Hydrodynamic evolution and jet energy loss in Cu+Cu collisions

0.25 MB·English

by  Bjoern Schenke

Hydrodynamic evolution and jet energy loss in Cu+Cu collisions
Bj¨orn Schenke,1,2 Sangyong Jeon,2 and Charles Gale2
1Physics Department, Bldg. 510A, Brookhaven National Laboratory, Upton, NY 11973, USA
2Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, H3A2T8, Canada
WepresentresultsfromahybriddescriptionofCu+Cucollisionsusing3+1dimensionalhydrody-
namics(music)forthebulkevolutionandaMonte-Carlo simulation (martini)fortheevolution of
high momentum partons in thehydrodynamicalbackground. Weexplorethelimits of this descrip-
tionbygoingtosmallsystemsizesanddeterminethedependenceondifferentfractionsofwounded
nucleon and binary collisions scaling of the initial energy density. We find that Cu+Cu collisions
are well described by thehybrid description at least up to 20% central collisions.
1 I. INTRODUCTION The hydrodynamic equations have the following gen-
1 eral form:
0
In order to learn about the range of applicability
2 ∂ ρ = J , (1)
of both hydrodynamics and energy loss mechanisms in t a −∇· a
n heavy-ioncollisions,we study Cu+Cucollisions at √s= where a runs from 0 to 4, labelling the energy, 3 compo-
a
J 200GeV and different centralities. Cu+Cu collisions are nents of the momentum and the net baryon density.
ideally suited for this because they are systems with a The task is to solve these equations together with the
2
number of participants that corresponds to that in pe- equation of state. The Kurganov-Tadmor(KT) method,
] ripheralAu+Aucollisions[1],andcanbestudiedexperi- combinedwithasuitablefluxlimiter,isanon-oscillatory
h mentallywithreduceduncertainties[2]. Oneshouldthus and simple central difference scheme with a small artifi-
p be able to study the transition from “soft” (hydro-like) cial viscosity that can also handle shocks very well It is
-
p features to “hard” features (jet-like). Riemann-solverfreeandhencedoes notrequirecalculat-
e Hydrodynamics assumes that the system is equili- ing the local characteristics.
h brated within a short time of the order of τ0 =0.5fm/c. Whendescribingheavy-ioncollisionsitisusefultoem-
[
1 Tlishioisnassbsuumt ipstuionnlickoeulyldtobehofuldlfiflolerdpfeorripchenertaralloCneus+.CHuenccoel-, ploy τ −ηs coordinates defined by
v itisimportanttostudyawiderangeofcentralityclasses t=τcoshηs,
5 to see when and for which pT range the assumption z =τsinhηs. (2)
2 breaks down.
4 In this work we are able to describe the entire exper- Then the conservation equation ∂µJµ =0 becomes
0
imentally covered p range. The soft or low-p sector
1. of the matter produTced is described using 3+1TD rela- ∂τ(τJτ)+∂ηsJηs +∂v(τJv)=0, (3)
0 tivistic hydrodynamics (music [3]) and the hard sector
1 (p >2GeV) with the Monte-Carlosimulation martini where
1 T
: [4], ∼which uses the hydrodynamic calculation as input Jτ =(coshηsJ0 sinhηsJ3), (4)
v and evolves the hard partons in the soft hydrodynamic Jηs =(coshη J3−sinhη J0), (5)
i s s
X background with the McGill-AMY (Arnold, Moore and −
Yaffe) energy loss approach which treats radiative [5, 6] whichisnothingbutaLorentzboostwiththespace-time
r
a and elastic processes [7]. rapidity η = tanh−1(z/t). The indices v and w refer to
s
We can therefore achieve a complete description of the transversex,y coordinates which are not affected by
Cu+Cucollisionsundertheassumptionthatbothhydro- the boost. Applying the same transformation to both
dynamicsandtheenergylossformalismarevalid. Know- indices of Tµν, one obtains
ingthatwereachthe limitsofapplicabilityofbothmod-
els particularlyfor large centralities,this study allows to ∂τ(τTττ)+∂ηs(Tηsτ)+∂v(τTvτ)+Tηsηs =0, (6)
pindownobservablesthataresensitivetoafailureofour
and
approach and draw conclusions about the nature of the
produced system in Cu+Cu collisions. ∂ (τTτηs)+∂ (Tηsηs)+∂ (τTvηs)+Tτηs =0, (7)
τ ηs v
II. SOFT PART - HYDRODYNAMICS and
∂ (τTτv)+∂ (Tηsv)+∂ (τTwv)=0, (8)
τ ηs w
To describe the soft part of the matter produced in a
heavy-ioncollisionweemployhydrodynamics. Morepre- These5equations,namelyEq.(3)forthenetbaryoncur-
cisely,we use the ideal3+1Drelativisticimplementation rent,andEqs.(6,7,8)fortheenergyandmomentumare
oftheKurganov-Tadmorscheme[8]–music–introduced the equations we solve with the KT scheme described in
in [3]. detail in [3, 8].
