Production of $\rho^{0}$ meson with large $p_T$ at NLO in heavy-ion collisions

0.17 MB·

by  Wei Dai

Production of ρ0 meson with large p at NLO in heavy-ion collisions
T
Wei Dai,1,2 Ben-Wei Zhang∗,1 and Enke Wang1
1Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics,
Central China Normal University, Wuhan 430079, China
2Physics Department, Tsinghua University, Beijing, China
(Dated: January 17, 2017)
Production of ρ0 meson at high pT in high-energy nuclear collisions is investigated for the first
timeatthenext-leading-orderintheQCDimprovedpartonmodel. Theρ0 fragmentationfunctions
(FFs) invacuumat anyscale Q areobtained byevolvingthrough NLODGLAPequationsanewly
developed initial parametrization of ρ0 FFs at a scale Q20 =1.5 GeV2 from a broken SU(3) model.
The numerical simulations of pT spectra of ρ0 meson in the elementary p+p collisions at NLO
7 giveadecentdescription ofSTARp+p data. InA+Areactions thejet quenchingeffect istaking
1 into account in the higher-twist approach by the effective medium-modified parton FFs due to
0 gluon radiation in the quark-gluon plasma, whose space-time evolution is described by a (3+1D)
2 hydrodynamical model. The nuclear modification factors for ρ0 meson and its double ratio with
π± nuclear modification in central Au+Au collisions at the RHIC are calculated and found to be
n in good agreement with STAR measurement. Predictions of ρ0 nuclear modification and the yield
a
J ratio ρ0/π0 in central Pb+Pb at the LHC are also presented, which shows that the ratio ρ0/π0 in
6 central Pb+Pb will approach to that in p+preactions when pT >12 GeV.
1
PACSnumbers: 12.38.Mh;25.75.-q;13.85.Ni

]
h
t A new state of matter of deconfined quarks and glu- oretical studies of hadrons with different types. An in-
-
l ons is expected to be produced in heavy ion collisions tersting type of identified hadrons with available data is
c
(HIC)atveryhighcollidingenergies. Whenanenergetic ρ0 meson, which is heavier than π0 and η, and also con-
u
n parton produced in the initial hard processes is travel- sists of the similar constituent quarks. We notice that
[ ing through this hot/dense QCD medium, a substantial even the theoretical calculations of the ρ0 productions

attrition of its energy is observed, which was referred to in p+p collisions with large p at both the RHIC and
1 T
v as jet quenching effect [1, 2]. Even with the develop- the LHC are absent due to the lack of knowledge of par-
7 ment of experiments and theories, di-hadron [3, 4], pho- tonfragmentationfunctions(FFs)forρ0 invacuum. Ina
4 ton triggered hadron [5, 6] and full jet observable [7–12] previousstudy[16]wehavepavedthewaytounderstand
1
emerged to constraint all the model descriptions of the identified hadron suppression pattern by calculating the
4
jet quenching patterns, the single inclusive hadron pro- productions of η meson and investigating the hadronra-
0
. duction suppressions, as the most intensively measured tios[16]. Inthis letter,weextendthisstudy toρ0 meson
1 and studied observable on jet quenching, is still indis- productionsandtheyieldratiosofρ0 andπ inA+Acol-
0
pensable to probe the properties of the QCD medium. lisions at the RHIC and the LHC. It is of great interest
7
1 By comparing the theoretical calculation with the mea- to seehow the alterationofthe jet chemistrybroughtby
: surements of the production spectra and its suppression thejetquenchingwilleventuallyaffecttheρ0 production
v
of π mesons, i.e, the most commonly observed hadrons, spectrum and the ratio of hadron yields [21–23].
