Next-to-Leading-Order study on the associate production of $J/\psi+\gamma$ at the LHC

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by  Rong Li

Next-to-Leading-Order study on the associate production of J/ψ +γ at the LHC
Rong Li1,3 and Jian-Xiong Wang2,3
1Department of Applied Physics, Xi’an Jiaotong University, Xi’an 710049, China.
2Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918(4), Beijing, 100049, China.
3Theoretical Physics Center for Science Facilities, CAS, Beijing, 100049, China.
(Dated: January 28, 2014)
TheassociateJ/ψ+γproductionattheLHCisstudiedcompletelyatnext-to-leading-order(NLO)
withintheframeworkofnonrelativisticQCD.Byusingthreesetsofcolor-octetlong-distancematrix
elements(LDMEs)obtainedinpreviouspromptJ/ψstudies,wefindthatonlyoneofthemcanresult
inapositivetransversemomentum(p )distributionofJ/ψproductionrateatlargep region. Based
t t
onreasonableconsiderationtocutdownbackground,ourestimationismeasurableuptop =50GeV
t
with present data sample collected at 8TeV LHC. All the color-octet LDMEs in J/ψ production
4
could be fixed sensitively by including this proposed measurement and our calculation, and then
1
confidentconclusion on J/ψ polarization puzzle could beachieved.
0
2
PACSnumbers: 12.38.Bx,13.25.Gv,13.60.Le
n
a
J Since the discoveryof heavy quarkoniumin the 1970s, resultsfromthreegroups[11–13]implythatthe χ2 fitto

7 the study on production and decay of J/ψ and Υ, plays extract the LDMEs of J/ψ production is very sensitive
2
an important role in the research on the perturbative toinputconditionduetotheapproximatelylinearcorre-

and nonperturbative aspects of QCD. In 1995, a new lationofthe three color-octetcontributionparts. There-
]
h factorizationframework,nonrelativisticQCD(NRQCD), fore,nosolidconclusiononthepolarizationofJ/ψ could
p hadbeenproposedto study the productionanddecayof beachieved,andotherrelevantreliableperturbativepre-
- heavy quarkonium [1]. It overcomes some shortcomings diction,whichisexperimentalmensurableandcanbreak
p
e in the prevalent color-single model(CSM) [2] and makes the linear correlation in previous fit, is expected. Is the
h theCSMbeapartofit. ByextractingtheNRQCDlong- studyonassociateJ/ψ+γ hadroproductionatfullQCD
[ distance matrix elements (LDMEs) from the matching NLOagoodcandidate? Ourstudyclearlyindicatesthat

between theoretical prediction and experimental data, itisaverygoodcandidatewithpresentdatasamplecol-
1
v the NRQCD calculation had given a well description lected at 8TeV LHC.
8 on the transverse momentum distribution (pt) of heavy Inanotherway,forΥhadroproduction,therearestud-
1 quarkoniumproductionathadroncollidersatleadingor-
iesonthep distributionofyieldandpolarizationforthe
9 der (LO) [3]. The phenomenological applications of the t
CSchannelatQCDNLO[5,6]andatthepartialnext-to-
6
NRQCD have been investigated extensively [4]. But the
. next-to-leading order [16]. The NLO QCD correction to
1 polarization of heavy quarkonium hadroproduction had
p distributionoftheyieldandpolarizationforΥ(1S,3S)
0 been an open question for more than ten years. t
via S-wave CO states is presented in Ref. [17], and the
4
NLO QCD correction to p distribution of the yield for
1 The next-to-leading order (NLO) QCD correction to t
: the J/ψ inclusive hadroproduction in the CSM signifi- Υ(1S) via all the CO states is presented in Ref. [18].
v
The complete NLO study on polarization of prompt Υ
i cantly enhanced the pt distribution [5] and changed the
X hadroproduction has been achieved in Ref. [19], which
polarizationfromtransversetolongitudinal[6]. Thelater
r study including the contribution from color-octet model can explain the recent measurement on the polarization
a (COM) parts(1S8 and 3S8) at QCD NLO still can not of Υ(1S,2S,3S) at the LHC by CMS collaboration[20].
