DSpace at VNU: Measurement of the chi(b) (3 P) mass and of the relative rate of chi(b1) (1 P) and chi(b2) (1 P) production

Published for SISSA by

Springer

Received: September 5, 2014
Accepted: October 1, 2014
Published: October 14, 2014

The LHCb collaboration
E-mail:
Abstract: The production of χb mesons in proton-proton collisions is studied using a data
√
sample 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 are identified
through their decays to Υ(1S)γ and Υ(2S)γ using photons that converted to e+ e− pairs
in the detector. The relative prompt production rate of χb1 (1P ) and χb2 (1P ) mesons
is measured as a function of the Υ(1S) transverse momentum in the χb rapidity range
2.0 < y < 4.5. A precise measurement of the χb (3P ) mass is also performed. Assuming a
mass splitting between the χb1 (3P ) and the χb2 (3P ) states of 10.5 MeV/c2 , the measured
mass of the χb1 (3P ) meson is
+1.5
2
m(χb1 (3P )) = 10515.7+2.2
−3.9 (stat)−2.1 (syst) MeV/c .

Keywords: Quarkonium, Hadron-Hadron Scattering, Flavor physics
ArXiv ePrint: 1409.1408

Open Access, Copyright CERN,
for the benefit of the LHCb Collaboration.
Article funded by SCOAP3 .

doi:10.1007/JHEP10(2014)088

JHEP10(2014)088

Measurement of the χb(3P ) mass and of the relative
rate of χb1(1P ) and χb2(1P ) production


Contents
1

2 Detector and data samples

2

3 Event reconstruction and selection

3

4 Sample composition and fit model

4

5 χb meson masses
5.1 Mass measurements
5.2 Systematic uncertainties

6
6

7

6 Relative rate of χb2 (1P ) and χb1 (1P ) production
6.1 Measurement of the relative rates
6.2 Systematic uncertainties

9
9
10

7 Results

12

8 Conclusion

13

The LHCb collaboration

17

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 chromodynamics (QCD). The quarkonium (cc and bb) states in which quarks have parallel spins
include the S-wave (J/ψ , Υ ) and the P -wave (χc , χb ) states, where each of the latter comprises a closely spaced triplet of J = 0, 1, 2 spin states (χcJ , χbJ ). In high-energy protonproton collisions at the LHC, qq pairs (q = c, b) are expected to be produced predominantly
via a hard gluon-gluon interaction followed by the formation of bound quarkonium states.

The production of the qq pair is described by perturbative QCD, while non-perturbative
QCD is needed for the description of the evolution of the qq pair to the bound state. Several models have been developed for this non-perturbative part such as 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. Recent studies support the leading role of the colour singlet mechanism [6, 7]. Measurements of the relative rate of J = 1
and J = 2 states provide information on the colour octet contribution. This relative rate
is also predicted to have the same dependence on the meson transverse momentum (pT ) in
χb and χc states, once the pT of the χb meson is scaled by the ratio of χc and χb masses [8].

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JHEP10(2014)088

1 Introduction


2

Detector and data samples

The LHCb detector [20] is a single-arm forward spectrometer covering the pseudorapidity
range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector
(VELO) surrounding the pp interaction region, a large-area silicon-strip detector station
located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The
tracking system provides a measurement of momentum, p, with a relative uncertainty that
varies from 0.4% at low momentum to 0.6% at 100 GeV/c. The total material 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 measured with a resolution
of (15 + 29/pT ) µm, where pT is in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photon, electron
and hadron candidates are identified by a calorimeter system consisting of scintillating-pad
and preshower detectors, an electromagnetic calorimeter (ECAL) and a hadronic calorimeter. The reconstruction of converted photons is described in section 3. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional chambers.

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

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JHEP10(2014)088

Measurements of χc production and the ratio of the χc1 and χc2 production crosssections have been made previously using various particle beams and energies [9–13]. All
the χb states are below the BB threshold (where B stands for b mesons) and therefore
can be studied through their radiative decays to the Υ mesons, in the same way as the χc
states 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 ) production
√
cross-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) transverse momentum from 5 to 25 GeV/c. The full LHCb sample is used, corresponding to an integrated
luminosity of 3.0 fb−1 . The observation in LHCb data of the recently observed χb (3P )
state [14, 15] is also presented. The measurement of its mass and of the mass splitting
between the χbJ (1P ) states (J = 1 and J = 2) provide useful information for testing 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 reconstructed
in 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 of
the χb1 and χb2 mass peaks, due to the improved energy resolution of converted photons
with respect to that of photons identified with the calorimeter. Any contribution from the
χb0 mesons decays is neglected, as their radiative decay rate is expected to be suppressed
by an order of magnitude compared to that of the χb2 meson [17, 19].