i
X the jet transport coefficient qˆis thus extracted to char- In this paper, firstly we employ a newly developed
r acterize the localproperties of the QCDmedium probed initial parametrization of ρ0 FFs in vacuum at a start-
a
by the energetic parton jets [13]. The higher twist mul- ing low energy scale Q2 = 1.5 GeV2, which is included
0
tiple scattering model description of the jet quenching in the SU(3) model fragmentation functions of vector
incorporatedwith perturbative quantum chromodynam- mesons[24,25]. ByevolvingthemthroughDGLAP evo-
ics(pQCD) improved parton model has successfully de- lution equations at NLO [26], we obtain parton FFs of
scribed the π0 and η productions and their suppressions ρ0 meson at any hard scale Q. The theoretical results of
in A+A collisions [14–17]. ρ0 productions in p+p collisions are provided up to the
next-to-leading order(NLO) in pQCD improved parton
The study of the identified hadron spectra at high p
T
otherthanπ0andηinHICcanfurtherconstrainandcast model, and we find that they describe the experimental
data rather well. Then we study ρ0 productionin A+A
insight into the hadron suppression pattern. Whereas a
collisionsatbothRHICandLHCbyincludingpartonen-
relatively large amount of data on the yields of identi-
ergylossinthehot/denseQCDmediumintheframework
tified hadrons at large p has been accumulated at the
T
ofhighertwistapproachofjetquenching[27,28]. Inthis
RHIC and the LHC [18–20], there are still very few the-
approach, the energy loss due to the multiple scattering
sufferedbyanenergeticpartontraversingthemediumare
takeninto accountby twist-4 processes,and the vacuum
∗[email protected] fragmentation functions are modified to the effectively
2
medium modified ones in high-energy nuclear collisions. functions named valence(V) and sea(γ). The inputs of
Therefore,wecancompute numerically forthe firsttime valence V(x,Q2), sea γ(x,Q2) and gluon D (x,Q2) FFs
0 0 g 0
ρ0 mesonyieldsinA+Acollisions. Wegiveadescription areparameterizedinto astandardpolynomialata start-
of ρ0 nuclear modification factor R (ρ0) at large p in ing low energy scale of Q2 =1.5 GeV2 such as:
AA T 0
Au+Au collisions at the RHIC to confront against the
experimentaldatabySTARCollaboration,andR (ρ0) Fi(x)=aixbi(1 x)ci(1+dix+eix2) (2)
AA −
inPb+PbcollisionsattheLHCtogiveatheoreticalpre-
These parameters are systematically fixed by fitting the
diction. The double ratioof R (ρ0)/R (π±) is calcu-
AA AA crosssectionatNLOwiththemeasurementsofLEP(ρ,ω)
latedandfoundtobe ingoodagreementwiththe exper- and SLD(φ,K⋆) at √s = 91.2 GeV. In Ref. [24, 25] the
imentaldata. Lastlyweexplorethefeaturesoftheρ0/π0 parameters of ρ0 FFs in vacuum at Q2 = 1.5 GeV2 are
ratios in both p+p and A+A collisions. listedandweobtainρ0 FFsatanyhardscaleD (x,Q2)
q,g
InNLOpQCDcalculation,the singleinclusivehadron
Q>2GeVby evolvingthemthroughDGLAP evolution
production can be factorized as the convolution of ele-
equations at NLO with the compute code invented in
mentary partonic scattering crosssections dσˆ/dtˆ, parton Ref. [26], then these ρ FFs D (x,Q2) are used in our
0 q,g
distribution functions (PDFs) inside the incoming parti-
numerical simulations.
cles and parton FFs to the final state hadrons [29]. In We observe that ρ0 FFs are dominated by quark con-
thispaperwesimplify theformulaforfurtherdiscussion:
stituents, which is demonstrated by Fig. 1. We have
plotted the parton FFs as a functions of fragmenting
1 dσ p dz
p dph =Z Fq(zT)·Dq→h(zh,pT) z2h fraction zh in the left panel of Fig. 1 at fixed scale of
T T h h Q2 =100 GeV2, and also the parton FFs as a functions
p dz
+Z Fg(zTh)·Dg→h(zh,pT) zh2h . (1) ionf tfihnealrisgthattepapnTelaotffiFxiegd. 1fr.agAmtetnhteintgypfircaacltizohn=zh0.=6,0w.6e
notice that the light quark fragmentation function show
Theaboveequationimpliesthatthehadronyieldinp+p aratherweakp dependence,andthecontributiontoρ0
T
collision will be determined by two factors: the initial
from quark fragmentationis much larger than that from
(parton-)jet spectrum F (p ) and the parton fragmen-
q,g T gluon (or strange quark) fragmentation.
