Quantum numbers of the Xð3872Þ state and orbital angular momentumin its ρ0J=ψ decay R.. The Xð3872Þ quantum numbers, such as total angular momentum J, parity P and charge conjuga-tion C,
Trang 1Quantum numbers of the Xð3872Þ state and orbital angular momentum
in its ρ0J=ψ decay
R Aaijet al.*
(LHCb Collaboration) (Received 23 April 2015; published 30 July 2015) Angular correlations in Bþ→ Xð3872ÞKþ decays, with Xð3872Þ → ρ0J=ψ, ρ0→ πþπ− and
J=ψ → μþμ−, are used to measure orbital angular momentum contributions and to determine the JPC
value of the Xð3872Þ meson The data correspond to an integrated luminosity of 3.0 fb−1of proton-proton
collisions collected with the LHCb detector This determination, for the first time performed without
assuming a value for the orbital angular momentum, confirms the quantum numbers to be JPC¼ 1þþ The
Xð3872Þ is found to decay predominantly through an S wave and an upper limit of 4% at 95% C.L is set on
the D-wave contribution
Bþ;0→ Xð3872ÞKþ;0, Xð3872Þ → πþπ−J=ψ, J=ψ →
lþl−decays by the Belle experiment[1]and subsequently
confirmed by other experiments[2–4].1Its production was
also studied at the LHC[5,6] However, the nature of this
state remains unclear The Xð3872Þ state is narrow, has a
mass very close to the D0¯D0 threshold and decays to
ρ0J=ψ and ωJ=ψ final states with comparable branching
fractions [7], thus violating isospin symmetry This
sug-gests that the Xð3872Þ particle may not be a simple c¯c state,
and exotic states such as D0¯D0molecules[8], tetraquarks
[9]or mixtures of states[10]have been proposed to explain
its composition The Xð3872Þ quantum numbers, such as
total angular momentum J, parity P and charge
conjuga-tion C, impose constraints on the theoretical models of
this state The orbital angular momentum L in the
Xð3872Þ decay may also provide information on its internal
structure
Observations of the Xð3872Þ → γJ=ψ and Xð3872Þ →
γψð2SÞ decays[11–13] imply positive C, which requires
the total angular momentum of the dipion system (Jππ) in
Xð3872Þ → πþπ−J=ψ decays to be odd The dipion mass,
Mðπþπ−Þ, is limited by the available phase space to be less
than 775 MeV, and so Jππ ≥ 3 can be ruled out since there
are no known or predicted mesons with such high spins at
such low masses.2 In fact, the distribution of Mðπþπ−Þ is
consistent with Xð3872Þ → ρ0J=ψ decays[6,14,15], in line
with Jππ ¼ 1, the only plausible value
The choices for JPC were narrowed down to two possibilities, 1þþ or 2−þ, by the CDF Collaboration, via
an analysis of the angular correlations in inclusively reconstructed Xð3872Þ → πþπ−J=ψ and J=ψ → μþμ− decays, dominated by prompt production in p ¯p collisions
[16] Using 1.0 fb−1 of pp collision data collected by LHCb, JPC¼ 2−þ was ruled out in favor of the 1þþ assignment, using the angular correlations in the same decay chain, with the Xð3872Þ state produced in Bþ → Xð3872ÞKþ decays [17] Both angular analyses assumed that the lowest orbital angular momentum between the Xð3872Þ decay products (Lmin) dominated the matrix element Significant contributions from Lminþ 2 ampli-tudes could invalidate the 1þþ assignment Since the phase-space limit on Mðπþπ−Þ is close to the ρ0 pole (775.3 0.3 MeV[7]), the energy release in the Xð3872Þ decay, Q ≡ MðJ=ψπþπ−Þ − MðJ=ψÞ − Mðπþπ−Þ, is a small fraction of the Xð3872Þ mass, making the orbital angular momentum barrier effective.3 However, an exotic component in Xð3872Þ could induce contributions from higher orbital angular momentum for models in which the size of the Xð3872Þ state is substantially larger than the compact sizes of the charmonium states Therefore, it is important to probe the Xð3872Þ spin-parity without any assumptions about L A determination of the magnitude of contributions from Lminþ 2 amplitudes for the correct JPC
is also of interest, since a substantial value would suggest