3

Event reconstruction and selection

The reconstruction and selection of χb candidates closely follows ref. [13]. Photons that
convert in the detector material are reconstructed from pairs of oppositely charged electron
candidates. Since the acceptance is lower for photons that convert in the VELO and the
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 the
VELO and the first tracking station upstream of the magnet. The e+ e− candidates are
required to be within the ECAL acceptance and to produce electromagnetic clusters that
have compatible coordinates in the non bending plane. Any photon whose position in
the ECAL is compatible with a straight line extrapolation of the electron track from the
first tracking station is considered as a bremstrahlung photon. Its energy is added to the
electron energy. If the same bremsstrahlung candidate is found for both the e+ and the e− ,
the photon energy is added randomly to one of the tracks. The e+ and e− tracks (corrected
for bremsstrahlung) are then extrapolated backwards in order to determine the conversion
point and a vertex fit is performed to reconstruct the photon momentum. The transverse
momentum of the photon candidate (pγT ) is required to be larger than 600 MeV/c and the
invariant mass of the e+ e− pair is required to be less than 50 MeV/c2 , which removes most
of the combinatorial background. The resulting purity of the photon sample is determined
from simulation to be about 99%.
The Υ candidate is reconstructed in its decay to the µ+ µ− final state. Each track must
be identified as a muon with pT > 2 GeV/c and p > 8 GeV/c. The two muons must originate
from a common vertex with vertex fit χ2 /ndf smaller than 25. Only Υ candidates with
transverse momentum (pΥT ) greater than 4 GeV/c are kept. Figure 1 shows the invariant
mass of Υ candidates. The mass resolution is about 43 MeV/c2 . The accepted mass ranges
for the Υ (1S) and for the Υ (2S) candidates are given in table 1.

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JHEP10(2014)088

The trigger consists of a hardware stage, based on information from the calorimeter
and 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 muon
candidates with pT > 1.76 GeV/c or dimuon candidates with a product of their pT larger
than (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, 22] with a specific
LHCb configuration [23]. Decays of hadronic particles are described by EvtGen [24],
in which final state radiation is generated using Photos [25]. The interaction of the
generated particles with the detector and its response are implemented using the Geant4
toolkit [26, 27] as described in ref. [28]. The simulated samples consist of events containing
at least one Υ 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
referred to as inclusive Υ in the following. In another sample, used for the estimation of
signal efficiencies and parametrisation, the Υ is required to originate from a χb meson. This
simulated sample is about 10 times larger than the data sample.


(n, m)

(1,1)

(2,1)

(3,1)

(3,2)

pΥT
pγT

> 4.0

> 4.0

> 5.0

> 6.0

> 0.6

> 0.9

> 1.3

> 0.7

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

( GeV/c)
( GeV/c)

Υ mass range

( MeV/c2 )

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

4

Sample composition and fit model

Two background sources are considered in the sample of χb candidates. One source is the
non-Υ background originating mainly from the Drell-Yan process where the dimuon pair
is combined with a photon. The second source is the combinatorial background where a
genuine Υ is combined with a random photon. The functions used for the fits are the sums
of a background and signal functions.
The χb1 and χb2 peaks are each parametrised with a double sided Crystal Ball (CB)
function [29]:

1 m∗ − mi
CBi (m ) ∝ exp −
2
σi

2

∗

if − αL <

–4–

m∗ − mi
< αR
σi

JHEP10(2014)088

The Υ and γ candidates are each associated with the primary vertex (PV) relative to
which they have the smallest impact parameter χ2 , defined as the difference between the χ2
of the PV reconstructed with and without the considered tracks. They are then combined
to form a χb candidate. The χb decay time has to be smaller than 0.1 ps (about 5 times the
observed resolution). Loose requirements are applied in order to reject combinatorial background and poorly reconstructed candidates using the following variables: the difference in
z-positions of the primary vertices associated with the Υ and γ candidates, the χ2 of the χb
candidate vertex fit 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 cosine of the angle between the photon momentum in the χb rest frame
and the χb momentum is required to be positive. This requirement halves the background
while preserving 92% of the 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 the
known Υ mass values [19]. This allows a nearly exact cancellation of the uncertainty due
to the Υ mass resolution and any possible bias on the Υ candidates mass. The χb mass
resolution is therefore dominated by the resolution on the photon energy. The requirements
on pΥT and pγT and the Υ signal mass ranges used for each χb (nP ) → Υ (mS)γ decay mode
are given in table 1.