tation functions Dq,g→h(zh,pT). In the following calcu-
lations, we utilize CTEQ6M parametrization for proton
PDFs [30],whichhasbeenconvolutedwithdσˆ/dtˆtoob- 102 1
u quark
tain Fq,g(pzTh). Here Dq,g→h(zh,pT) represents the vac- 10 s quark
uum parton FFs, which denote the possibilities of scat- 1 Q2=100 GeV2
gluon
teredquarkorgluonfragmentingintohadronhwithmo- 10−1
z=0.6
mentumfractionzh. Theycanbegivenbycorresponding g10−2 g10−1 h
parametrization for different final-state hadrons. So po- Dq,10−3 Dq,
tentially, we could predict all the identified hadron pro-
10−4 u quark
ductions in p+p collision as long as the fragmentation
functionsareavailable. Notethatthefactorizationscale, 10−5 sg qluuoanrk 10−2
renormalization scale and fragmentation scale are usu- 10−6
ally chosento be the same and proportionalto pT ofthe 10−70 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4 6 8 10 12 14 16 18
leading hadron in the final-state. z p(GeV)
T
To accurately determine the p+ p reference, parton
FIG.1: Left: partonfragmentationfunctionsasafunctionof
FFs in vacuum as a non-perturbative input, should be
pT at fixed zh = 0.6; Right: parton fragmentation functions
available. SofaritisstillimpossibletoderivepartonFFs as a function of z at fixedscale Q2 =100 GeV2.
h
fromthefirst-principleofQCDandacommonpracticeis
to make phenomenological parametrizations by compar-
ing perturbative QCD calculations with the data. Un- Theexistenceoftheρ0 mesonfragmentationfunctions
like π and charged hadrons, until now there are very at NLO allows us to calculate the single inclusive vec-
few satisfatory parametrizations of parton FFs for the tor meson productions as a function of the final state
vector mesons due to the paucity of the relevant data. hadronp inpQCDattheaccuracyofNLO.Fig.2shown
T
Fortunately, a broken SU(3) model is recently proposed the confrontation of the theoretical calculation with the
to provide a systematic description of the vector mesons STAR data [18], the results at the scale µ=0.5p agree
T
production [24, 25]. To reduced the complexity of the wellwiththedataforρ0,thus inthe furthercalculations
meson octet fragmentation functions, the SU(3) flavor in nucleus-nucleus collisions, the scales will be fixed to
symmetry is introduced with a symmetry breaking pa- be 0.5p to provide a fairly good p+p baseline.
T
rameter. In addition, isospin and charge conjugation in-
variance of the vector mesons ρ(ρ+,ρ−,ρ0) are assumed A hot and dense QCD matter is created shortly after
to further reduce independent unknown quark FFs into the high energy central nucleus-nucleus collisions. Be-
3
10−3 ρ0 p+p µ=0.5p LO sity, temperature,fraction of the hadronic phase and the
T fourflowvelocityateverytime-spacepointsareprovided,
-23)cV10−4 ρ0 p+p µ=0.5pT nLO olefftthoenljyetontreapnaspraomrteptearraqˆm0τe0t,etrhqˆe parnoddutchteotfimineitiτal wvahluene
e 0 0
b G STAR 200 GeV the QCD medium is initially formed. This parameter
m10−5 controlsthestrengthofjet-mediuminteraction,evenfur-
p (
3d thermore the amount of the energy loss of the energetic
3σ/d10−6 jets. In the calculations we use the values of qˆ0τ0 in pre-
E vious studies [14–16], which give very nice description of
single π and η productions in HIC. Moreover, we have
10−7
used the EPS09s parametrization set of nuclear PDFs
f (x ,µ2) by considering the initial-state cold nuclear
a/A a
10−8 matter effects [33].