an anomalously large size of the Xð3872Þ state In this article, we extend our previous analysis [17] of five-dimensional angular correlations in Bþ → Xð3872ÞKþ, Xð3872Þ → ρ0J=ψ, ρ0→ πþπ−, J=ψ → μþμ− decays to accomplish these goals The integrated luminosity of the data sample has been tripled by adding 8 TeV pp collision data collected in 2012
*Full author list given at the end of the article
1The inclusion of charge-conjugate states is implied in this
article
2
We use mass and momentum units in which c ¼ 1
Published by the American Physical Society under the terms of
distri-bution of this work must maintain attridistri-bution to the author(s) and
the published article’s title, journal citation, and DOI
3 Dimuon candidates are constrained to the known J=ψ mass[7]
PHYSICAL REVIEW D 92, 011102(R) (2015)
Trang 2The LHCb detector is a single-arm forward spectrometer
covering the pseudorapidity range 2 < η < 5, described
in detail in Refs [18,19] The Xð3872Þ candidate
selec-tion, which is based on reconstructing Bþ→ ðJ=ψ → μþμ−Þ
πþπ−Kþ candidates using particle identification
informa-tion and transverse momentum (pT) thresholds and
requir-ing separation of tracks and the Bþvertex from the primary
pp interaction vertex, is improved relative to that of
Ref [17] The signal efficiency is increased by lowering
requirements on pTfor muons from 0.90 to 0.55 GeV and
for hadrons from 0.25 to 0.20 GeV The background is
further suppressed without significant loss of signal by
requiring Q < 250 MeV The Xð3872Þ mass resolution
(σΔM) is improved from about 5.5 to 2.8 MeV by
constraining the Bþ candidate to its known mass and
requiring its momentum to point to a pp collision vertex
in the kinematic fit of its decay The distribution ofΔM ≡
Mðπþπ−J=ψÞ − MðJ=ψÞ is shown in Fig.1 A Crystal Ball
function [20] with symmetric tails is used to model the
signal shape, while the background is assumed to be linear
An unbinned maximum-likelihood fit yields 1011 38
Bþ → Xð3872ÞKþ decays and 1468 44 background
entries in the 725 < ΔM < 825 MeV range used in the
angular analysis The signal purity is 80% within2.5σΔM
from the signal peak From studying the Kþπþπ− mass
distribution, the dominant source of the background is
found to be Bþ→J=ψK1ð1270Þþ, K1ð1270Þþ→ Kþπþπ−
decays
Angular correlations in the Bþdecay chain are analyzed
using an unbinned maximum-likelihood fit to determine the
Xð3872Þ quantum numbers and orbital angular momentum
in its decay The probability density function (P) for each
JPC hypothesis, JX, is defined in the five-dimensional
angular spaceΩ≡ðcosθX;cosθρ;ΔϕX;ρ;cosθJ=ψ;ΔϕX;J=ψÞ,
whereθX,θρandθJ=ψare the helicity angles[21–23]in the Xð3872Þ, ρ0 and J=ψ decays, respectively, and ΔϕX;ρ, ΔϕX;J=ψ are the angles between the decay planes of the Xð3872Þ particle and of its decay products The quantity P
is the normalized product of the expected decay matrix element (M) squared and of the reconstruction efficiency (ϵ), PðΩjJXÞ ¼ jMðΩjJXÞj2ϵðΩÞ=IðJXÞ, where IðJXÞ ¼RjMðΩjJXÞj2ϵðΩÞdΩ The efficiency is averaged over the πþπ− mass using a simulation [24–28] of the Xð3872Þ → ρ0J=ψ, ρ0→ πþπ− decay The line shape of the ρ0 resonance can change slightly depending on the Xð3872Þ spin hypothesis The effect on ϵðΩÞ is very small and is neglected The angular correlations are obtained using the helicity formalism[16],
jMðΩjJXÞj2¼ X
Δλ μ ¼−1;þ1
λ J=ψ ;λ ρ ¼−1;0;þ1
AλJ=ψ;λρ DJX
0;λ J=ψ −λ ρð0; θX; 0Þ
D1λρ;0ðΔϕX;ρ; θρ; 0Þ
D1λJ=ψ;ΔλμðΔϕX;J=ψ; θJ=ψ; 0Þj2; ð1Þ where the λ’s are particle helicities, Δλμ¼ λμþ− λμ− and
DJλ1;λ2 are Wigner functions [21–23] The helicity cou-plings, AλJ=ψ;λ ρ, are expressed in terms of the LS couplings, BLS, with the help of Clebsch-Gordan coefficients, where L
is the orbital angular momentum between theρ0 and the J=ψ mesons, and S is the sum of their spins,
AλJ=ψ;λρ¼X
L
X S
λJ=ψ −λρ λJ=ψ−λρ
!