2
To close the set of equations (3, 6, 7, 8) we must centrality % hbi [fm]
provide a nuclear equation of state (ε,ρ) which re- 0-5 1.61
P
latesthe localthermodynamicquantities. The presented
0-6 1.76
calculations all employ an equation of state extracted
0-10 2.28
from recent lattice QCD calculations [9]. There, several
5-10 2.95
parametrizations of the equation of state which interpo-
6-15 3.47
late between the lattice data at high temperature and
a hadron-resonance gas in the low temperature region 10-15 3.83
were constructed. We adopt the parametrization “s95p- 10-20 4.16
v1”(and callitEOS-L inthe following),where the fit to 15-20 4.55
the lattice data was done above T = 250MeV, and the 15-25 4.82
entropy density was constrained at T = 800MeV to be
20-30 5.4
95% of the Stefan-Boltzmann value. Furthermore, one
25-35 5.92
”data-point” was added to the fit to make the peak in
30-40 6.4
the trace anomaly higher. See Ref. [9] for more details
on this parametrization of the nuclear equation of state.
TABLE I. Average impact parameters in selected centrality
The initialization of the energy density is done using classes from theoptical Glauber model.
theGlaubermodel(seeRef. [10]andreferencestherein):
Before the collision the density distribution of the two
nuclei is described by a Woods-Saxon parametrization Theparametersη andσ aretunedtodataandwill
flat η
ρ be quoted below.
0
ρA(r)= , (9) The impact parameter b is taken to be the average
1+exp[(r R)/d]
− impact parameter b for a givencentrality class and de-
h i
with R = 4.163fm and d = 0.606fm for Cu nuclei. The terminedusingthe opticalGlauber model(seee.g. [18]).
normalization factor ρ0 is set such that d3rρA(r)=A. The obtained values are listed in Table I.
With the above parameters we get ρ =R0.17fm−3. The spectrum of produced hadrons of species i with
0
The nuclear thickness function degeneracy g is given by the Cooper-Frye formula [19]:
i
∞
dN dN
TA(x,y)=Z−∞dzρA(x,y,z), (10) Ed3p = dypTdpTdφp =giZΣf(uµpµ)pµd3Σµ, (14)
where r = x2+y2+z2, can be used to express both with the distribution function
the densitypof wounded nucleons nWN and binary col-
1 1
elinsieorngsyndeBnCsi(tsyeoeree.ngt.roRpeyf.de[n3s])it.yWscahleetshweriththneWdNepoorsnitBeCd f(uµpµ)= (2π)3exp((uµpµ−µi)/TFO)±1, (15)
is not clear from first principles. SPS data suggests that
where T is the freeze-out temperature, uµ is the flow
the final state particle multiplicity is proportionalto the FO
velocity of the fluid, and the energy is given by the in-
number of woundednucleons. At RHIC energies a viola-
variant expression E = uµp . In practice, we determine
tionofthisscalingwasfound(theparticleproductionper µ
the freeze-out hyper-surface geometrically using a trian-
woundednucleonisafunctionincreasingwithcentrality.
gulation of the three dimensional hyper-surface that is
Thisisattributedtoasignificantcontributionfromhard
embeddedinfour-dimensionalspace-time. Thedetailsof
processes, scaling with the number of binary collisions).
this algorithm are described in Ref. [3].
