model) MeV/c2,

where the first uncertainty is experimental (statistical and systematic) and the secondaccounts for varying ∆m12 from 9.0 to 12.0 MeV/c2 and r12 by ±30%. This result is inagreement with the theoretical prediction of Ref. [17], m(χb1(3P )) = 10516 MeV/c2.

The first measurement of the relative ratio of χb1 to χb2 cross-sections is performedfor the χb(1P ) state in the rapidity range 2.0 < y < 4.5 for pΥT from 5 to 25 GeV/c. Theresults agree with CMS preliminary results [28] and with theory expectation based onLHCb χc measurements [13]. The data indicate a deviation from the rise predicted by theLO NRQCD model at low pT and show a better agreement with a flat dependence.

14

Acknowledgements

We thank A. Luchinsky and A. Likhoded for providing the LO NRQCD predictions. Weexpress 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); NSFC (China); CNRS/IN2P3 (France);BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO(The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO(Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (UnitedKingdom); NSF (USA). The Tier1 computing centres are supported by IN2P3 (France),KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC(Spain), GridPP (United Kingdom). We are indebted to the communities behind themultiple open source software packages on which we depend. We are also thankful forthe computing resources and the access to software R&D tools provided by Yandex LLC(Russia). Individual groups or members have received support from EPLANET, MarieSk lodowska-Curie Actions and ERC (European Union), Conseil general de Haute-Savoie,Labex ENIGMASS and OCEVU, Region Auvergne (France), RFBR (Russia), XuntaGaland GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851(United Kingdom).

References

[1] R. Baier and R. Ruckl, Hadronic collisions: a quarkonium factory, Z. Phys. C19(1983) 251.

[2] V. Kartvelishvili, A. Likhoded, and S. Slabospitsky, D meson and ψ meson productionin hadronic interactions, Sov. J. Nucl. Phys. 28 (1978) 678.

[3] E. L. Berger and D. Jones, Inelastic photoproduction of J/ψ and Υ by gluons, Phys.Rev. D23 (1981) 1521.

[4] G. T. Bodwin, E. Braaten, and G. Lepage, Rigorous QCD analysis of inclusiveannihilation and production of heavy quarkonium, Phys. Rev. D51 (1995) 1125; G. T.Bodwin, E. Braaten, and G. Lepage, Erratum: Rigorous QCD analysis of inclusiveannihilation and production of heavy quarkonium, Phys. Rev. D55 (1997) 5853.

[5] Y. Q. Ma, K. Wang, and K. T. Chao, QCD radiative corrections to χcJ production athadron colliders, Phys. Rev. D83 (2011) 111503, arXiv:1002.3987.

[6] J.-P. Lansberg, On the mechanisms of heavy-quarkonium hadroproduction, Eur. Phys.J. C61 (2009) 693, arXiv:0811.4005.

[7] J. Campbell, F. Maltoni, and F. Tramontano, QCD corrections to J/ψ and Υ produc-tion at hadron colliders, Phys. Rev. Lett. 98 (2007) 252002, arXiv:hep-ph/0703113.

15

[8] A. Likhoded, A. Luchinsky, and S. Poslavsky, Production of χb-mesons at LHC, Phys.Rev. D86 (2012) 074027, arXiv:1203.4893.

[9] WA11 collaboration, Y. Lemoigne et al., Measurement of hadronic production of theχ++1 (3507) and the χ++

2 (3553) through their radiative decay to J/ψ , Phys. Lett. B113(1982) 509.

[10] HERA-B collaboration, I. Abt et al., Production of the charmonium states χc1 andχc2 in proton nucleus interactions at

√s = 41.6 GeV, Phys. Rev. D79 (2009) 012001,

arXiv:0807.2167.

[11] CDF collaboration, A. Abulencia et al., Measurement ofσχc2B(χc2 → J/ψγ)/σχc1B(χc1 → J/ψγ) in pp collisions at

√s = 1.96 TeV,

Phys. Rev. Lett. 98 (2007) 232001, arXiv:hep-ph/0703028.

[12] CMS collaboration, S. Chatrchyan et al., Measurement of the relative prompt produc-tion rate of χc2 and χc1 in pp collisions at

√s = 7 TeV, Eur. Phys. J. C72 (2012)

2251, arXiv:1210.0875.