×
0 λJ=ψ−λρ λJ=ψ−λρ
Possible values of L are constrained by parity conservation,
PX ¼ PJ=ψPρð−1ÞL¼ ð−1ÞL In the previous analyses
[14,16,17], only the minimal value of the angular momen-tum, Lmin, was allowed Thus, for the preferred JPC¼ 1þþ hypothesis, the D wave was neglected allowing only S-wave decays In this work all L values are allowed in
Eq (2) The corresponding BLS amplitudes are listed in TableI Values of JXup to 4 are analyzed Since the orbital angular momentum in the Bþ decay equals JX, high values are suppressed by the angular momentum barrier In fact, the highest observed spin of any resonance produced in B decays is 3[29,30] Since P is insensitive to the overall normalization of the BLScouplings and to the phase of the matrix element, the BLSamplitude with the lowest L and S
is set to the arbitrary reference value (1,0) The set of other possible complex BLS amplitudes, which are free parameters in the fit, is denoted asα
) [MeV]
ψ ) - M(J/
ψ J/
-π
+
π
M = M(
Δ
740 760 780 800 820
0
20
40
60
80
100
120
140
160
LHCb
FIG 1 (color online) Distribution of ΔM for Bþ→
J=ψKþπþπ− candidates The fit of the Xð3872Þ signal is
displayed The solid (blue), dashed (red) and dotted (green)
lines represent the total fit, signal component and background
component, respectively
Trang 3The function to be minimized is −2 ln LðJX; αÞ ≡
−sw2PN data
i¼1 wilnPðΩijJX; αÞ, where LðJX; αÞ is the
unbinned likelihood, and Ndata is the number of selected
candidates The background is subtracted using the sPlot
technique[31]by assigning a weight, wi, to each candidate
based on itsΔM value (see Fig.1) No correlations between
ΔM and Ω are observed Prompt production of Xð3872Þ in
pp collisions gives negligible contribution to the selected
sample Statistical fluctuations in the background
subtrac-tion are taken into account in the log-likelihood value via
a constant scaling factor, sw¼PN data
i¼1 wi=PNdata
i¼1 wi2 The efficiency ϵðΩÞ is not determined on an event-by-event
basis, since it cancels in the likelihood ratio except for
the normalization integrals A large sample of simulated
events, with uniform angular distributions, passed through
a full simulation of the detection and the data selection
process, is used to carry out the integration,
IðJXÞ ∝PN MC
i¼1 jMðΩijJXÞj2, where NMC is the number
of reconstructed simulated events The negative log
like-lihood is minimized for each JX value with respect to free
BLS couplings, yielding their estimated set of values ˆα
Hereinafter,LðJXÞ ≡ LðJX; ˆαÞ
The1þþ hypothesis gives the highest likelihood value.
From angular momentum and parity conservation, there are
two possible values of orbital angular momentum in the
Xð3872Þ decay for this JPC value, L ¼ 0 or 2 For the
S-wave decay, the total spin of theρ0and J=ψ mesons must
be S ¼ 1; thus B01 is the only possible LS amplitude For
the D-wave decay, two values are possible, S ¼ 1 or 2,
corresponding to the amplitudes B21and B22, respectively
The squared magnitudes of both of these D-wave
ampli-tudes are consistent with zero, as demonstrated by the
ratios jB21j2=jB01j2¼ 0.002 0.004 and jB22j2=jB01j2¼
0.007 0.008 Overall, the D-wave significance is only 0.8
standard deviations as obtained by applying Wilks theorem
to the ratio of the likelihood values with the D-wave
amplitudes floated in the fit and with them fixed to zero
The total D-wave fraction depends on the BLS amplitudes,
fD≡RjMðΩÞDj2dΩ=R
jMðΩÞSþDj2dΩ, where MðΩÞD
is the matrix element restricted to the B21 and B22 amplitudes only andMðΩÞSþD is the full matrix element
To set an upper limit on fD, we populate the four-dimensional space of complex B21 and B22 parameters
TABLE I Parity-allowed LS couplings in the Xð3872Þ →
ρ0J=ψ decay For comparison, we also list a subset of these
couplings corresponding to the lowest L, used in the previous
determinations[14,16,17]of the Xð3872Þ quantum numbers
BLS
1−þ B10; B11; B12; B32 B10; B11; B12
2−þ B11; B12; B31; B32 B11; B12
2þþ B02; B20; B21; B22; B42 B02
3−þ B12; B30; B31; B32; B52 B12
3þþ B21; B22; B41; B42 B21; B22
4−þ B31; B32; B51; B52 B31; B32
4þþ B22; B40; B41; B42; B62 B22
D
f
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
LHCb
FIG 2 (color online) Likelihood-weighted distribution of the D-wave fraction The distribution is normalized to unity
200
-+
=0 alt X
=1
PC
J
200
-+
=1 alt X
=1
PC
J
) ]
++
(1
L