Candidates / (10 MeV/c2)

2000

LHCb

1500

1000

0

9000

9500

10000

10500

11000

m(µ +µ -) [MeV/c2]

Figure 1. Invariant dimuon mass of the Υ candidates after the event selection requirements and
before the Υ mass range requirement. The distribution is fitted with the sum (blue line) of a
double-sided Crystal Ball function for each Υ state (dashed red line for Υ (1S), dotted pink line for
Υ (2S), dash-dotted green line for Υ (3S)) and a second-order polynomial for the background (not
shown). The hatched red bands show the signal regions and the hatched blue bands show the mass
sidebands used for background studies.
2)
(nL /αL )nL exp(− 12 αL
(nL /αL − αL − (m∗ − mi )/σi )nL
2)
(nR /αR )nR exp(− 12 αR
CBi (m∗ ) ∝
(nR /αR − αR + (m∗ − mi )/σi )nR

CBi (m∗ ) ∝

if

m∗ − mi
< −αL
σi

if

m∗ − mi
> αR ,

σi

(4.1)

where the index i = 1(2) refers to the χb1 (χb2 ) CB function. The CB left tail accounts
for events with unreconstructed bremsstrahlung, while the right tail accounts for events
with overcorrected bremsstrahlung. Simulation shows that the same tail parameters αR
and nL,R can be used for all the χbi (nP ) states, nL = nR = 2.5 and αR = 1.0, while
different values of αL have to be used: αL = 0.20, 0.25 and 0.30, for the χbi (1P ), χbi (2P )
and χbi (3P ) shapes, respectively. Since in the study of χc states it was found that the CB
tail parameters were similar in data and simulation [13], the values found with simulation
are used for the χb . The CB width, σ, increases with the mass difference between the
considered χb and Υ states. Fits to the mass distributions of χb (1P ) → Υ (1S)γ and
χb (2P ) → Υ (1S)γ candidates indicate that the width is 10% − 20% larger in data than
in simulation. Therefore, the CB width is fixed to the value found with simulated events
increased 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 mass
sidebands shown in figure 1 and given in table 1. The mass distribution of these candidates
is fitted with an empirical function
fbkg (m∗ ) ∝ arctan

m∗ − m0
c

–5–

+b

m∗
−1 +a,

m0

(4.2)

JHEP10(2014)088

500


5
5.1

χb meson masses
Mass measurements

The masses of the χb mesons are determined using unbinned maximum likelihood fits to the
χb mass distributions using the parametrisation described in section 4. Figures 2 (a) and
(b) show the mass distributions for the χb (1P ) → Υ (1S)γ and χb (2P ) → Υ (1S)γ decays
with the fit results overlaid. In these fits the free parameters are m1 , A1 , ∆m12 , r12 and
Acomb . Table 2 reports the resulting mass determinations for these states compared to the
world average values [19]. A small bias is expected on the measured masses, attributed to
unreconstructed bremsstrahlung of the e+ e− pair. This bias is proportional to the Q-value
of 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 measurements
given in table 2 are not corrected for this bias and are consistent with such a bias. On the
other hand the χb (3P ) mass measured using the χb (3P ) → Υ (mS)γ transitions is corrected
for the bias estimated with simulation, −3.0 ± 2.0 MeV/c2 and −0.5 ± 0.5 MeV/c2 for m = 1
and m = 2, respectively, where the uncertainties cover possible discrepancies between data
and simulation.
In the case of the χb (3P ) meson, the mass splitting and the relative yields are also

fixed, as the spin-1 and spin-2 peaks cannot be separated. Theory predictions vary from 9
to 12 MeV/c2 [16, 17] for ∆m12 and this parameter is fixed to 10.5 MeV/c2 . The value of r12
is fixed based on theoretical predictions [17] and our experimental measurement. It can be
expressed as the product of the ratio of branching fractions to Υ γ and of the ratio of production cross-sections of the χb2 (3P ) and χb1 (3P ) states. Predictions for branching fractions
are found in refs. [17, 18]. The predictions from ref. [17] agree well with the experimental
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 is expected to be
the same for the χb (3P ) and χb (1P ) mesons and thus, using the measurement detailed in
section 6, we obtain σ(χb2 (nP ))/σ(χb1 (nP )) = 0.9 ± 0.2.