0 1
givethesatisfiedpredictiononthepolarizationofJ/ψ[7]. In addition to the study on important inclusive heavy
In Ref. [8], the study on P-wave charmonium hadropro- quarkonium hadroproduction, study on the associate
duction with the feeddown from χ to J/ψ had been hadroproduction of heavy quarkonium and photon (or
cJ
obtained at QCD NLO. Soon after the p distribution of W±,Z0 bosons) was proposed as a supplemental chan-
t
J/ψproductionrateatfullNLOQCDhadbeengivenby nel to probe the gluon content in the proton [21] or to
twogroups[9,10]. Thenafter two years,the p distribu- investigate the production mechanism of heavy quarko-
t
tions on polarization for direct J/ψ hadroproduction at nium [22]. The NLO QCD correction to J/ψ+W±(Z0)
full NLO QCD were presented by two group [11, 12]. A hadbeencalculatedinRef.[23]. Ourstudy[24]showsthe
few months later, a complete study [13] on the polariza- NLOQCDcorrectiontotheassociateJ/ψ+γ hadropro-
tion of prompt J/ψ hadroproduction with the feeddown duction in the CSM enhanced the p distribution largely
t
contributionfromχ included wasgiven,anditpresent in the high momentum region and changed the polar-
cJ
thefirstresultatQCDNLOwhichcanbecomparedwith ization from transverse to longitudinal. The relevant
the experimentalmeasurementsdirectly since allthe po- study [25] can reproduce our results in a partial NLO
larizationmeasurementsareforpromptJ/ψ. Therecent calculation. To obtain an experimental measurable ob-
measurements at the LHC by CMS [14] and LHCb [15] servable at full QCD NLO, we present the study on as-
showdisagreementwiththeprediction[13]. However,the sociate J/ψ +γ hadroproduction at the NLO with full
2
COM contribution in this work. QQ¯ pairradiatingthesoftgluonanditcanbe factorized
In the NRQCD framework the inclusive production of as an amplitude square of QQ¯[3S8, 3S1]+γ hadropro-
1 1
J/ψ+γ can be factorized as ductiontimesasoftfactorwhichcontainsoftdivergence.
This divergence can be absorbed into the redefinition of
the QQ¯[3S8, 3S1] LDMEs at NLO and there are finite
σ(p+p¯→J/ψ+γ+X)=XZ dx1dx2 (1) parts being1left.1Therefore, except the direct calculation
i,j of QQ¯[3P8] state we also have to take into account the
Gi(x )Gj(x )σˆ(ij (QQ¯) +γ+X) OJ/ψ . J
× p 1 p¯ 2 → n h n i contributionfromtheleftparts,whichwecalltheq-term
parts.
Here Gi(j) are the parton distribution functions(PDFs), After generating the Fortran codes of these processes
p(p¯)
σˆ presents the parton level cross section, and OJ/ψ individually by using the Feynman Diagram Calculation
n
h i (FDC) package [28] , we had checked the cancelation of
are the LDMEs. The relevant parton level processes are
infrared and ultraviolet divergence, the gauge invariance
listed as following
and the cut-independence respectively. Because of the
g+g QQ¯[3S1,1S8,3S8,3P8]+γ, (2) complexityoftheanalyticexpressionsweusethequadru-
g+g Q→Q¯[3S1,1S18,3S08,3P18]+Jγ+g, (3) ple precisionprograminsomeofthe calculationto avoid
→ 1 0 1 J the numerical instability.
q+q¯ QQ¯[3S1,1S8,3S8,3P8]+γ, (4)
→ 1 0 1 J To obtain the numerical results, we choose the follow-
q+q¯ QQ¯[1S8,3S8,3P8]+γ+g, (5) ing parameters and cut conditions. The charm quark
→ 0 1 J
q(q¯)+g QQ¯[3S1,1S8,3S8,3P8]+γ+q(q¯). (6) mass mc is set as 1.5GeV and will vary from 1.4GeV to
→ 1 0 1 J 1.6GeV to estimate the related uncertainty. The renor-
In addition to the pt(J/ψ) distribution of the J/ψ+γ malization and factorization scales are set to µr = µf =
hadroproduction at QCD NLO, the related polarization µ = (2m )2+p2 and it will vary from µ /2 to 2µ
0 c t 0 0
observable α of J/ψ is also studied. α is measured by to estipmate the uncertainties. The NRQCD scale µ
Λ
using the angulardistribution ofthe decayedlepton pair is chosen as m . As for the experimental conditions,
c
in helicity frame and related to the spin density matrix we use √s = 7,8,14TeV at the LHC, the rapidity cuts
of J/ψ as y 3, or pseudo-rapidity cut η 1.45 and
J/ψ,γ γ
|pγ <1.|5,≤3,5,15GeVcuts. The fine stru|ctu|re≤constantis
t
dσ11/dpt dσ00/dpt chosen as 1 . The CTEQ6L1 and the CTEQ6M PDFs
α(pt)= − . (7) 128
dσ11/dpt+dσ00/dpt and the corresponding αs running formula are used to
calculate the LO and the NLO numerical results [29].