alt X
(J
L
= -2ln[
t
-1
LHCb 3 fb
200
-+
=2 alt X
J J PC =1 ++ J alt X =2 ++ ++
=1
PC
J
200
-+
=3 alt X
=1
PC
J
t
Experiments / 25 0
200
-+
=4 alt X
=1
PC
J
t
++
=4 alt X
=1
PC
J
FIG 3 (color online) Distributions of the test statistic
t ≡ −2 ln½LðJalt
XÞÞ=Lð1þþÞ, for the simulated experiments under the JPC¼ Jalt
X hypothesis (blue solid histograms) and under the JPC ¼ 1þþ hypothesis (red dashed histograms) The values
of the test statistics for the data, tdata, are shown by the solid vertical lines
QUANTUM NUMBERS OF THE Xð3872Þ STATE AND … PHYSICAL REVIEW D 92, 011102(R) (2015)
Trang 4with uniformly distributed points in a large region around
the B21and B22fit values (14 standard deviations in each
parameter) For each point we determine the likelihood
value from the data and an fD value via numerical
integration of the matrix element squared The distribution
of fDvalues weighted by the likelihood values is shown in
Fig.2 It peaks at 0.4% with a non-Gaussian tail at higher
values An upper limit of fD< 4% at 95% C.L is
determined using a Bayesian approach
The likelihood ratio t ≡ −2 ln½LðJalt
XÞ=Lð1þþÞ is used
as a test variable to discriminate between the 1þþ and
alternative spin hypotheses considered (JaltX) The values of
t in the data (tdata) are positive, favoring the1þþ
assign-ment They are incompatible with the distributions of t
observed in experiments simulated under various JaltX
hypotheses, as illustrated in Fig 3 To quantify these
disagreements we calculate the approximate significance
of rejection (the p-value) of JaltX asðtdata− htiÞ=σðtÞ, where
hti and σðtÞ are the mean and rms deviations of the t
distribution under the Jalt
X hypothesis In all spin configu-rations tested, we exclude the alternative spin hypothesis
with a significance of more than 16 standard deviations
Values of t in data are consistent with those expected in the
1þþ case as shown in Fig. 3, with fractions of simulated
1þþ experiments with t < tdata in the 25%–91% range
Projections of the data and of the fit P onto individual
angles show good consistency with the1þþassignment as
illustrated in Fig 4 Inconsistency with the other assign-ments is apparent when correlations between various angles are exploited For example, the data projection onto cosθX
is consistent only with the1þþfit projection after requiring
j cos θρj > 0.6 (see Fig 5), while inconsistency with the other quantum number assignments is less clear without the cosθρ requirement
The selection criteria are varied to probe for possible biases from the background subtraction and the efficiency corrections By requiring Q < 0.1 GeV, the background level is reduced by more than a factor of 2, while losing only 20% of the signal By tightening the requirements on the pT of the π, K and μ candidates, we decrease the signal efficiency by around 75% with a similar reduction in the background level In all cases, the significance of the rejection of the disfavored hypotheses is compatible with that expected from the simulation Likewise, the best fit fD values determined for these subsamples of data change within the expected statistical fluctuations and remain consistent with the upper limit we have set
In summary, the analysis of the angular correlations in
Bþ→ Xð3872ÞKþ, Xð3872Þ → πþπ−J=ψ, J=ψ → μþμ− decays, performed for the first time without any assumption about the orbital angular momentum in the Xð3872Þ decay,
50
100
150
ψ
J/
θ
cos
ψ
X,J/
Δφ
50
100
150
X
θ
cos
LHCb
Data
++
=1
PC
J
θ cos -1 -0.5 0 0.5
0
50
100
150
ρ
θ
cos
[rad]
Δφ
ρ
X,
Δφ
FIG 4 (color online) Background-subtracted distributions of
all angles for the data (points with error bars) and for the1þþfit
projections (solid histograms)
Candidates / 0.2 20
40 60
Candidates / 0.2 20
40 60
Candidates / 0.2 20
40 60
Candidates / 0.2 20
40 60
X
θ cos -1 -0.5 0 0.5 1
Candidates / 0.2 0 20 40 60
X
θ cos -0.5 0 0.5 1
++
=4 PC J
FIG 5 (color online) Background-subtracted distribution of cosθX for candidates with j cos θρj > 0.6 for the data (points with error bars) compared to the expected distributions for various Xð3872Þ JPCassignments (solid histograms) with the BLS ampli-tudes obtained by the fit to the data in the five-dimensional angular space The fit displays are normalized to the observed number of the signal events in the full angular phase space
Trang 5confirms that the eigenvalues of total angular momentum,