10−9
4 6 8 10 12 14 16 18 20
p 1
T
FIG.2: Numerical calculation of theρ0 production in p+p 0.8 ρρ00 @@RRHHIICC NLOLO
STAR data
collisions atRHIC200GeVcomparingwith STAR[18]data.
0.6
RAA
0.4
fore a fast parton fragmented into identified hadrons in
the vacuum, it should suffer energy loss due to multiple 0.2
scattering with the parton in medium. In higher twist
0
approach, the multiple scattering is described by twist-
4
4 processes of hard scattering and will lead to effective
3 @RHIC NLO
m16o]:dificationofthe vacuumfragmentationfunctions [14– ρ0π±/RRAAAA 2 @STRAHRI Cd aLtOa
1
α (Q2) Q2 dℓ2
D˜h(z ,Q2) = Dh(z ,Q2)+ s T 0
q h q h 2π Z0 ℓ2T 6 8 10 pT1(G2eV) 14 16 18
1 dz z
×Zzh z h∆γq→qg(z,x,xL,ℓ2T)Dqh( zh) FduIGct.io3n:suTpopprepssainoenl:inN0u−me1r0i%calAcua+lcuAlautioconlliosfiotnhseatρ0RHprIoC-
z
+∆γq→gq(z,x,xL,ℓ2T)Dgh( zh)i, (3) 2d0a0taG; eBVotatotmbopthanLelO: adnodubNleLrOa,ticoomcaplcaurilnatgiownitohfSRTAρA0AR/R[1Aπ8±A]
where ∆γq→qg(z,x,xL,ℓ2T) and ∆γq→gq(z,x,xL,ℓ2T) = both at LO and NLO,also comparing with STAR data.
∆γq→qg(1−z,x,xL,ℓ2T) are the medium modified split-
ting functions [27, 28]. We average the above medium
modifiedfragmentationfunctionsovertheinitialproduc-
tionpositionandjetpropagationdirection,scaledbythe With the framework introduced above, we calculate
number of binary nucleon-nucleon collisions at the im- thesingleinclusiveρ0 productionsinheavyioncollisions
pactparameterbinA+Acollisionstoreplacethevacuum up to the NLO. The nuclear modification factor R as
AA
fragmentation functions in Eq. (1). We can extract the a function of the final state p is therefore calculated to
T
jet transport parameter qˆ from medium modified split- demonstratethe suppressionofthe productionspectrum
tingfunctions∆γq→qg,gq mentionedintheaboveEq.(3), in A+A collisions relative to that in p+p collision:
theqˆisrelatedtothelocalpartondensitydistributionin
themediumwhenenergeticpartonjetprobed. Therefore R (b)= dσAhB/dyd2pT (4)
thespace-timeevolutionofthemediumalterthevalueof AB NAB(b)dσh /dyd2p
bin pp T
qˆrelativetotheinitialvalueofitlocatedatthecenterof
the overlap region at initial time of the QGP formation. In the 0 10% most central Au+Au collisions at RHIC
−
Product of the four momentum of the jet and the four 200 GeV, we calculate ρ0 productions at typical values
flow velocity of the medium along the jet propagation of qˆ = 1.2 GeV2/fm and τ = 0.6 fm at the RHIC [16].
