High-$p_T$ Hadron Spectra, Azimuthal Anisotropy and Back-to-Back Correlations in High-energy Heavy-ion Collisions

0.3 MB·English

by  Xin-Nian Wang

LBNL-52533
High-p Hadron Spectra, Azimuthal Anisotropy and Back-to-Back Correlations
T
in High-energy Heavy-ion Collisions
Xin-Nian Wang
Nuclear Science Division, MS70R0319,
Lawrence Berkeley National Laboratory, Berkeley, CA 94720
(April 20, 2003)
Theobservedsuppressionofhigh-pT hadronspectra,finiteazimuthalanisotropy,disappearanceof
jet-likeback-to-backcorrelations,andtheircentralitydependenceinAu+AucollisionsatRHICare
showntobequantitativelydescribedbyjetquenchingwithinapQCDpartonmodel. Thedifference
4
0 between h± and π0 suppression in intermediate pT is consistent with the observed (K + p)/π
0 enhancementwhichshoulddisappearatpT >6GeV/c. Thesuppressionofback-to-backcorrelations
2 isshowntobedirectlyrelatedtothemediummodificationofjetfragmentationfunctions(FF)similar
to direct-photon triggered FF’s.
n
PACS numbers: 12.38.Mh, 24.85.+p; 25.75.-q
a
J