Here the ”1” and ”0” mean the transverse and lon-
The involved LDMEs were extracted at the NLO by
gitudinal polarization of J/ψ at the matrix element
different group with different consideration [10, 12, 13,
level. The calculations of spin density matrix for the
30]. In Ref. [31] the authors investigated these LDME
QQ¯[3S1,3S8,1S8] are as what have been done in other
1 1 0 sets and concluded that the universality of LDMEs is
similar processes [7].
challenged. ThetwoLDME setsinRef.[10,12]arefrom
In handling the processes in the COM, there are two
the same group, and we use their former results on the
aspects which are different from the color-singlet case.
combinationofLDMEsinRef.[10]toestimatenumerical
Thefirstisisthatinprocess(6)γ haschancetocollinear results since the feeddown contribution from χ and ψ′
c
with quark or anti-quark q(q¯) in final states in some re-
had been considered there, which could affect the theo-
gion of the phase space. This infrared divergence will
retical prediction largely as discussed in Ref. [13]. We
cancel the infrared divergence in the QED correction of
list these LDME sets in table I. For the LDMEs in Ref-
pp J/ψ +g. Because we observe the photon in the erence [10], only the combinations of them, MJ/ψ and
fina→l states, it means that we have to impose a cut on 0,r0
MJ/ψ, are given as
this process to isolate a photon from the quark jet [26] 1,r1
r
pit ≤pγt 11−ccoossRδγi for Rγi <δ0. (8) M0J,/rψ0 =hOJ/ψ(1S08)i+ m02chOJ/ψ(3P08)i, (9)
− 0 MJ/ψ = OJ/ψ(3S8) + r1 OJ/ψ(3P8) , (10)
The definitions of the pi, pγ, cosR and the δ can be 1,r1 h 1 i m2h 0 i
t t γi 0 c
find in Ref. [26]. Here we set δ =0.7. For the considera-
0
tionontheexperimentalmeasurement,wealsosetcut-off where r =3.9, r =-0.56, MJ/ψ = 0.074 and MJ/ψ =
on the transverse momentum of the photon(pγ). There- 0.0005. W0 ith req1uiringthe L0D,rM0 Es to be positive1w,re1 set
t
fore the numerical results will rely heavily on this con- the three individual color-octet LDMEs from the above
dition. The second is that the color-octet P-wave parts combinations under two conditions in table I, which we
have additional infrared divergence which will be factor- will refer to as ”Ma extension” in the following parts.
ized into the LDMEs by using the same method as in ItisshowninFig.1thatthecolor-octet3P8 state,just
J
Ref.[27]. InthecalculationofrealprocessQQ¯[3P8]+γ+ like 3S8 and 1S8 state, gives a positive short distance
J 1 0
g hadroproduction, there is a soft divergence related to coefficient in all p region in contrast to J/ψ inclusive
t
3
√s=14TeV.Theshadedbandrepresentsthe uncertain-
TABLE I: The NRQCD LDMEs hOJ/ψ(n)i extracted by ties estimated by varying the m , the renormalization
c
three groups in Ref. [10, 12, 13, 30] at the NLO with
scale µ and factorization scale µ . The plots show that
hOJ/ψ(3S11)i=1.32 (1.16) GeV3 usedin Ref.[30](intheoth- the uncrertainties of production rfate become larger and
ers). The NRQCD LDMEs in Ma extension1 and extension2
that of α become smaller as p increasing. The COM
are determined from thecombination extracted in Ref. [10]. t
contribution on production rate dominant over that of
CSMandareabout2orderslargerthanthecolor-singlet
ones at p = 50GeV. We also plot the p distribution
n 1S08,GeV3 3S18,GeV3 3P08,GeV5 with the LtDME sets in Ref. [30] and [13],tthe absolute
Butenschoen[30] 0.0497 0.0022 −0.0161 valueofthe numericalresultsareusedinthe p distribu-
t
tionofproductionratesince they become negativewhen
Gong[13] 0.097 −0.0046 −0.0214
p > 13GeV, and αs in both cases are out of physical
t
Chao[12] 0.089 0.0030 0.0126 region when p >10GeV.