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JHEP10(2014)088

where m0 , a, b and c are free parameters. This function is then used to parametrise the
non-Υ background contribution with all parameters fixed to the fitted values. The shape
of the combinatorial background is estimated using the inclusive Υ simulated sample and
parametrised with eq. (4.2). All parameters are fixed to the values found with simulation
except for the normalisation. In the case of the χb (3P ) → Υ (2S)γ transition, this shape
does not reproduce the data properly and the value of the m0 parameter is therefore left
free in the fit. This discrepancy is due to mismodeling of the pΥT spectrum in simulation
and is accounted for in the systematic uncertainties.
The fits have at most six 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 χb1 CB
function A1 , the ratio of the χb2 to χb1 CB amplitudes r12 , the normalisation of the combinatorial background Acomb and the m0 parameter for the combinatorial background shape.


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

(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

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. The values
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 statistical only.

To summarise, the value r12 = 0.47 × 0.9 = 0.42 is used in the fits to the mass
distributions 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 is
also performed and the result is reported in the last column of table 3. Figure 2 shows the
results of these fits. The χb (3P ) → Υ (1S)γ and χb (3P ) → Υ (2S)γ decays are seen with
a statistical significance, determined from the likelihood ratio of the fits with background
only and with signal plus background hypotheses, of 6.0σ and 3.6σ respectively. The total
statistical significance determined with the simultaneous fit is 6.9σ.
5.2

Systematic uncertainties

The systematic uncertainties on the measurement of the χb (nP ) (n = 1, 2) mass splitting
and 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)γ is less
than 2% for χb (1P ) and χb (2P ) mesons [19]. In order to estimate the systematic uncertainty
due to the presence of a χb0 or another unknown state, a third CB function is added to
the fit, with a peak position fixed to the world average value for the χb (nP ) for n = 1, 2
and left free for the χb (3P ). The resulting yield of χb0 mesons is compatible with zero.
The Gaussian width of the CB function is varied within ±10% to cover possible differences
between data and simulation. For these two fit variations, the differences between results of

the nominal and alternative fits are taken as systematic uncertainties, added in quadrature
and referred to as signal uncertainty in table 4.

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JHEP10(2014)088

(n, m)


Candidates / (5.0 MeV/c2)

Candidates / (3.0 MeV/c2)

120
100

(a) χ b(1P )→Υ (1S )γ

LHCb

80
60
40

90

LHCb

(b) χ b(2P )→Υ (1S )γ

80
70
60
50
40
30

Candidates / (6.0 MeV/c2)

40
35

9800

9850

9900

0

9950

m(µ µ γ )-m(µ µ )+m(Υ (1S )) [MeV/c2]

(c) χ b(3P )→Υ (1S )γ

Candidates / (6.0 MeV/c2)

0

9750

10

LHCb

30
25
20
15
10

10100

25

10200

10300

10400

m(µ µ γ )-m(µ µ )+m(Υ (1S )) [MeV/c2]

(d) χ b(3P )→Υ (2S )γ

LHCb

20

15

10

5

5

10400

10500

10600

10700

m(µ µ γ )-m(µ µ )+m(Υ (1S ))

0

10800

[MeV/c2]

45
40
35

Candidates / (6.0 MeV/c2)

Candidates / (6.0 MeV/c2)

0

(e) Simultaneous fit to χ (3P )→Υ (1S,2S )γ

χ b(3P )→Υ (1S )γ

b

LHCb

30
25
20
15
10

10500

10600

10700

10800

m(µ µ γ )-m(µ µ )+m(Υ (2S )) [MeV/c2]

30

25

(f) Simultaneous fit to χ (3P )→Υ (1S,2S )γ
b
χ (3P )→Υ (2S )γ
LHCb
b

20
15
10
5

5
0

10400

10400

10500

10600

10700

m(µ µ γ )-m(µ µ )+m(Υ (1S ))

0

10800

[MeV/c2]

10400

10500

10600

10700

10800

m(µ µ γ )-m(µ µ )+m(Υ (2S )) [MeV/c2]

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

–8–

JHEP10(2014)088

20
20

6
6.1

Relative rate of χb2 (1P ) and χb1 (1P ) production
Measurement of the relative rates