[13] LHCb collaboration, R. Aaij et al., Measurement of the relative rate of prompt χc0,χc1 and χc2 production at

√s = 7 TeV, JHEP 10 (2013) 115, arXiv:1307.4285.

[14] ATLAS collaboration, G. Aad et al., Observation of a new χb state in radiativetransistions to Υ (1S) and Υ (2S) at ATLAS, Phys. Rev. Lett 108 (2012) 152001,arXiv:1112.5154.

[15] D0 collaboration, V. Abazov et al., Observation of a narrow mass state decayinginto Υ(1S) + γ in pp collisions at

√s = 1.96 TeV, Phys. Rev. D86 (2012) 031103,

arXiv:1203.6034.

[16] L. Motyka and K. Zalewski, Mass spectra and leptonic decay widths of heavy quarkonia,Eur. Phys. J. C4 (1998) 107.

[17] W. Kwong and J. Rosner, D-wave quarkonium levels of the Υ family, Phys. Rev. D38(1988) 279.

[18] J. Ferretti and G. Galata, Quark structure of the X(3872) and χb(3P ) resonances,arXiv:1401.4431.

[19] Particle Data Group, J. Beringer et al., Review of particle physics, Phys. Rev. D86(2012) 010001, and 2013 partial update for the 2014 edition.

[20] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3(2008) S08005.

16

[21] T. Sjostrand, S. Mrenna, and P. Skands, PYTHIA 6.4 physics and manual, JHEP05 (2006) 026, arXiv:hep-ph/0603175; T. Sjostrand, S. Mrenna, and P. Skands,A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852,arXiv:0710.3820.

[22] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCbsimulation framework, Nuclear Science Symposium Conference Record (NSS/MIC)IEEE (2010) 1155.

[23] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth.A462 (2001) 152.

[24] P. Golonka and Z. Was, PHOTOS Monte Carlo: A precision tool for QED correctionsin Z and W decays, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026.

[25] Geant4 collaboration, J. Allison et al., Geant4 developments and applications, IEEETrans. Nucl. Sci. 53 (2006) 270; Geant4 collaboration, S. Agostinelli et al., Geant4:A simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250.

[26] M. Clemencic et al., The LHCb simulation application, Gauss: design, evolution andexperience, J. Phys.: Conf. Ser. 331 (2011) 032023.

[27] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-primeand Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986,DESY-F31-86-02.

[28] CMS collaboration, Measurement of the σ(χb2(1P ))/σ(χb1(1P )) production crosssection in pp collisions at

√s = 8 TeV, CMS-PAS-BPH-13-005.

[29] LHCb collaboration, R. Aaij et al., Study of χb meson production in pp collisionsat√s=7 and 8 TeV and observation of the decay χb → Υ(3S)γ, arXiv:1407.7734,

submited to Eur. Phys. J. C.