As in [3] the shape of the initial energy density distri-
bution in the transverse plane is parametrized as
III. HARD PART - MONTE-CARLO JET
W(x,y,b)=(1 α)n (x,y,b)+αn (x,y,b), (11)
WN BC
− EVOLUTION
whereαdeterminesthefractionofthecontributionfrom
binary collisions,and we will study the effect ofdifferent
The hard part of the system is described using the
choices for α. Monte-Carlo simulation martini [4]. At the core of
Forthelongitudinalprofileweemploytheprescription martini lies the McGill-AMY formalism for jet evolu-
used in Refs. [11–17]. It is composed of a flat region
tion in a dynamical thermal medium. This evolution
aroundη =0,andofhalfaGaussianintheforwardand
s is governed by a set of coupled Fokker-Planck-type rate
backward direction:
equations of the form
(ηs ηflat/2)2 ∞
H(η )=exp | |− θ(η η /2) . (12) dP(p) dΓ(p+k,k) dΓ(p,k)
s (cid:20)− 2σ2 | s|− flat (cid:21) = dk P(p+k) P(p) (1,6)
η dt Z−∞ (cid:18) dk − dk (cid:19)
The full energy density distribution is then given by
where dΓ(p,k)/dk is the transition rate for processes
ε(x,y,η ,b)=ε H(η )W(x,y,b)/W(0,0,0). (13) where partons of energy p lose energy k.
s 0 s
3
In the finite temperature field theory approach of
AMY, radiative transition rates can be calculated by 104 PHENIX Cu+Cu 200GeV 0-5%, 5-10%/10, 10-15%/100, 15-20%/500, 20-30%/4000
meansofintegralequations[6]whichcorrectlyreproduce MUSIC Cu+Cu α=0.1, b=1.61fm, 2.95fm, 3.83fm, 4.55fm, 5.4fm
both the Bethe-Heitler and the LPM results in their re- dpT 102 MUSIC Cu+Cu α=1, b=1.61 fm, 2.95fm, 3.83fm, 4.55fm, 5.4fm
spective limits [20]. Transition rates for the processes p T 100
g gg, q(q¯) q(q¯)g, and g qq¯are included as well y π-
as→elastic proc→esses employing→the transition rates com- N/d 10-2
d
puted in [7]. Furthermore, gluon-quark and quark-gluon π) 10-4
conversion due to Compton and annihilation processes, 2
aswellasthe QEDprocessesofphotonradiationq qγ (1/ 10-6
→
and jet-photon conversions [21, 22] are implemented.
-8
Inmartini,Eq.(16)issolvedusingMonteCarlometh- 10
0 1 2 3 4 5
ods,keepingtrackofeachindividualparton,ratherthan
p [GeV]
the probability distributions P. This method provides T
information on the full microscopic event configuration
in the high momentum regime, including correlations,
FIG. 1. Transverse momentum spectra of negative pions for
which allows for a very detailed analysis and offers a di-
differentcentralityclasses comparedtopreliminaryPHENIX
rect interface between theory and experiment.
data. The collisions go from central(top) tomore peripheral
In a full heavy-ion event, the number of individual
(bottom).
nucleon-nucleon collisions that produce partons with a
certain minimal transverse momentum pmin is deter-
T
mined from the total inelastic cross-section,provided by
pythia, which is also used to generate those individual where T is the local temperature. For partons that stay
hard collisions. The initial transverse positions of the above that threshold, the evolution ends once they en-
hard collisions are determined by the initial jet density ter the hadronic phase of the background medium. In
distribution the mixed phase or a crossover region, processes occur
only for the QGP fraction. When all partons have left
AB(b,r⊥)= TA(r⊥+b/2)TB(r⊥−b/2), (17) the QGP phase, hadronization is performed by pythia,
P T (b)
AB to which the complete information on all final partons is
passed. Because pythia uses the Lund string fragmen-
which is determined by the nuclear thickness (10) and
tation model [25, 26], it is essential to keep track of all
overlap functions
color strings during the in-medium evolution. For more
TAB(b)= d2r⊥TA(r⊥)TB(r⊥+b). (18) informationon the details of martini please refer to [4].