The production cross-section ratio of the χb2 (1P ) and χb1 (1P ) mesons is measured in three
pΥT ranges of different size (the bin limits are given in table 5) using
Nχb2 εχb1 B(χb1 → Υ (1S)γ)
σ(χb2 )
=
,
σ(χb1 )
Nχb1 εχb2 B(χb2 → Υ (1S)γ)

(6.1)

where σ(χbJ ) (J = 1, 2) is the χbJ (1P ) meson production cross-section; NχbJ is the χbJ (1P )
yield; εχbJ is the efficiency to trigger, detect, reconstruct and select a χbJ meson including
the contribution from the approximately 20% probability for a photon to convert upstream

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JHEP10(2014)088

Imperfect modelling of the background is also considered as a possible source of systematic uncertainty. The normalisation of the non-Υ background is varied within the
uncertainty 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

using only the low or the high mass sideband. Therefore no systematic uncertainty is assigned from the non-Υ background modelling. The shape of the combinatorial background
is particularly sensitive to the m0 value, therefore this parameter is varied within twice
its uncertainty. In the case of the χb (3P ) → Υ (2S)γ transition, where the value of m0 is
left free in the fit, the value found in simulation is used in an alternative fit, leading to a
change of 0.1 MeV/c2 on the χb (3P ) mass. The fit range is also varied by ±100 MeV/c2 on
both sides. The differences between results of the nominal fit and these two alternative fits
are taken as systematic uncertainties and added in quadrature. The resulting systematic
uncertainty is referred to as background uncertainty.
The uncertainty on the mass bias (2.0 and 0.5 MeV/c2 for the χb (3P ) mass measurement based on the transition to Υ (1S) and Υ (2S) respectively) is assigned as systematic
uncertainty. For the simultaneous fit to the two χb (3P ) mass distributions, the two biases are varied independently within their uncertainties and the largest variation is taken
as systematic uncertainty. A small bias is expected on the χb (1P ) mass splitting and is
estimated to be at most 0.10 MeV/c2 , which is added as a systematic uncertainty. No
significant 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
in the nominal fit. They are varied independently within their expected uncertainties in
order to evaluate the associated systematic uncertainties. The mass splitting, ∆m12 , is
varied between 9 and 12 MeV/c2 and the r12 parameter is varied by ±30%, which includes
theoretical uncertainties and the precision on the χb (1P ) production ratio measured in this
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 uncertainty
is the quadratic sum of all individual uncertainties.


∆m12 (1P)

∆m12 (2P)

m(χb1 (3P))

m(χb1 (3P))

m(χb1 (3P))

from Υ (1S)

from Υ (2S)

combined

±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

r12

-

-

+0.7
−0.4

+0.1
−0.2

+1.2
−1.6
+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

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

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

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

of the first tracking station; and B(χb1 (1P ) → Υ (1S)γ) = (33.9 ± 2.2)% and B(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 the
detector due to the magnetic field. The efficiency of converted photon reconstruction and
selection relative to non-converted photons is measured in ref. [13] and ranges from about
1% at pγT of 600 MeV/c to 3% at pγT of 2000 MeV/c. These numbers include the conversion
probability. 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 ratio
differs from unity because the pΥT spectrum is different for χb1 and χb2 in Pythia 8, as
expected [8]. The ratio of efficiencies is also calculated assuming equal pT spectra. It is
still 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 and
background functions described in section 4. In these fits the mass of the χb1 state and the
mass 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 is
shown in figure 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 section 5.2)

are investigated and reported in table 6. Additional systematic checks relevant only for
the relative rates of χb2 (1P ) and χb1 (1P ) are detailed as follows.

– 10 –

JHEP10(2014)088

Signal


70
60

(a) 5 < p TΥ < 10 GeV/ c

Candidates / (4.0 MeV/c2)

Candidates / (4.0 MeV/c2)

80

LHCb

χ b(1P )→Υ (1S )γ

50
40
30
20

50
45
40
35

Candidates / (4.0 MeV/c2)

χ b(1P )→Υ (1S )γ

25
20
15
10
5

9800

9850

9900

0

9950

m(µ µ γ )-m(µ µ )+m(Υ (1S )) [MeV/c2]

9750

9800

9850

9900

9950

m(µ µ γ )-m(µ µ )+m(Υ (1S )) [MeV/c2]