parity and charge conjugation of the Xð3872Þ state are 1þþ
These quantum numbers are consistent with those predicted
by the molecular or tetraquark models and with the
χc1ð23P1Þ charmonium state [32], possibly mixed with a
molecule[10] Other charmonium states are excluded No
significant D-wave fraction is found, with an upper limit of
4% at 95% C.L The S-wave dominance is expected in the
charmonium or tetraquark models, in which the Xð3872Þ
state has a compact size An extended size, such as that
predicted by the molecular model, implies more favorable
conditions for the D wave However, conclusive
discrimi-nation among models is difficult because quantitative
predictions are not available
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
(France); BMBF, DFG, HGF and MPG (Germany); 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 Kingdom); and NSF (U.S.) The Tier1 computing centers are supported by IN2P3 (France), KIT and BMBF
Netherlands), PIC (Spain) and 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 research and development tools provided by Yandex LLC (Russia) Individual groups or members have received support from EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851 (United Kingdom)
[1] S.-K Choi et al (Belle Collaboration),Phys Rev Lett 91,
[2] D Acosta et al (CDF Collaboration),Phys Rev Lett 93,
[3] V M Abazov et al (D0 Collaboration),Phys Rev Lett 93,
[4] B Aubert et al (BABAR Collaboration),Phys Rev D 71,
[5] R Aaij et al (LHCb Collaboration), Eur Phys J C 72,
1972 (2012)
[6] S Chatrchyan et al (CMS Collaboration),J High Energy
Phys 04 (2013) 154
[7] K A Olive et al (Particle Data Group),Chin Phys C 38,
[8] N A Tornqvist, Phys Lett B 590, 209 (2004)
[9] L Maiani, F Piccinini, A D Polosa, and V Riquer,Phys
[10] C Hanhart, Y S Kalashnikova, and A V Nefediev, Eur
[11] B Aubert et al (BABAR Collaboration),Phys Rev D 74,
[12] V Bhardwaj et al (Belle Collaboration),Phys Rev Lett
[13] R Aaij et al (LHCb Collaboration),Nucl Phys B886, 665
(2014)
[14] S.-K Choi et al (Belle Collaboration), Phys Rev D 84,
[15] A Abulencia et al (CDF Collaboration), Phys Rev Lett
[16] A Abulencia et al (CDF Collaboration), Phys Rev Lett
[17] R Aaij et al (LHCb Collaboration),Phys Rev Lett 110,
[18] A A Alves, Jr et al (LHCb Collaboration),J Instrum 3,
[19] R Aaij et al (LHCb Collaboration),Int J Mod Phys A 30,
[20] T Skwarnicki, Ph.D thesis, Institute of Nuclear Physics
of the Polish Academy of Sciences, 1986 [Deutsches Elektronen-Synchrotron Report No DESY-F31-86-02,
1986 (unpublished)], http://inspirehep.net/record/230779/ files/230779.pdf
[21] M Jacob and G C Wick,Ann Phys (N.Y.) 7, 404 (1959) [22] J D Richman, Report No CALT-68-1148, 1984,http://charm physics.ucsb.edu/people/richman/ExperimentersGuideTo
[23] S U Chung,Phys Rev D 57, 431 (1998) [24] T Sjöstrand, S Mrenna, and P Skands, J High Energy Phys 05 (2006) 026
[25] I Belyaev et al., in Proceedings of the IEEE Nuclear Science Symposium Conference Record (NSS/ MIC), Knoxville, TN, 2010 (IEEE, New York, 2011),
p 1155
[26] D J Lange, Nucl Instrum Methods Phys Res., Sect A
462, 152 (2001) [27] J Allison et al (GEANT4 Collaboration),IEEE Trans Nucl Sci 53, 270 (2006); S Agostinelli et al (GEANT4 Collabo-ration), Nucl Instrum Methods Phys Res., Sect A 506,
250 (2003) [28] M Clemencic, G Corti, S Easo, C R Jones, S Miglioranzi, M Pappagallo, and P Robbe,J Phys Conf
QUANTUM NUMBERS OF THE Xð3872Þ STATE AND … PHYSICAL REVIEW D 92, 011102(R) (2015)
Trang 6[29] R Aaij et al (LHCb Collaboration),Phys Rev Lett 113,
[30] R Aaij et al (LHCb Collaboration), Phys Rev D 90,
[31] M Pivk and F R Le Diberder, Nucl Instrum Methods
[32] N N Achasov and E V Rogozina, Xð3872Þ; IGðJPCÞ ¼
0þð1þþÞ, as the χ1cð2PÞ charmonium,arXiv:1501.03583
R Aaij,38B Adeva,37M Adinolfi,46A Affolder,52Z Ajaltouni,5S Akar,6 J Albrecht,9 F Alessio,38M Alexander,51
S Ali,41G Alkhazov,30P Alvarez Cartelle,53A A Alves Jr.,57S Amato,2S Amerio,22Y Amhis,7L An,3L Anderlini,17,a
J Anderson,40M Andreotti,16,b J E Andrews,58R B Appleby,54O Aquines Gutierrez,10F Archilli,38P d’Argent,11
A Artamonov,35M Artuso,59E Aslanides,6G Auriemma,25,cM Baalouch,5S Bachmann,11J J Back,48A Badalov,36
C Baesso,60W Baldini,16,38R J Barlow,54C Barschel,38S Barsuk,7W Barter,38V Batozskaya,28V Battista,39A Bay,39
L Beaucourt,4 J Beddow,51F Bedeschi,23I Bediaga,1 L J Bel,41I Belyaev,31E Ben-Haim,8 G Bencivenni,18