Z
The initial parton distribution functions can be selected IV. RESULTS
with the help of the Les Houches Accord PDF Interface
(LHAPDF) [23]. Isospin symmetry is assumed and nu-
We begin by presenting results for the soft transverse
clear effects on the parton distribution functions are in-
momentum region obtained entirely by music. We al-
cluded using the EKS98 [24] parametrization.
ways compare three different parametrizations, which
As discussed above, the soft medium is described by
essentially differ by the contribution of binary collision
hydrodynamics. Before the hydrodynamic evolution be-
scaling of the initial energy density distribution (see Eq.
gins (τ < τ ), the partons shower as in vacuum. During
0 (11)). The details of the parameter sets are listed in Ta-
the medium evolution, individual partons move through
ble II.
the backgroundaccordingto their velocity. Probabilities
to undergo an interaction are determined in the local
fluid cell rest frame using the transition rates and the
local temperature. The boost into the local fluid rest- Fig. 1showsthetransversemomentumspectraofneg-
frame is performed using the flow velocities provided by ative pions for different centralities compared to prelim-
the hydro calculation. inary data from PHENIX (see e.g. [27]). For the most
If a process occurs, the radiated or transferred energy central collisions both parametrizations describe the ex-
is sampled from the transition rate of that process. In perimental data reasonably well for p < 2GeV. The
T
case of an elastic process,the transferred transversemo- larger the impact parameter, the lower th∼e p at which
T
mentum is also sampled, while for radiative processes the description using hydrodynamics fails. For 20-30%
collinear emission is assumed. central collisions the calculation begins to deviate from
Radiated partons are further evolved if their momen- the experimental data at approximately p > 1.5GeV.
T
tum is above a certain threshold p 2 3GeV. Generally, the calculation with larger α lead∼s to harder
min
≃ −
The overall evolution of a parton stops once its energy spectra. For anti-protons we find a very similar behav-
in a fluid cell’s rest frame falls below the limit of 4T, ior, shown in Fig. 2. In this case the result is generally
4
α τ0[fm] ε0[GeV/fm3] εFO[GeV/fm3] TFO[MeV] ηflat ση
0.1 0.55 20 0.14 ≈140 4 1.2
0.5 0.55 26 0.14 ≈140 4 1.2
1 0.55 29 0.14 ≈140 4 1.2
TABLE II.Parameter sets.
300
102 PHENIX Cu+Cu 200GeV p_ 0-5%, 5-10%/10, 10-15%/100, 15-20%/500, 20-30%/4000 PHOBOS prelim. 0-6%, 6-15%, 15-25%, 25-35%
dpT 100 MMUUSSIICC CCuu++CCuu αα==01.,1 b, =b1=.17.67 6fmfm, ,2 2.9.955fmfm, ,3 3.8.833fmfm, ,4 4.5.555fmfm, ,5 5.4.4fmfm 250 MMMUUUSSSIIICCC CCCuuu+++CCCuuu ααα===001..,15 b,, =bb1==.117..677f66mff,mm 3,, .334..744f77mff,mm 4,, .448..288f22mff,mm 5,, .559..299f22mffmm
p T p_ 200
dy 10-2 η
N/ N/d 150
) d 10-4 d
π 100
2
1/ 10-6
(
50
-8
10
0 1 2 3 4 5 0
-6 -4 -2 0 2 4 6
p [GeV]
T
η
FIG. 2. Transverse momentum spectra of anti-protons for FIG.3. Centralitydependenceofpseudorapiditydistributions
differentcentralityclasses compared topreliminaryPHENIX of charged hadrons compared to preliminary PHOBOS data
data. The experimental data is underestimated because of [30] (open symbols). Calculations using α = 0.1 describe all
theassumption of chemical equilibrium. centrality classes very well, while larger α lead to deviations
for larger centralities.