17

LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6, J. Albrecht9,F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P. Alvarez Cartelle37, A.A. Alves Jr25,38,S. Amato2, S. Amerio22, Y. Amhis7, L. An3, L. Anderlini17,g, J. Anderson40, R. Andreassen57,M. Andreotti16,f , J.E. Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38,A. Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S. Bachmann11,J.J. Back48, A. Badalov36, C. Baesso60, W. Baldini16, R.J. Barlow54, C. Barschel38, S. Barsuk7,W. Barter47, V. Batozskaya28, V. Battista39, A. Bay39, L. Beaucourt4, J. Beddow51,F. Bedeschi23, I. Bediaga1, S. Belogurov31, K. Belous35, I. Belyaev31, E. Ben-Haim8,G. Bencivenni18, S. Benson38, J. Benton46, A. Berezhnoy32, R. Bernet40, M.-O. Bettler47,M. van Beuzekom41, A. Bien11, S. Bifani45, T. Bird54, A. Bizzeti17,i, P.M. Bjørnstad54,T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N. Bondar30,38,W. Bonivento15,38, S. Borghi54, A. Borgia59, M. Borsato7, T.J.V. Bowcock52, E. Bowen40,C. Bozzi16, T. Brambach9, J. van den Brand42, J. Bressieux39, D. Brett54, M. Britsch10,T. Britton59, J. Brodzicka54, N.H. Brook46, H. Brown52, A. Bursche40, G. Busetto22,r,J. Buytaert38, S. Cadeddu15, R. Calabrese16,f , M. Calvi20,k, M. Calvo Gomez36,p,P. Campana18,38, D. Campora Perez38, A. Carbone14,d, G. Carboni24,l, R. Cardinale19,38,j ,A. Cardini15, L. Carson50, K. Carvalho Akiba2, G. Casse52, L. Cassina20, L. Castillo Garcia38,M. Cattaneo38, Ch. Cauet9, R. Cenci58, M. Charles8, Ph. Charpentier38, M. Chefdeville4,S. Chen54, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26, K. Ciba38, X. Cid Vidal38,G. Ciezarek53, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47, J. Closier38, V. Coco38, J. Cogan6,E. Cogneras5, L. Cojocariu29, P. Collins38, A. Comerma-Montells11, A. Contu15, A. Cook46,M. Coombes46, S. Coquereau8, G. Corti38, M. Corvo16,f , I. Counts56, B. Couturier38,G.A. Cowan50, D.C. Craik48, M. Cruz Torres60, S. Cunliffe53, R. Currie50, C. D’Ambrosio38,J. Dalseno46, P. David8, P.N.Y. David41, A. Davis57, K. De Bruyn41, S. De Capua54,M. De Cian11, J.M. De Miranda1, L. De Paula2, W. De Silva57, P. De Simone18, D. Decamp4,M. Deckenhoff9, L. Del Buono8, N. Deleage4, D. Derkach55, O. Deschamps5, F. Dettori38,A. Di Canto38, H. Dijkstra38, S. Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Suarez37,D. Dossett48, A. Dovbnya43, K. Dreimanis52, G. Dujany54, F. Dupertuis39, P. Durante38,R. Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49,38, U. Egede53, V. Egorychev31,S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L. Eklund51, I. El Rifai5,Ch. Elsasser40, S. Ely59, S. Esen11, H.-M. Evans47, T. Evans55, A. Falabella14, C. Farber11,C. Farinelli41, N. Farley45, S. Farry52, RF Fay52, D. Ferguson50, V. Fernandez Albor37,F. Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M. Fiore16,f , M. Fiorini16,f , M. Firlej27,C. Fitzpatrick39, T. Fiutowski27, M. Fontana10, F. Fontanelli19,j , R. Forty38, O. Francisco2,M. Frank38, C. Frei38, M. Frosini17,38,g, J. Fu21,38, E. Furfaro24,l, A. Gallas Torreira37,D. Galli14,d, S. Gallorini22, S. Gambetta19,j , M. Gandelman2, P. Gandini59, Y. Gao3,J. Garcıa Pardinas37, J. Garofoli59, J. Garra Tico47, L. Garrido36, C. Gaspar38, R. Gauld55,L. Gavardi9, G. Gavrilov30, A. Geraci21,v, E. Gersabeck11, M. Gersabeck54, T. Gershon48,Ph. Ghez4, A. Gianelle22, S. Gianı39, V. Gibson47, L. Giubega29, V.V. Gligorov38, C. Gobel60,D. Golubkov31, A. Golutvin53,31,38, A. Gomes1,a, C. Gotti20, M. Grabalosa Gandara5,R. Graciani Diaz36, L.A. Granado Cardoso38, E. Grauges36, G. Graziani17, A. Grecu29,E. Greening55, S. Gregson47, P. Griffith45, L. Grillo11, O. Grunberg62, B. Gui59, E. Gushchin33,Yu. Guz35,38, T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S. Hall53,B. Hamilton58, T. Hampson46, X. Han11, S. Hansmann-Menzemer11, N. Harnew55,