3
2

4 Thedegradationofhigh-pT partonsduringtheirprop- tering cross sections and tA(b) is the nuclear thickness
agation in the dense medium can provide critical infor- function normalized to d2bt (b) = A. We will use a
v A
0 mation necessary for detection and characterization of hard-sphere model of nuRclear distribution in this paper.
1 the strongly interacting matter produced in high-energy TheK 1.3 2factorisusedtoaccountforhigherorder
≈ −
0 heavy-ion collisions. Because of radiative parton en- pQCDcorrections. The partondistributionsper nucleon
5 ergy loss induced by multiple scattering, the final high- f (x ,Q2,r) inside the nucleus are assumed to be fac-
a/A a
0 p hadron spectra from jet fragmentation are expected torizable into the parton distributions in a free nucleon
T
3 to be significantly suppressed [1]. Such a phenomenon, given by the MRS D ′ parameterization [11] and the
0 −
knownasjetquenching,wasobservedforthefirsttimein impact-parameterdependent nuclearmodificationfactor
/
h Au+Au collisionsat the Relativistic Heavy-ionCollider [12,13]. The initial transverse momentum distribution
-t (RHIC) [2,3]. One also observes the disappearance of gA(kT,Q2,b) is assumed to havea Gaussianform with a
l back-to-backjet-likehadroncorrelations[4]andfiniteaz- width that includes both an intrinsic part in a nucleon
c
u imuthal anisotropy [5] of high-pT hadron spectra. These and nuclear broadening. Details of this model and sys-
n threeseeminglyunrelatedhigh-p phenomenaareallpre- tematic data comparisons can be found in Ref. [9].
T
: dictedasconsequencesofjetquenching[1,6–8]. Together, As demonstrated in recent studies, a direct conse-
v
i theycanprovideunprecedentedinformationontheprop- quence of partonenergy loss is the medium modification
X
erties of dense matter produced at RHIC. of FF’s [14,15] which can be well approximated by [16]
r In this Letter, we will study these three high-p
a T
pphQeCnDompenaartosnimmulotadneelotuhsalyt winitchluindeas lionwiteiastl onrudcelera(rLOkT) Dh/c(zc,Q2,∆Ec)=(1−e−h∆λLi)(cid:20)zzcc′Dh0/c(zc′,Q2)
btornoaedneenrginygl,opssa.rtWonesphoaindtowouintgthaantdamneednihuamnciendd(uKce+dpp)a/rπ- +h∆λLizzg′Dh0/g(zg′,Q2)(cid:21)+e−h∆λLiDh0/c(zc,Q2), (2)
ratioleadsnaturallytodifferentsuppressionofh±andπ0 c
spectraatintermediatep range. Wewillalsoshowthat
T provided that the actual energy loss is about 1.6 times
the suppression of back-to-back correlations is directly
of the input value. Here z′ = p /(p ∆E ),
related to the medium modification of hadron-triggered c T Tc − c
z′ = ∆L/λ p /∆E are the rescaled momentum frac-
FF’s similar to a direct-photon triggered FF [10]. g h i T c
tions and ∆E is the total parton energy loss during
c
InaLOpQCDmodel[9],theinclusivehigh-p hadron
T ∆L/λ number of scatterings. The FF’s in free space
cross section in A+A collisions is given by Dh 0 (zi,Q2)aregivenbytheBBKparameterization[17].
h/c c
dσh We assume a 1-dimensionalexpanding medium with a
AB =K d2bd2rdx dx d2k d2k
dyd2pT aXbcdZ a b aT bT vgleurosenpdreonfisleitoyfρpga(rτt,icri)pathnattnuisclperoonps.orTtihoenaavletroagtheenutmrabnesr-
tA(r)tB(b r)gA(kaT,r)gA(kbT, b r) of scatterings along the parton propagating path is then
| − | | − |
f (x ,Q2,r)f (x ,Q2, b r)
a/A a b/B b
| − | τ0+∆L
Dh/c(zc,Q2,∆Ec)dσ(ab cd), (1) h∆L/λi=Z dτσρg(τ,b,~r+~nτ), (3)
πzc dtˆ → τ0
where z = p /p , y = y , σ(ab cd) are parton scat- where∆L(b,~r,φ)isthedistanceajet,producedat~r,has
c T Tc c
→
1
to travel along~n at an azimuthal angle φ relative to the with bremsstrahlung and effectively shuts off energy loss
reaction plane in a collision with impact-parameter b. for lower energy partons.
Shown in Fig. 1 are the calculated nuclear modifica-
tion factors R (p ) = dσh / NAB dσh for hadron
AB T AB h bini pp
11 spectra (y < 0.5) in Au+Au collisions at √s = 200
GeV,asc|om| paredtoexperimentaldata. Here, NAB =
h bini
d2bd2rt (r)t (~b ~r ). To fit the observed π0 sup-
A B
| − |
pRression in the most central collisions, we have used
--11 (solid lines) µ0 = 1.5 GeV, ǫ0 = 1.07 GeV/fm and
1100
λ = 1/(σρ ) = 0.3 fm with the new HIJING param-
0 0
11 eterization [13] of parton shadowing. The hatched area
(alsoinotherfiguresinthispaper)indicatesavariationof
ǫ = 0.3GeV/fm. The hatchedboxes aroundR =1
0 AB
±
represent experimental errors in overall normalization.
Alternatively,onehasto setµ =1.3GeVandǫ =1.09
0 0
--11
when EKS parameterization [12] of parton shadowing is
1100
used(dot-dashedlines). Withoutpartonenergyloss,the
11 spectra is slightly enhanced at p =2 5 GeV/c due to
T
−
nuclear k broadening even with parton shadowing.
T