below the data because of the assumed chemical equilib-
0.2
rium (see Ref. [3]), the overall shape of the spectra is STAR Cu+Cu 200 GeV h+/- 10-20%
however well reproduced for low p . CuCu EOS-L h+/- α=0.1, 4.16fm
T CuCu EOS-L h+/- α=0.5, 4.16fm
Although we find harder spectra in the case of α = 1 0.15 CuCu EOS-L h+/- α=1, 4.16fm
it is unclear which parametrization is favored solely by
studying the p spectra of pions and anti-protons. The
T 2 0.1
centralitydependenceofchargedparticlepseudo-rapidity v
distributions in Fig. 3 reveals a much more obvious dif-
ference. While inthecaseα=0.1theexperimentaldata 0.05
isverywelldescribedforallshowncentralityclasses,the
calculations using α = 0.5 and α = 1 only describe the
0
mostcentraldatatowhichtheparameterswereadjusted,
0 0.5 1 1.5 2 2.5
butdifferincreasinglywithincreasingimpactparameter.
p [GeV]
It is remarkable how well the p integrated pseudo- T
T
rapidity distributions are described even for very large
pseudorapidities and impact parameters. This indicates
that for low p , i.e., p < 1GeV, hydrodynamics works FIG.4. Elliptic flowcoefficient v2 as afunction of transverse
T T momentumfor10-20%centraleventscomparedtoSTARdata
well, hinting at that the∼low momentum modes equili-
[28].
brate fast enough even in small systems, while higher
momentum modes do not.
Next, we present the elliptic flow parameter v and
2
compare to STAR data [28]. Because we do not include tions,atleastforAu+Aucollisions[29]. Thedependence
fluctuations, we do notexpect the centrality dependence on the α parameter is as expected. Larger α meaning
of elliptic flow to be reproduced. See Ref. [29] for a higher initial eccentricity, leads to stronger elliptic flow.
demonstration of the importance of fluctuations on el- To draw further conclusions from this comparison a de-
liptic flow observables. In Fig. 4 we show results for tailed event-by-event study is needed.
10-20%central events, a centrality class in which v (p ) Extracting the evolution information from the hydro-
2 T
was found to be well described by smooth initial condi- dynamicsimulation,i.e.,thetemperatureandflowveloc-
5
104 1.2
PHENIX prelim. Cu+Cu 200 GeV π- 0-5% PHENIX prelim. Cu+Cu 200 GeV, 0-10% central
dpTT 102 SMMTUAARSRITC ICN buI= +b1C=.71u6. 27fm060f m G, eαVs= π0-. 302-10% 0 .18 AAAMMMYYY +++ eeelll 333+++111DDD MMMUUUSSSIIICCC HHHyyydddrrrooo αααsss===000...333222 ααα===001...150 bbb===222...222888 fffmmm
N/dy p 10-20 π- 0π RAA 0.6
d 10 0.4
)
π
2
1/ 10-4 0.2
(
0
-6
10 0 2 4 6 8 10 12 14
0 1 2 3 4 5 6 7 p [GeV]
T
p [GeV]
T
FIG. 6. Nuclear modification factor for neutral pions in 0-
FIG. 5. Transverse momentum spectrum of negative pions 10% central Cu+Cu collisions compared to preliminary data
from the hydrodynamic calculation music (dashed line) and from PHENIX.
martiniusingmusicinput(solidline)comparedtodatafrom
PHENIX (preliminary) and STAR[31].
1.2
1
ities as functions oftime and spatialcoordinates,we can
usethisinformationasaninputforthe simulationofthe 0.8
evolution of the hard degrees of freedom, martini. AA
R 0.6
This way we can compute the hard part of the spec- 0
π
trum and combine results for the soft and hard part as
0.4
PHENIX prelim. Cu+Cu 200 GeV, 10-20% central
done in Fig.5 for negative pions. The additional free
AMY + el 3+1D MUSIC Hydro αs=0.32 α=0.1 b=4.16 fm
pmaarratminetierisththaet srtergounlagtecsoutphleinagmcoounnsttaonft,enwehrigcyhlwosesfiinx 0 .02 AAMMYY ++ eell 33++11DD MMUUSSIICC HHyyddrroo ααss==00..3322 αα==01..50 bb==44..1166 ffmm
at α = 0.32. The value of transverse momentum up
s 0 2 4 6 8 10 12 14
to where hydrodynamics alone provides a good descrip-
p [GeV]
tion and beyond which the contribution from jets be- T
comes important decreases with decreasing system size.