35
30

(c) 15 < p ΥT < 25 GeV/ c

25

χ b(1P )→Υ (1S )γ

LHCb

20
15
10
5
0

9750

9800

9850

9900

9950

m(µ µ γ )-m(µ µ )+m(Υ (1S )) [MeV/c2]

Figure 3. Distribution of m∗ (µ+ µ− γ) ≡ m(µ+ µ− γ) − m(µ+ µ− ) + m(Υ ) for χb (1P ) candidates
with fit projections overlaid for each of the three ranges in pΥT : (a) 5–10 GeV/c, (b) 10–15 GeV/c
and (c) 15–25 GeV/c. The cyan dotted line show the non-Υ background, the grey dashed line shows
the combinatorial background, the red dashed line the χb1 contribution, the green dash-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
of the 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 the
uncertainty 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 pT
spectrum of χb production as discussed in section 6.1. In order to assess the uncertainty
due to the shape of the pT spectrum, the simulated χb2 (χb1 ) spectrum is changed to
be identical to the simulated χb1 (χb2 ) spectrum. The relative difference in the ratio of
efficiencies is taken as a systematic uncertainty.
The fit is also performed on simulated data and a mean bias of (−4 ± 4)% is observed
on the relative yields. A systematic uncertainty of ±4% is added to take the possible bias
into account. The values of the χb1 (1P ) mass m1 and of the mass splitting ∆m12 are
also varied within their uncertainties from table 2. The variation of the result is taken as
systematic uncertainty and is added in quadrature to the uncertainty referred to as signal.

– 11 –

JHEP10(2014)088

9750

LHCb

30

10
0

(b) 10 < p ΥT < 15 GeV/ c


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

+0.10
−0.16

+0.12
−0.13

+0.13
−0.14

Total

Table 6 lists the systematic uncertainties on the relative rates. The total systematic
uncertainty is the quadratic sum of all individual uncertainties. The ratio of cross-sections
is also affected by the uncertainties on the branching fraction of χb (1P ) → Υ (1S)γ, leading
to 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,
+2.5
2

m(χb1 (3P )) = 10509.0+5.0
−2.6 (stat)−2.4 (syst) MeV/c ,

is derived from the radiative transition to the Υ (1S) meson, where the χb (3P ) is observed
with a statistical significance of 6.0σ. Another measurement,
2
m(χb1 (3P )) = 10518.5+1.9
−1.3 (stat) ± 0.6(syst) MeV/c ,

is derived from the radiative transition to the Υ (2S) transition, where evidence is found for
the χb (3P ) with a statistical significance of 3.6σ. The systematic uncertainty related to r12
is largely uncorrelated between the Υ (2S) and Υ (1S) channels as the branching fractions
of χbi to final states involving Υ (1S) and to Υ (2S) mesons can be different. By treating
the systematic uncertainties related to the mass splitting and to the mass bias as fully
correlated and all other uncertainties as uncorrelated, the two results for the χb1 (3P ) mass
2
differ by 9.3+3.2
−5.2 (stat) ± 2.0(syst) MeV/c . A combined fit is performed leading to
+1.5
2
m(χb1 (3P )) = 10515.7+2.2
−3.9 (stat)−2.1 (syst) MeV/c .

In these measurements, the relative rate of χb2 to χb1 , is assumed to be r12 = 0.42 for
the two transitions. The χb1 (3P ) mass result exhibits a linear dependence on the assumed

– 12 –

JHEP10(2014)088

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


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)

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 due to
the uncertainty on the branching fractions.

8

Conclusion

The radiative decays of χb mesons to Υ mesons are reconstructed with photons converting
in the detector material. Owing to the good energy resolution obtained with converted
photons, the χb (1P ) states are separated and the mass splitting between the χb1 (1P ) and
χb2 (1P ) is measured. The χb (3P ) mass is measured using its radiative decays to the Υ (1S)
and Υ (2S) mesons yielding,
+1.5
2
m(χb1 (3P )) = 10515.7+2.2
−3.9 (stat)−2.1 (syst) MeV/c .