S Benson,38J Benton,46 A Berezhnoy,32R Bernet,40 A Bertolin,22M.-O Bettler,38 M van Beuzekom,41 A Bien,11
S Bifani,45T Bird,54A Birnkraut,9A Bizzeti,17,dT Blake,48F Blanc,39J Blouw,10S Blusk,59V Bocci,25A Bondar,34
N Bondar,30,38 W Bonivento,15 S Borghi,54M Borsato,7T J V Bowcock,52 E Bowen,40C Bozzi,16S Braun,11
D Brett,54M Britsch,10T Britton,59J Brodzicka,54N H Brook,46A Bursche,40J Buytaert,38S Cadeddu,15
R Calabrese,16,b M Calvi,20,eM Calvo Gomez,36,f P Campana,18D Campora Perez,38L Capriotti,54A Carbone,14,g
G Carboni,24,h R Cardinale,19,iA Cardini,15P Carniti,20 L Carson,50K Carvalho Akiba,2,38R Casanova Mohr,36
G Casse,52L Cassina,20,e L Castillo Garcia,38M Cattaneo,38Ch Cauet,9 G Cavallero,19R Cenci,23,jM Charles,8
Ph Charpentier,38M Chefdeville,4 S Chen,54S.-F Cheung,55N Chiapolini,40M Chrzaszcz,40,26X Cid Vidal,38
G Ciezarek,41P E L Clarke,50 M Clemencic,38H V Cliff,47J Closier,38V Coco,38J Cogan,6E Cogneras,5
V Cogoni,15,k L Cojocariu,29G Collazuol,22P Collins,38A Comerma-Montells,11A Contu,15,38A Cook,46
M Coombes,46S Coquereau,8 G Corti,38M Corvo,16,bB Couturier,38G A Cowan,50 D C Craik,48 A Crocombe,48
M Cruz Torres,60S Cunliffe,53R Currie,53C D’Ambrosio,38
J Dalseno,46P N Y David,41A Davis,57K De Bruyn,41
S De Capua,54M De Cian,11J M De Miranda,1L De Paula,2W De Silva,57P De Simone,18C.-T Dean,51D Decamp,4
M Deckenhoff,9 L Del Buono,8 N Déléage,4D Derkach,55O Deschamps,5F Dettori,38B Dey,40A Di Canto,38
F Di Ruscio,24H Dijkstra,38S Donleavy,52F Dordei,11M Dorigo,39A Dosil Suárez,37D Dossett,48 A Dovbnya,43
K Dreimanis,52L Dufour,41G Dujany,54F Dupertuis,39P Durante,38 R Dzhelyadin,35A Dziurda,26A Dzyuba,30
S Easo,49,38U Egede,53V Egorychev,31S Eidelman,34S Eisenhardt,50 U Eitschberger,9 R Ekelhof,9 L Eklund,51
I El Rifai,5Ch Elsasser,40S Ely,59S Esen,11H M Evans,47T Evans,55A Falabella,14 C Färber,11 C Farinelli,41
N Farley,45S Farry,52R Fay,52D Ferguson,50V Fernandez Albor,37F Ferrari,14F Ferreira Rodrigues,1M Ferro-Luzzi,38
S Filippov,33M Fiore,16,38,bM Fiorini,16,bM Firlej,27C Fitzpatrick,39T Fiutowski,27P Fol,53M Fontana,10
F Fontanelli,19,iR Forty,38O Francisco,2M Frank,38C Frei,38M Frosini,17J Fu,21E Furfaro,24,hA Gallas Torreira,37
D Galli,14,gS Gallorini,22,38S Gambetta,19,iM Gandelman,2P Gandini,55Y Gao,3 J García Pardiñas,37J Garofoli,59
J Garra Tico,47L Garrido,36D Gascon,36C Gaspar,38U Gastaldi,16R Gauld,55L Gavardi,9G Gazzoni,5A Geraci,21,l
D Gerick,11E Gersabeck,11M Gersabeck,54T Gershon,48Ph Ghez,4A Gianelle,22S Gianì,39V Gibson,47L Giubega,29
V V Gligorov,38C Göbel,60D Golubkov,31A Golutvin,53,31,38 A Gomes,1,m C Gotti,20,e M Grabalosa Gándara,5
R Graciani Diaz,36L A Granado Cardoso,38E Graugés,36 E Graverini,40G Graziani,17A Grecu,29E Greening,55
S Gregson,47P Griffith,45L Grillo,11O Grünberg,63B Gui,59E Gushchin,33Yu Guz,35,38T Gys,38C Hadjivasiliou,59
G Haefeli,39C Haen,38S C Haines,47S Hall,53 B Hamilton,58T Hampson,46X Han,11S Hansmann-Menzemer,11
N Harnew,55S T Harnew,46J Harrison,54J He,38T Head,39V Heijne,41K Hennessy,52P Henrard,5 L Henry,8
J A Hernando Morata,37E van Herwijnen,38M Heß,63 A Hicheur,2 D Hill,55M Hoballah,5 C Hombach,54
W Hulsbergen,41T Humair,53N Hussain,55D Hutchcroft,52D Hynds,51M Idzik,27P Ilten,56R Jacobsson,38A Jaeger,11
J Jalocha,55E Jans,41A Jawahery,58F Jing,3 M John,55D Johnson,38C R Jones,47C Joram,38B Jost,38N Jurik,59
S Kandybei,43W Kanso,6 M Karacson,38T M Karbach,38,† S Karodia,51M Kelsey,59I R Kenyon,45M Kenzie,38
T Ketel,42B Khanji,20,38,e C Khurewathanakul,39 S Klaver,54K Klimaszewski,28O Kochebina,7M Kolpin,11
I Komarov,39R F Koopman,42P Koppenburg,41,38M Korolev,32L Kravchuk,33K Kreplin,11M Kreps,48G Krocker,11
Trang 7P Krokovny,34F Kruse,9 W Kucewicz,26,n M Kucharczyk,26V Kudryavtsev,34K Kurek,28T Kvaratskheliya,31
V N La Thi,39D Lacarrere,38G Lafferty,54A Lai,15D Lambert,50R W Lambert,42G Lanfranchi,18C Langenbruch,48
B Langhans,38T Latham,48C Lazzeroni,45R Le Gac,6J van Leerdam,41J.-P Lees,4R Lefèvre,5A Leflat,32
J Lefrançois,7O Leroy,6T Lesiak,26B Leverington,11Y Li,7T Likhomanenko,65,64M Liles,52R Lindner,38C Linn,38
F Lionetto,40B Liu,15S Lohn,38I Longstaff,51J H Lopes,2 P Lowdon,40D Lucchesi,22,oH Luo,50A Lupato,22
E Luppi,16,bO Lupton,55F Machefert,7F Maciuc,29O Maev,30K Maguire,54S Malde,55A Malinin,64G Manca,15,k