0 0
path in the collision frame are also included. The theoretical calculation can explain the data at large
The space-time evolutionaryinformations of the QCD p region in the top panel of Fig. 3 for ρ0 meson. We
T
medium are given by a full three-dimensional (3+1D) note that the nuclear suppression factor of ρ0 is similar
ideal hydrodynamics description [31, 32]. Parton den- to the one for π0, as demonstrated by the double ratio
4
1
10−4
0.8 PPbb++PPbb 22..7766 TTeeVV
10−5
00--55%%
p+p 200 GeV ρ0 g
action0.6 Apu++pA u2 0200 0G GeVe Vρ 0ρ q0 g -23)ceV 1100−−76 qqq00===122...826 GGGeeeVVV222///fffmmm
Fr0.4 Au+Au 200 GeV ρ0 q mb G 10−8 0
0.2 3p (d 10−9
σ/
3Ed10−10
04 6 8 10 12 14 16 18 10−11
p(GeV)
T
0.8
FIG. 4: Gluon and quark contribution fraction of the total
yield both in p+pand Au+Auat RHIC 0.6
A
A
R
0.4
0.2
Rρ0 /Rπ± inthebottompanelofFig.3,whichisaround 0 20 40 60 80
AA AA
1 with results at NLO. In the above plots, we also cal- p (GeV)
T
culate the case at leading order accuracy which shows a FIG.5: Numericalpredictionoftheρ0productionin0−10%
small enhancement at lower p . Pb+Pb collisions at LHC 2.76 GeV
T
To understand better the nature of the suppression
pattern,wecalculatethegluon(quark)contributionfrac- 2
tionofthetotalyieldbothinp+pandAu+Aucollisions
in Fig.4. Itis similarto η andπ0 productions whichare ρ0/π0 p+p @RHIC
dominated by quark fragmentation process contribution 1.5 ρ0/π0 p+p @LHC
athighp regioneitherinp+porinAu+Au(moregen- ρ0/π0 Au+Au @RHIC
T
erally, in A+A) , and the jet quenching effect is to sup- ρ0/π0 Pb+Pb @LHC
o
pressthegluonfragmentingcontributionbutenhancethe ti 1
a
quark contribution. Therefore the crossing point when r
the fractionalcontributionsof quarkandgluonfragmen-
tations are equal, will move towardlower p in Au+Au
T 0.5
collision.
We also predict the ρ0 productions in the 0 10% 0
− 10 20 30 40 50 60 70 80 90
most central Pb+Pb collisions with √sNN = 2.76 TeV p(GeV)
T
attheLHCinFig.5withtypicalvaluesofqˆ whichhave
0
beenusedto describe bothproductions ofsingleπ andη FIG. 6: ρ0 π0 production ratio as a function of final state
mesons at the LHC [14–16]. We can see with increasing pT calculated both in p+p and A+A collisions at RHICand
p , the nuclear modification factor for ρ0 meson goes up LHC
T
slowly.
To compare the different trends of π0 and ρ0 spectra,
relatively weak dependence on z and p , then we have:
we plot the ratio ρ0/π0 as a function of the transverse h T
mcoollmiseionntuamtRpHTICineFniegr.gy6.anOdnLeHcaCneonbersgeryv,ethtehraattiinoρp0+/πp0 Ratio(ρ0/π0)= ddpση/ddσpπ0
T T
increases with the p . Though the jet quenching effect
may alter the ratio aTlittle bit in A+A at lower pT, as R Fq(pzTh) Dq→ρ0(zh,pT)dzzh2h ΣqDq→ρ0(hzhi,pT) .
tphTatbeincopm+espl,aersgpeer,citahlleyraattitohienLAHC+wAitchomhiegshvererpy c.lose ≈ R Fq(pzTh) Dq→π0(zh,pT)dzzh2h ≈ ΣqDq→π0(hzhi,pT)
T
Thus, while quark and gluonmay lose different fractions
of their energies, at very high p region, the ratio ρ0/π0
T
We note that at high p productions of both ρ0 and in A+A collisions should approximately be determined
T
π0 are dominated by quark contribution (for example, only by quark FFs in vacuum with p shift because of
T
see Fig. 4). If at high p quark FFs of ρ0 and π0 have a parton energy loss. As we see quark FFs at large scale
T
5
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