This result is compatible with the measurement performed by LHCb with the radiative decays to the Υ (3S) meson that uses non-converted photons [31], m(χb1 (3P )) =
10511.3 ± 1.7(stat) ± 2.5(syst) MeV/c2 . Since the photon reconstruction is based on different subdetectors, the experimental systematic uncertainties are uncorrelated, while the

– 13 –

JHEP10(2014)088

fraction of χb1 decays and varies from 10517.6 to 10515.2 when the χb2 /χb1 yield ratio
changes from zero to 0.5. This result is compatible with and significantly more precise than
that 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 χb2
states [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 ranges
using eq. (6.1). The results are given in table 7. Figure 4 (a) shows a comparison of
the measured values with LO NRQCD predictions from ref. [8]. The common systematic
uncertainty (9.0%) due to the branching fraction of χb → Υ (1S)γ is not shown. Theory
predicts the χc and χb ratio of production cross-section to be the same when the χc pT
value is scaled by the ratio of the χb and χc masses [8]. As the χb (χc ) and Υ (J/ψ ) pT are

strongly 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 axis
scaled accordingly is also shown for comparison. The χb results are in good agreement with
the scaled χc results. These results are not precise enough to establish the deviation from
unity predicted by theory at low pT , but the agreement is better with a flat dependence.
Our results are also in agreement with the CMS results [30] as shown on figure 4 (b).


2.5

LHCb χ

b

(a)

LHCb χc scaled
LO NRQCD

2

σ(χb2) / σ(χb1)

σ(χb2) / σ(χb1)

3

b

LHCb χc scaled

CMS χ

b

1

1

0

LHCb χ

(b)

1.5

1.5

0.5

2

0.5
2.08

10

12

14

16

18

20

22 24
p Υ [GeV/c]

χb unpolarised
10

15

20

25

T

30

35
40
p Υ [GeV/c]
T

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 uncertainties 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 by
m(χb )/m(χc ) = 2.8. Panel (b) compares this measurement (empty squares) to CMS results [30]
(filled squares) and to the scaled LHCb χc results (empty circles). The error bars are the total
experimental uncertainties and do not include the uncertainties on the branching fractions.

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 second
accounts for varying ∆m12 from 9.0 to 12.0 MeV/c2 and r12 by ±30%. This result is in
agreement 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 performed
for the χb (1P ) state in the rapidity range 2.0 < y < 4.5 for pΥT from 5 to 25 GeV/c.
The results agree with CMS results [30] and with theory expectation based on LHCb
χc measurements [13]. The data indicate a deviation from the rise predicted by the LO
NRQCD model at low pT and show a better agreement with a flat dependence.

Acknowledgments
We thank A. Luchinsky and A. Likhoded for providing the LO NRQCD predictions. We
express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the
LHCb 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 (United

– 14 –

JHEP10(2014)088

6

0
5


Kingdom); NSF (U.S.A.). 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 the multiple open source software packages on which we depend. We are also thankful for the computing resources and the access to software R&D tools provided by Yandex LLC (Russia).
Individual groups or members have received support from EPLANET, Marie SklodowskaCurie Actions and ERC (European Union), Conseil g´en´eral de Haute-Savoie, Labex ENIGMASS and OCEVU, R´egion Auvergne (France), RFBR (Russia), XuntaGal and GENCAT
(Spain), Royal Society and Royal Commission for the Exhibition of 1851 (United Kingdom).

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The LHCb collaboration

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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. D´el´eage4 , D. Derkach55 , O. Deschamps5 , F. Dettori38 , A. Di Canto38 , H. Dijkstra38 ,
S. Donleavy52 , F. Dordei11 , M. Dorigo39 , A. Dosil Su´arez37 , 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. F¨arber11 , 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. Garc´ıa Pardi˜
nas37 , J. Garofoli59 , J. Garra Tico47 ,
36
38
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L. Garrido , C. Gaspar , R. Gauld , L. Gavardi , G. Gavrilov30 , A. Geraci21,v , E. Gersabeck11 ,
M. Gersabeck54 , T. Gershon48 , Ph. Ghez4 , A. Gianelle22 , S. Gian`ı39 , V. Gibson47 , L. Giubega29 ,
V.V. Gligorov38 , C. G¨obel60 , D. Golubkov31 , A. Golutvin53,31,38 , A. Gomes1,a , C. Gotti20 ,
M. Grabalosa G´andara5 , R. Graciani Diaz36 , L.A. Granado Cardoso38 , E. Graug´es36 ,
G. Graziani17 , A. Grecu29 , E. Greening55 , S. Gregson47 , P. Griffith45 , L. Grillo11 , O. Gr¨
unberg62 ,
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 , 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 ,