t
Ma extension1 0.074 0.0005 0 From the results at the first and second columns of
Fig.2, we know that the p distribution of J/ψ + γ
Ma extension2 0 0.011 0.019 t
hadroproduction rate is good observable to distinguish
differentLDMEsets. Isitmeasurableornotatthe8GeV
LHCwithpresent23fb−1 integratedluminosity? Tosup-
pressthebackgroundefficiently,pγ >15GeVcutonpho-
t
ton is applied, together with y <2.4 and η <1.45
J/ψ γ
| | | |
for photon reconstruction efficiency consideration. The
plots in the third column of Fig.2 show that the p dis-
t
tributions of J/ψ production rate in the COM with Ma
extensionLDMEsetsareabout10(100)timeslargerthan
thatintheCSM.TheothertwoLDMEsetsgivetheposi-
tivepredictionsinlowerp regionandnegativeoneswhen
t
p is largerthan 31 GeV. When p is largerthan 20GeV,
t t
the results show many differences on the J/ψ polariza-
tionpredictionsαwiththeCSM(COM)mechanismand
three LDME sets. It is mentionable that only real pro-
cesses at QCD NLO contribute when pJ/ψ <15GeV.
t
Insummary,wepresentthestudyonassociateJ/ψ+γ
hadroproductionattheNLOwithfullCOMcontribution
at the LHC. Our numerical results show that the contri-
bution from color-octet channels enhances the differen-
tial cross section about 2 order in the large p region.
t
FIG. 1: The ratio of dσ(3PJ8)/dσ(1S08) and dσ(3S18)/dσ(1S08) As for the J/ψ polarization,the color-octetcontribution
as functions of pt. changesitfromlongitudinalonetotransverseone. From
alltheplotsinFig.2,itismanifestlythatthemostimpor-
tantuncertaintycomesfromthethevariationofLDMEs.
hadroproductionatQCDNLOcasewherethecolor-octet TheLDMEsetsofButenschoenandGongleadtotheun-
3P8stategivesnegativeshortdistancecoefficientinlarge physicalp distributionofproductionrate(negative)and
J t
p region. The difference makes the p distribution of polarizationobservableα(outofrange-1to1)atlargep
t t t
J/ψ+γ production rate an observable which can break range, while the LDME set of Ma extension gives physi-
the linear correlationin previous fit. cal ones at all the p range. Even within Ma extension,
t
The first column of Fig.2 presents the results at √s= the p distributions of production rate areof huge differ-
t
7TeV. In order to investigate the dependence on pγ cut, ence ( 10 times at p = 50GeV) between the extension2
t t
we plot the p distribution of production rate and polar- and extension1. The polarization observable α changes
t
izationobservableαwithdifferentpγ cutsandtwosetsof fromslightlylongitudinalinextension1to thetransverse
t
theLDMEsinMaextension. Theplotsshowthatthede- in extension2.
pendenceonpγt cutdecreaseswiththeincreaseofpt(J/ψ) In conclusion, the theoretical predictions are sensitive
and different pγt cuts make the pt distribution shift par- to the LDMEs heavily and can break the linear correla-
allel in contrast to the color-singlet channel in Ref. [24] tion in previous fit. To obtain an experimental measur-
where the pt distribution of J/ψ production rate and α able observable at the 8GeV LHC with present 23fb−1
are insensitive to the the pγt cut in the same pt region. integrated luminosity, pγt > 15GeV cut on the observed
The reasonis that 3P8 and 1S8 channelin the COMare photon is applied to efficiently suppress the background
J 0
sensitive to the cuts. and η <1.45isused. Withtheseconditions,thephoton
γ
| |
In the second column in Fig.2, we give results at reconstructionefficiencyislargerthan0.7andweuse0.7
4
FIG.2: Thep (J/ψ)distributionsforJ/ψ+γ production(upperparts)andpolarization(lowerparts)withdifferentconditions.
t
Figures in the same column are of the same conditions and line types. The shaded band in the second column represent the
uncertainty from variation of µ & µ and m . The third column shows results with pγ >15GeV and different LDME sets.
f r c t
inthefollowingestimation,Br(J/ψ µ++µ−)=0.05is including this proposed measurement and our calcula-
→
alsousedtorepresentreconstructionofJ/ψfromtheob- tion.
servedµ++µ− pair. Thenthe plots inthe thirdcolumn WethankDr. BinGong,Hong-FeizhangandLu-Ping
of Fig.2 indicates that 800-1600 events at p = 17Gev Wan for helpful discussions. Rong Li also thanks Qiang
t
and 16-80 events at p = 50GeV could be reconstructed Liforthediscussionontheisolationofphoton. Thiswork
t
from the sample data. Therefore, the p distribution of issupportedbytheNationalNaturalScienceFoundation
t
productionrateis experimentalmeasurablewith present of China (No. 11105152, 10935012, and No. 11005137),
data sample collected at 8TeV LHC. All the color-octet DFG and NSFC (CRC110), and by CAS under Project
LDMEs in J/ψ production could be fixed sensitively by No. INFO-115-B01.
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