G Mancinelli,6P Manning,59A Mapelli,38J Maratas,5J F Marchand,4U Marconi,14C Marin Benito,36P Marino,23,38,j
R Märki,39J Marks,11G Martellotti,25M Martinelli,39D Martinez Santos,42F Martinez Vidal,66D Martins Tostes,2
A Massafferri,1 R Matev,38A Mathad,48Z Mathe,38C Matteuzzi,20 A Mauri,40B Maurin,39A Mazurov,45
M McCann,53J McCarthy,45A McNab,54R McNulty,12B Meadows,57F Meier,9 M Meissner,11 M Merk,41
D A Milanes,62M.-N Minard,4 D S Mitzel,11J Molina Rodriguez,60S Monteil,5M Morandin,22P Morawski,27
A Mordà,6M J Morello,23,jJ Moron,27A B Morris,50R Mountain,59F Muheim,50J Müller,9K Müller,40V Müller,9
M Mussini,14B Muster,39P Naik,46T Nakada,39R Nandakumar,49I Nasteva,2M Needham,50N Neri,21S Neubert,11
N Neufeld,38M Neuner,11 A D Nguyen,39T D Nguyen,39C Nguyen-Mau,39,pV Niess,5 R Niet,9 N Nikitin,32
T Nikodem,11D Ninci,23 A Novoselov,35D P O’Hanlon,48
A Oblakowska-Mucha,27V Obraztsov,35S Ogilvy,51
O Okhrimenko,44R Oldeman,15,k C J G Onderwater,67B Osorio Rodrigues,1 J M Otalora Goicochea,2A Otto,38
P Owen,53A Oyanguren,66A Palano,13,qF Palombo,21,rM Palutan,18J Panman,38A Papanestis,49M Pappagallo,51
L L Pappalardo,16,bC Parkes,54G Passaleva,17G D Patel,52M Patel,53C Patrignani,19,iA Pearce,54,49A Pellegrino,41
G Penso,25,sM Pepe Altarelli,38S Perazzini,14,g P Perret,5L Pescatore,45K Petridis,46A Petrolini,19,iM Petruzzo,21
E Picatoste Olloqui,36B Pietrzyk,4T Pilař,48
D Pinci,25A Pistone,19S Playfer,50M Plo Casasus,37T Poikela,38F Polci,8
A Poluektov,48,34I Polyakov,31E Polycarpo,2A Popov,35D Popov,10B Popovici,29C Potterat,2E Price,46J D Price,52
J Prisciandaro,39A Pritchard,52 C Prouve,46V Pugatch,44 A Puig Navarro,39G Punzi,23,tW Qian,4 R Quagliani,7,46
B Rachwal,26J H Rademacker,46B Rakotomiaramanana,39M Rama,23M S Rangel,2I Raniuk,43N Rauschmayr,38
G Raven,42F Redi,53S Reichert,54M M Reid,48A C dos Reis,1S Ricciardi,49S Richards,46M Rihl,38K Rinnert,52
V Rives Molina,36 P Robbe,7,38A B Rodrigues,1 E Rodrigues,54 J A Rodriguez Lopez,62P Rodriguez Perez,54
S Roiser,38V Romanovsky,35 A Romero Vidal,37M Rotondo,22J Rouvinet,39T Ruf,38 H Ruiz,36P Ruiz Valls,66
J J Saborido Silva,37N Sagidova,30P Sail,51B Saitta,15,kV Salustino Guimaraes,2 C Sanchez Mayordomo,66
B Sanmartin Sedes,37 R Santacesaria,25C Santamarina Rios,37M Santimaria,18E Santovetti,24,hA Sarti,18,s
C Satriano,25,cA Satta,24D M Saunders,46D Savrina,31,32M Schiller,38H Schindler,38M Schlupp,9M Schmelling,10
T Schmelzer,9B Schmidt,38O Schneider,39A Schopper,38M.-H Schune,7R Schwemmer,38B Sciascia,18A Sciubba,25,s
A Semennikov,31 I Sepp,53N Serra,40J Serrano,6L Sestini,22 P Seyfert,11M Shapkin,35I Shapoval,16,43,b
Y Shcheglov,30T Shears,52L Shekhtman,34V Shevchenko,64A Shires,9 R Silva Coutinho,48G Simi,22M Sirendi,47
N Skidmore,46I Skillicorn,51 T Skwarnicki,59E Smith,55,49 E Smith,53J Smith,47M Smith,54H Snoek,41
M D Sokoloff,57,38F J P Soler,51F Soomro,39D Souza,46B Souza De Paula,2B Spaan,9P Spradlin,51S Sridharan,38
F Stagni,38M Stahl,11S Stahl,38O Steinkamp,40O Stenyakin,35F Sterpka,59S Stevenson,55S Stoica,29S Stone,59
B Storaci,40S Stracka,23,jM Straticiuc,29U Straumann,40R Stroili,22L Sun,57W Sutcliffe,53K Swientek,27
S Swientek,9 V Syropoulos,42M Szczekowski,28P Szczypka,39,38 T Szumlak,27S T’Jampens,4
T Tekampe,9
M Teklishyn,7 G Tellarini,16,bF Teubert,38C Thomas,55 E Thomas,38J van Tilburg,41V Tisserand,4M Tobin,39
J Todd,57S Tolk,42L Tomassetti,16,b D Tonelli,38S Topp-Joergensen,55 N Torr,55E Tournefier,4S Tourneur,39
K Trabelsi,39 M T Tran,39M Tresch,40A Trisovic,38A Tsaregorodtsev,6 P Tsopelas,41N Tuning,41,38 A Ukleja,28
A Ustyuzhanin,65,64 U Uwer,11C Vacca,15,kV Vagnoni,14 G Valenti,14A Vallier,7 R Vazquez Gomez,18
P Vazquez Regueiro,37C Vázquez Sierra,37S Vecchi,16J J Velthuis,46M Veltri,17,uG Veneziano,39M Vesterinen,11
B Viaud,7 D Vieira,2 M Vieites Diaz,37X Vilasis-Cardona,36,f A Vollhardt,40D Volyanskyy,10D Voong,46
A Vorobyev,30V Vorobyev,34C Voß,63J A de Vries,41R Waldi,63C Wallace,48 R Wallace,12J Walsh,23
S Wandernoth,11J Wang,59D R Ward,47N K Watson,45D Websdale,53A Weiden,40M Whitehead,48D Wiedner,11
G Wilkinson,55,38M Wilkinson,59M Williams,38M P Williams,45M Williams,56F F Wilson,49J Wimberley,58
J Wishahi,9W Wislicki,28M Witek,26G Wormser,7S A Wotton,47S Wright,47K Wyllie,38Y Xie,61Z Xu,39Z Yang,3 QUANTUM NUMBERS OF THE Xð3872Þ STATE AND … PHYSICAL REVIEW D 92, 011102(R) (2015)
Trang 8X Yuan,34O Yushchenko,35M Zangoli,14 M Zavertyaev,10,vL Zhang,3 Y Zhang,3