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JHEP10(2014)088

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. Lef`evre5 , A. Leflat32 ,
J. Lefran¸cois7 , 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. M¨arki39 , J. Marks11 ,
G. Martellotti25 , A. Martens8 , A. Mart´ın S´anchez7 , 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. Mord`
a6 , M.J. Morello23,t , J. Moron27 , A.-B. Morris50 , R. Mountain59 , F. Muheim50 ,
K. M¨
uller40 , 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. Pilaˇr48 , 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 ,
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 ,


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Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil
Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
Center for High Energy Physics, Tsinghua University, Beijing, China
LAPP, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France
LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France
Fakult¨

at Physik, Technische Universit¨
at Dortmund, Dortmund, Germany
Max-Planck-Institut f¨
ur Kernphysik (MPIK), Heidelberg, Germany
Physikalisches Institut, Ruprecht-Karls-Universit¨
at Heidelberg, Heidelberg, Germany
School of Physics, University College Dublin, Dublin, Ireland
Sezione INFN di Bari, Bari, Italy
Sezione INFN di Bologna, Bologna, Italy
Sezione INFN di Cagliari, Cagliari, Italy
Sezione INFN di Ferrara, Ferrara, Italy
Sezione INFN di Firenze, Firenze, Italy
Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
Sezione INFN di Genova, Genova, Italy
Sezione INFN di Milano Bicocca, Milano, Italy
Sezione INFN di Milano, Milano, Italy
Sezione INFN di Padova, Padova, Italy
Sezione INFN di Pisa, Pisa, Italy
Sezione INFN di Roma Tor Vergata, Roma, Italy
Sezione INFN di Roma La Sapienza, Roma, Italy
Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´
ow, Poland
AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,
Krak´
ow, Poland
National Center for Nuclear Research (NCBJ), Warsaw, Poland

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JHEP10(2014)088

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. V´azquez 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 and A. Zvyagin38 .


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– 20 –

JHEP10(2014)088

38

Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele,
Romania
Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk,
Russia

Institute for High Energy Physics (IHEP), Protvino, Russia
Universitat de Barcelona, Barcelona, Spain
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
European Organization for Nuclear Research (CERN), Geneva, Switzerland
Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland
Physik-Institut, Universit¨
at Z¨
urich, Z¨
urich, Switzerland
Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The
Netherlands
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
University of Birmingham, Birmingham, United Kingdom
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
Department of Physics, University of Warwick, Coventry, United Kingdom
STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
Imperial College London, London, United Kingdom
School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
Department of Physics, University of Oxford, Oxford, United Kingdom
Massachusetts Institute of Technology, Cambridge, MA, United States
University of Cincinnati, Cincinnati, OH, United States
University of Maryland, College Park, MD, United States
Syracuse University, Syracuse, NY, United States
Pontif´ıcia Universidade Cat´

olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated
to 2
Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated
to 3
Institut f¨
ur Physik, Universit¨
at Rostock, Rostock, Germany, associated to 11
National Research Centre Kurchatov Institute, Moscow, Russia, associated to 31
Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain, associated
to 36
Van Swinderen Institute, University of Groningen, Groningen, The Netherlands, associated to 41
Celal Bayar University, Manisa, Turkey, associated to 38
Universidade Federal do Triˆ
angulo Mineiro (UFTM), Uberaba-MG, Brazil
P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia
Universit`
a di Bari, Bari, Italy
Universit`
a di Bologna, Bologna, Italy
Universit`
a di Cagliari, Cagliari, Italy
Universit`
a di Ferrara, Ferrara, Italy
Universit`
a di Firenze, Firenze, Italy
Universit`
a di Urbino, Urbino, Italy


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– 21 –

JHEP10(2014)088

s

Universit`
a di Modena e Reggio Emilia, Modena, Italy
Universit`
a di Genova, Genova, Italy
Universit`
a di Milano Bicocca, Milano, Italy
Universit`
a di Roma Tor Vergata, Roma, Italy
Universit`

a di Roma La Sapienza, Roma, Italy
Universit`
a della Basilicata, Potenza, Italy
AGH - University of Science and Technology, Faculty of Computer Science, Electronics and
Telecommunications, Krak´
ow, Poland
LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
Hanoi University of Science, Hanoi, Viet Nam
Universit`
a di Padova, Padova, Italy
Universit`
a di Pisa, Pisa, Italy
Scuola Normale Superiore, Pisa, Italy
Universit`
a degli Studi di Milano, Milano, Italy
Politecnico di Milano, Milano, Italy