For central Au+Au collisions the value lies between 3 FIG. 7. Nuclear modification factor for neutral pions in 10-
and 4GeV [3], while Fig.5 shows that for Cu+Cu it lies 20% central Cu+Cu collisions compared to preliminary data
around 2GeV for central collisions, and from Fig.1 one from PHENIX.
can read off that it decreases more when going to larger
centralities.
Next,westudythenuclearmodificationfactorforneu-
of ideal hydrodynamics with our energy loss mechanism
tral pions, defined by
begins to fail to describe Cu+Cu systems at centralities
1 dN (b)/d2p dy > 20%. Remember that hydrodynamics using α = 0.1
AA T
RAA = N (b) dN /d2p dy , (19) ∼described the bulk data well, while deviations from ex-
coll pp T
perimental data at more peripheral collisions are large
where N (b) is the number of binary collisions at for α=0.5 and α=1 (Fig.3).
coll
given impact parameter b. The reference spectrum On the other hand α = 1 works best for R . This
AA
dN /d2p dy for p+p collisions was computed in [4]. indicatesthattheenergylossmechanismitselfleadsto a
pp T
Figures 6 to 9 show the nuclear modification factor tooweakcentralitydependencewhenusingthe“correct”
R for different centrality classes. The value of α was hydrodynamic background (α = 0.1). Using a hydro-
AA s
chosen to match the experimental data in the most cen- background with a larger centrality dependence of the
tral collisions best, but when going to larger centrality density (α = 1) then works against this problem. Note,
classes the impact parameter is the only quantity that however,that for all α the results for R lie within the
AA
is changed. We see that all hydrodynamic backgrounds experimental error bars. The effect of non-zero viscosity
(α 0.1,0.5,1 ) lead to good agreement with the ex- and event-by-event fluctuations [29] remains to be stud-
∈ { }
perimentaldatainthetwomostcentralbins(Figs.6and ied.
7). All calculations, but most significantly the one using Finally we study high momentum photon production
α = 0.1, deviate from the 20-30% and 30-40% central in Cu+Cu collisions. Photons in the high p regionpro-
T
experimental data. This indicates that the combination ducedinnuclearcollisionsaredominantlydirectphotons,
6
1.2 1.6
1.4
1
1.2
0.8
1
A
0π RA 0.6 γRAA 0.8
0.4 0.6
PHENIX prelim. Cu+Cu 200 GeV, 20-30% central
AMY + el 3+1D MUSIC Hydro αs=0.32 α=0.1 b=5.4 fm 0.4 PHENIX prelim. Cu+Cu 200 GeV, 0-10% central
0 .02 AAMMYY ++ eell 33++11DD MMUUSSIICC HHyyddrroo ααss==00..3322 αα==01..50 bb==55..44 ffmm 0.2 AAMMYY ++ eellaassttiicc ++ MMUUSSIICC HHyyddrroo,, ααss==00..3322,, bb==22..2288 ffmm,, αα==10.1
0 2 4 6 8 10 12 14 0
4 6 8 10 12 14 16
p [GeV]
T p [GeV]
T
FIG. 8. Nuclear modification factor for neutral pions in 20-
30% central Cu+Cu collisions compared to preliminary data FIG. 10. Nuclear modification factor for photons in 0-10%
from PHENIX. centralCu+Cu collisions compared topreliminary datafrom
PHENIX.
1.2
dataisconsistentwithRγ =1andsoisthecalculation
AA
1 for a wide range of p . The rise above one for p <
T T
6GeV stems fromthe contribution ofin-medium photo∼n
0.8
production. Unfortunatelythecurrentexperimentaldata
A
RA 0.6 does not allow to distinguish whether this contribution
0 is present or not.