18

S.T. Harnew46, J. Harrison54, J. He38, T. Head38, V. Heijne41, K. Hennessy52, P. Henrard5,L. Henry8, J.A. Hernando Morata37, E. van Herwijnen38, M. Heß62, A. Hicheur1, D. Hill55,M. Hoballah5, C. Hombach54, W. Hulsbergen41, P. Hunt55, N. Hussain55, D. Hutchcroft52,D. Hynds51, M. Idzik27, P. Ilten56, R. Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41,P. Jaton39, A. Jawahery58, F. Jing3, M. John55, D. Johnson38, C.R. Jones47, C. Joram38,B. Jost38, N. Jurik59, S. Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38, S. Karodia51,M. Kelsey59, I.R. Kenyon45, T. Ketel42, B. Khanji20, C. Khurewathanakul39, S. Klaver54,K. Klimaszewski28, O. Kochebina7, M. Kolpin11, I. Komarov39, R.F. Koopman42,P. Koppenburg41,38, M. Korolev32, A. Kozlinskiy41, L. Kravchuk33, K. Kreplin11, M. Kreps48,G. Krocker11, P. Krokovny34, F. Kruse9, W. Kucewicz26,o, M. Kucharczyk20,26,38,k,V. Kudryavtsev34, K. Kurek28, T. Kvaratskheliya31, V.N. La Thi39, D. Lacarrere38,G. Lafferty54, A. Lai15, D. Lambert50, R.W. Lambert42, G. Lanfranchi18, C. Langenbruch48,B. Langhans38, T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van Leerdam41, J.-P. Lees4,R. Lefevre5, A. Leflat32, J. Lefrancois7, S. Leo23, O. Leroy6, T. Lesiak26, M. Lespinasse4,B. Leverington11, Y. Li3, T. Likhomanenko63, M. Liles52, R. Lindner38, C. Linn38, F. Lionetto40,B. Liu15, S. Lohn38, I. Longstaff51, J.H. Lopes2, N. Lopez-March39, P. Lowdon40, H. Lu3,D. Lucchesi22,r, H. Luo50, A. Lupato22, E. Luppi16,f , O. Lupton55, F. Machefert7,I.V. Machikhiliyan31, F. Maciuc29, O. Maev30, S. Malde55, A. Malinin63, G. Manca15,e,G. Mancinelli6, A. Mapelli38, J. Maratas5, J.F. Marchand4, U. Marconi14, C. Marin Benito36,P. Marino23,t, R. Marki39, J. Marks11, G. Martellotti25, A. Martens8, A. Martın Sanchez7,M. Martinelli39, D. Martinez Santos42, F. Martinez Vidal64, D. Martins Tostes2, A. Massafferri1,R. Matev38, Z. Mathe38, C. Matteuzzi20, A. Mazurov16,f , M. McCann53, J. McCarthy45,A. McNab54, R. McNulty12, B. McSkelly52, B. Meadows57, F. Meier9, M. Meissner11, M. Merk41,D.A. Milanes8, M.-N. Minard4, N. Moggi14, J. Molina Rodriguez60, S. Monteil5, M. Morandin22,P. Morawski27, A. Morda6, M.J. Morello23,t, J. Moron27, A.-B. Morris50, R. Mountain59,F. Muheim50, K. Muller40, M. Mussini14, B. Muster39, P. Naik46, T. Nakada39,R. Nandakumar49, I. Nasteva2, M. Needham50, N. Neri21, S. Neubert38, N. Neufeld38,M. Neuner11, A.D. Nguyen39, T.D. Nguyen39, C. Nguyen-Mau39,q, M. Nicol7, V. Niess5,R. Niet9, N. Nikitin32, T. Nikodem11, A. Novoselov35, D.P. O’Hanlon48, A. Oblakowska-Mucha27,V. Obraztsov35, S. Oggero41, S. Ogilvy51, O. Okhrimenko44, R. Oldeman15,e,C.J.G. Onderwater65, M. Orlandea29, J.M. Otalora Goicochea2, P. Owen53, A. Oyanguren64,B.K. Pal59, A. Palano13,c, F. Palombo21,u, M. Palutan18, J. Panman38, A. Papanestis49,38,M. Pappagallo51, L.L. Pappalardo16,f , C. Parkes54, C.J. Parkinson9,45, G. Passaleva17,G.D. Patel52, M. Patel53, C. Patrignani19,j , A. Pearce54, A. Pellegrino41, M. Pepe Altarelli38,S. Perazzini14,d, P. Perret5, M. Perrin-Terrin6, L. Pescatore45, E. Pesen66, K. Petridis53,A. Petrolini19,j , E. Picatoste Olloqui36, B. Pietrzyk4, T. Pilar48, D. Pinci25, A. Pistone19,S. Playfer50, M. Plo Casasus37, F. Polci8, A. Poluektov48,34, E. Polycarpo2, A. Popov35,D. Popov10, B. Popovici29, C. Potterat2, E. Price46, J. Prisciandaro39, A. Pritchard52,C. Prouve46, V. Pugatch44, A. Puig Navarro39, G. Punzi23,s, W. Qian4, B. Rachwal26,J.H. Rademacker46, B. Rakotomiaramanana39, M. Rama18, M.S. Rangel2, I. Raniuk43,N. Rauschmayr38, G. Raven42, S. Reichert54, M.M. Reid48, A.C. dos Reis1, S. Ricciardi49,S. Richards46, M. Rihl38, K. Rinnert52, V. Rives Molina36, D.A. Roa Romero5, P. Robbe7,A.B. Rodrigues1, E. Rodrigues54, P. Rodriguez Perez54, S. Roiser38, V. Romanovsky35,A. Romero Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, H. Ruiz36, P. Ruiz Valls64,J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B. Saitta15,e, V. Salustino Guimaraes2,C. Sanchez Mayordomo64, B. Sanmartin Sedes37, R. Santacesaria25, C. Santamarina Rios37,