A Zhelezov,11A Zhokhov,31and L Zhong3
(LHCb Collaboration)
1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil 2
Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China 4
LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
6 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France 8
LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany 10
Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
12 School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy 14
Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy 16
Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy 18
Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy 20
Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy 22
Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy 24
Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy 26
Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,
Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland 29
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia 31
Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia 33
Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia
35 Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain 37
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland 39
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland 41
Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine 44
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom 46
H.H Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 48
Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom 50
School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 52
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
Trang 953Imperial College London, London, United Kingdom 54
School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom 56
Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States 58
University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States 60
Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil (associated with Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil) 61
Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China (associated with Center for High Energy Physics, Tsinghua University, Beijing, China) 62
Departamento de Fisica, Universidad Nacional de Colombia, Bogota, Colombia (associated with LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France)
63
Institut für Physik, Universität Rostock, Rostock, Germany (associated with Physikalisches Institut,
Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany) 64
National Research Centre Kurchatov Institute, Moscow, Russia (associated with Institute of Theoretical
and Experimental Physics (ITEP), Moscow, Russia) 65
Yandex School of Data Analysis, Moscow, Russia (associated with Institute of Theoretical and
Experimental Physics (ITEP), Moscow, Russia) 66
Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain
(associated with Universitat de Barcelona, Barcelona, Spain) 67
Van Swinderen Institute, University of Groningen, Groningen, The Netherlands (associated with Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands)
†Deceased.
aAlso at Università di Firenze, Firenze, Italy
b
Also at Università di Ferrara, Ferrara, Italy
cAlso at Università della Basilicata, Potenza, Italy
d
Also at Università di Modena e Reggio Emilia, Modena, Italy
eAlso at Università di Milano Bicocca, Milano, Italy
f
Also at LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
gAlso at Università di Bologna, Bologna, Italy
h
Also at Università di Roma Tor Vergata, Roma, Italy
iAlso at Università di Genova, Genova, Italy
j
Also at Scuola Normale Superiore, Pisa, Italy
kAlso at Università di Cagliari, Cagliari, Italy
l
Also at Politecnico di Milano, Milano, Italy
mAlso at Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
n
Also at AGH - University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland
o
Also at Università di Padova, Padova, Italy
pAlso at Hanoi University of Science, Hanoi, Viet Nam
q
Also at Università di Bari, Bari, Italy
rAlso at Università degli Studi di Milano, Milano, Italy
s
Also at Università di Roma La Sapienza, Roma, Italy
tAlso at Università di Pisa, Pisa, Italy
u
Also at Università di Urbino, Urbino, Italy
vAlso at P.N Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia
QUANTUM NUMBERS OF THE Xð3872Þ STATE AND … PHYSICAL REVIEW D 92, 011102(R) (2015)