π
0.4
PHENIX prelim. Cu+Cu 200 GeV, 30-40% central
AMY + el 3+1D MUSIC Hydro αs=0.32 α=0.1 b=6.4 fm
0.2 AMY + el 3+1D MUSIC Hydro αs=0.32 α=0.5 b=6.4 fm V. CONCLUSIONS AND OUTLOOK
0 AMY + el 3+1D MUSIC Hydro αs=0.32 α=1.0 b=6.4 fm
0 2 4 6 8 10 12 14
We studied the applicabilityof botha 3+1Dhydrody-
p [GeV]
T namic model and the McGill-AMY jet energy loss and
evolution scheme to Cu+Cu collisions of different cen-
tralities. Because the created system is smaller than in
FIG. 9. Nuclear modification factor for neutral pions in 30-
Au+Au collisions the limits of the models are already
40% central Cu+Cu collisions compared to preliminary data
reached at a smaller impact parameter. The precise de-
from PHENIX.
termination of these limits and the determination of ob-
servables that are sensitive to the failing of the models
was the main objective of this work.
fragmentation photons, and jet-plasma photons. Direct The hydrodynamic evolution was computed using
photons are included in pythia. Apart from leading or- the relativistic 3+1D implementation of the Kurganov-
der direct photons, pythia produces additional photons Tadmor scheme, dubbed music, while the evolution of
emitted during the vacuum showers, which in part over- the hard degrees of freedom was simulated using the
lapwithphotonsfromnext-to-leadingordercalculations. Monte-Carlo simulation martini. With these, we were
Fragmentation photons are also part of those produced abletocomparecalculationstoexperimentalobservables
intheshower. Forheavy-ionreactionsmartiniaddsthe over the full range of measured transverse momentum.
veryrelevantjet-medium photons fromphotonradiation As expected, the quality of the description of trans-
q qγ (bremsstrahlung photons) and jet-photon con- versemomentumspectraofidentifiedhadronsusingonly
→
versionviaComptonandannihilationprocesses. Thefull hydrodynamics depends on the system size. While in
vacuumshowerisincludedinthecalculation-mostofthe Au+Aucollisionsthespectraincentralcollisionsaretyp-
shower photons will be emitted before the medium has icallywelldescribeduptop 3GeV,inCu+Cuwefind
T
≈
formed and the parton has realized that it has formed. deviations at approximately 2GeV for central collisions,
For more details on the implementation see [4]. and lower p for larger centralities.
T
In Fig.10 we present the nuclear modification factor Thehydrodynamiccalculationofthecentralitydepen-
forphotonscomparedtopreliminarydatafromPHENIX dence of pseudorapidity distributions agrees very well
(also see [27]) in central collisions. Again, the reference with the experimental data when we use 90% wounded
spectrum from p+p collisions was computed in [4]. The nucleon scaling and 10% binary collisions scaling of the
7
initial energy density distribution. The parameter set 20%centralbinsagreewellwithexperimentaldata,devi-
using 100% binary collision scaling does not reproduce ationsbegin forcentralities largerthan 20%. This might
the centrality classes above 10%. We therefore conclude indicate that the used energy loss mechanism does not
that mostly wounded nucleon scaling provides a better have the correct density and/or system size dependence
description of experimental data. In this case, the result forthesmallsystemsstudiedhere. Thecurrenterrorbars
shows that the low transverse momentum modes that do not permit a more precise quantitative statement.
dominate the distribution are thermalized, even in 30-
40% central collisions, which is in agreement with the
result for the transverse momentum spectra. ACKNOWLEDGMENTS
Including the contribution from jets by employing
martini, which uses the hydrodynamic evolution as in- B.P.S.thanksRoyLaceyforhelpwithlocatingtheex-
put, we were able to describe the complete pion spec- perimental data. This work was supported in part by
tra in central collisions. The study of RAA for pions the Natural Sciences and Engineering Research Coun-
allows to pin down the point where the combined ideal cil of Canada. B.P.S. gratefully acknowledges a Richard
hydrodynamics+McGill-AMY evolution breaks down. H. Tomlinson Postdoctoral Fellowship by McGill Uni-
The trend seen in the description of the centrality de- versity. B.P.S. was supported in part by the US De-
pendence of R agrees least with experimental data partment of Energy under DOE Contract No.DE-AC02-
AA
when using α = 0.1, which is preferred by the low mo- 98CH10886, and by a Lab Directed Research and De-
mentum spectra. While calculations for 0-10% and 10- velopment Grant from BrookhavenScience Associates.
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