19

E. Santovetti24,l, A. Sarti18,m, C. Satriano25,n, A. Satta24, D.M. Saunders46, D. Savrina31,32,M. Schiller42, H. Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O. Schneider39,A. Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18, A. Sciubba25, A. Semennikov31,I. Sepp53, N. Serra40, J. Serrano6, L. Sestini22, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f ,Y. Shcheglov30, T. Shears52, L. Shekhtman34, V. Shevchenko63, A. Shires9, R. Silva Coutinho48,G. Simi22, M. Sirendi47, N. Skidmore46, T. Skwarnicki59, N.A. Smith52, E. Smith55,49,E. Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D. Sokoloff57, F.J.P. Soler51, F. Soomro39,D. Souza46, B. Souza De Paula2, B. Spaan9, A. Sparkes50, P. Spradlin51, S. Sridharan38,F. Stagni38, M. Stahl11, S. Stahl11, O. Steinkamp40, O. Stenyakin35, S. Stevenson55, S. Stoica29,S. Stone59, B. Storaci40, S. Stracka23,38, M. Straticiuc29, U. Straumann40, R. Stroili22,V.K. Subbiah38, L. Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V. Syropoulos42,M. Szczekowski28, P. Szczypka39,38, T. Szumlak27, S. T’Jampens4, M. Teklishyn7,G. Tellarini16,f , F. Teubert38, C. Thomas55, E. Thomas38, J. van Tilburg41, V. Tisserand4,M. Tobin39, S. Tolk42, L. Tomassetti16,f , D. Tonelli38, S. Topp-Joergensen55, N. Torr55,E. Tournefier4, S. Tourneur39, M.T. Tran39, M. Tresch40, A. Trisovic38, A. Tsaregorodtsev6,P. Tsopelas41, N. Tuning41, M. Ubeda Garcia38, A. Ukleja28, A. Ustyuzhanin63, U. Uwer11,V. Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37,C. Vazquez Sierra37, S. Vecchi16, J.J. Velthuis46, M. Veltri17,h, G. Veneziano39, M. Vesterinen11,B. Viaud7, D. Vieira2, M. Vieites Diaz37, X. Vilasis-Cardona36,p, A. Vollhardt40,D. Volyanskyy10, D. Voong46, A. Vorobyev30, V. Vorobyev34, C. Voß62, J.A. de Vries41,R. Waldi62, C. Wallace48, R. Wallace12, J. Walsh23, S. Wandernoth11, J. Wang59, D.R. Ward47,N.K. Watson45, D. Websdale53, M. Whitehead48, J. Wicht38, D. Wiedner11, G. Wilkinson55,M.P. Williams45, M. Williams56, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28,M. Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, S. Wu3, K. Wyllie38, Y. Xie61, Z. Xing59,Z. Xu39, Z. Yang3, X. Yuan3, O. Yushchenko35, M. Zangoli14, M. Zavertyaev10,b, L. Zhang59,W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3, A. Zvyagin38.

1Centro Brasileiro de Pesquisas Fısicas (CBPF), Rio de Janeiro, Brazil2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil3Center for High Energy Physics, Tsinghua University, Beijing, China4LAPP, Universite de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France5Clermont Universite, Universite Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France6CPPM, Aix-Marseille Universite, CNRS/IN2P3, Marseille, France7LAL, Universite Paris-Sud, CNRS/IN2P3, Orsay, France8LPNHE, Universite Pierre et Marie Curie, Universite Paris Diderot, CNRS/IN2P3, Paris, France9Fakultat Physik, Technische Universitat Dortmund, Dortmund, Germany10Max-Planck-Institut fur Kernphysik (MPIK), Heidelberg, Germany11Physikalisches Institut, Ruprecht-Karls-Universitat Heidelberg, Heidelberg, Germany12School of Physics, University College Dublin, Dublin, Ireland13Sezione INFN di Bari, Bari, Italy14Sezione INFN di Bologna, Bologna, Italy15Sezione INFN di Cagliari, Cagliari, Italy16Sezione INFN di Ferrara, Ferrara, Italy17Sezione INFN di Firenze, Firenze, Italy18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy19Sezione INFN di Genova, Genova, Italy20Sezione INFN di Milano Bicocca, Milano, Italy21Sezione INFN di Milano, Milano, Italy22Sezione INFN di Padova, Padova, Italy

20

23Sezione INFN di Pisa, Pisa, Italy24Sezione INFN di Roma Tor Vergata, Roma, Italy25Sezione INFN di Roma La Sapienza, Roma, Italy26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland27AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,Krakow, Poland28National Center for Nuclear Research (NCBJ), Warsaw, Poland29Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia35Institute for High Energy Physics (IHEP), Protvino, Russia36Universitat de Barcelona, Barcelona, Spain37Universidad de Santiago de Compostela, Santiago de Compostela, Spain38European Organization for Nuclear Research (CERN), Geneva, Switzerland39Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland40Physik-Institut, Universitat Zurich, Zurich, Switzerland41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands42Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, TheNetherlands43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine44Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine45University of Birmingham, Birmingham, United Kingdom46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom48Department of Physics, University of Warwick, Coventry, United Kingdom49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom51School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom53Imperial College London, London, United Kingdom54School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom55Department of Physics, University of Oxford, Oxford, United Kingdom56Massachusetts Institute of Technology, Cambridge, MA, United States57University of Cincinnati, Cincinnati, OH, United States58University of Maryland, College Park, MD, United States59Syracuse University, Syracuse, NY, United States60Pontifıcia Universidade Catolica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2

61Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to 3

62Institut fur Physik, Universitat Rostock, Rostock, Germany, associated to 11

63National Research Centre Kurchatov Institute, Moscow, Russia, associated to 31

64Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain, associated to 36

65Van Swinderen Institute, University of Groningen, Groningen, The Netherlands, associated to 41

66Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triangulo Mineiro (UFTM), Uberaba-MG, BrazilbP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, RussiacUniversita di Bari, Bari, ItalydUniversita di Bologna, Bologna, ItalyeUniversita di Cagliari, Cagliari, Italy

21

fUniversita di Ferrara, Ferrara, ItalygUniversita di Firenze, Firenze, ItalyhUniversita di Urbino, Urbino, ItalyiUniversita di Modena e Reggio Emilia, Modena, ItalyjUniversita di Genova, Genova, ItalykUniversita di Milano Bicocca, Milano, ItalylUniversita di Roma Tor Vergata, Roma, ItalymUniversita di Roma La Sapienza, Roma, ItalynUniversita della Basilicata, Potenza, ItalyoAGH - University of Science and Technology, Faculty of Computer Science, Electronics andTelecommunications, Krakow, PolandpLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, SpainqHanoi University of Science, Hanoi, Viet NamrUniversita di Padova, Padova, ItalysUniversita di Pisa, Pisa, ItalytScuola Normale Superiore, Pisa, ItalyuUniversita degli Studi di Milano, Milano, ItalyvPolitecnico di Milano, Milano, Italy

22