The flatp dependence ofthe π0 suppressionis acon-
T
sequence of the strong energy dependence of the par-
--11 ton energy loss, which is also observed by other re-
1100
cent studies [21]. The slight rise of R at p < 4
222 444 666 888 111000 222 444 666 888 111000 AB T
GeV/c in the calculation is due to the detailed balance
effect in the effective parton energy loss. In this region,
FIG.1. Nuclear modification factors for hadron spectra in
one expects the fragmentation picture to gradually lose
Au+Au collisions as compared to data from STAR [3] and
its validity and other non-perturbative effects [22] be-
PHENIX [2]. See text for a detailed explanation.
come important that will give an enhanced (K +p)/π
ratio in central Au + Au collisions. To include this
Accordingtorecenttheoreticalstudies[8,15,16]theto-
effect, we add a soft component to kaon and baryon
tal parton energy loss in a finite and expanding medium
FF’s that is proportional to the pion FF with a weight
can be written as a path integral,
N (b,r) /[1+exp(2p 15)]. The functional form
bin Tc
∼h i −
dE τ0+∆L τ τ and parameters are adjusted so that (K +p)/π 2 at
∆E ≈hdLi1dZτ0 dτ τ−0ρ00ρg(τ,b,~r+~nτ), (4) apnTd∼ap3prGoaeVch/ecsiintstphe+mpovsatluceenattrapl A>u+5 AGueVc/oc≈ll.isiTohnes
T
where ρ is the averaged initial gluon density at τ in resultant suppression for total charged hadrons and the
0 0
a central collision and dE/dL is the average par- centrality dependence agree well with the STAR data.
1d
ton energy loss over a hdistancei R in a 1-d expand- One can relate h± and π0 suppressionvia the (K+p)/π
A
ing medium with an initial uniform gluon density ρ0. ratio: RAh±A =RAπ0A[1+(K+p)/π]AA/[1+(K+p)/π]pp. It
The corresponding energy loss in a static medium with is clear from the data that (K+p)/π becomes the same
a uniform gluon density ρ0 over a distance RA is [16] for Au+Au and p+p collisions at pT > 5 GeV/c. To
dE0/dL=(RA/2τ0) dE/dL 1d. Inthehigh-energylimit, demonstrate the sensitivity to the parameterized parton
h i
the parton energy loss has a logarithmic energy depen- energy loss in the intermediate p region, we also show
T
dence [18]. However, for a parton with finite initial en- Rh± in 0-5% centrality (dashed line) for µ = 2.0 GeV
AA 0
ergy the energy loss has a stronger energy dependence and ǫ =2.04 GeV/fm without the soft component.
0
becauseofrestrictedphasespaceforbremsstrahlung[19].
Since jets produced in the central core of the dense
Detailedbalancebetweeninducedgluonemissionandab-
medium are suppressed due to parton energy loss, only
sorptionwill further increasethe energydependence [20]
thosejetsthatareproducednearthesurfaceemergefrom
for a parton with finite initial energy. In this paper we
the medium. The observed high-p hadron multiplic-
T
will use an effective quark energy loss
ity should be proportional to the number of surviving
jets in the outer layerof the overlappedvolumewhich in
dE
1d =ǫ0(E/µ0 1.6)1.2/(7.5+E/µ0), (5) turn is approximately proportional to the total number
hdLi −
of participant nucleons. The nuclear modification factor
fromthe numericalresultsinRef.[20]. Thedetailedbal- normalized by N should decrease with centrality.
binary
h i
ance reduces the effective parton energy loss and at the Thisagreeswellwiththeobservedcentralitydependence.
same time increasesthe energy dependence. The thresh- Thissurfaceemissionpicturealsogivesanaturalgeomet-
old is a consequence of gluon absorption that competes rical limit of the azimuthal anisotropy [23].
2
In non-central collisions, the average path length of similarly to the direct-photon triggered FF [10] in γ-
parton propagation will vary with the azimuthal angle jet events. Here, z = p /ptrig and integration over
T T T
relativetothereactionplane. Thisleadstoanazimuthal y < ∆y is implied. In a simple parton model, the
1,2
dependence of the total partonenergy loss and therefore t|wo|jets should be exactly back-to-back. The initial k
T
azimuthal asymmetry of high-pT hadron spectra [7,8]. distribution in our model will give rise to a Gaussian-
Suchasymmetryisanotherconsequenceofpartonenergy like angular distribution. In addition, we also take into
loss and yet it is not sensitive to the nuclear kT broad- account the intra-jet distribution using a Gaussian form
ening and parton shadowing. Shown in Fig. 2 is v2(pT) with a width of kT =0.8 GeV/c.
(second Fourier coefficient of the azimuthal angle distri- h i
bution)ofchargedhadronsgeneratedfrompartonenergy Shown in Fig. 3 are the calculated back-to-back cor-
loss(dot-dashed)ascomparedtopreliminarySTARdata relations for charged hadrons in Au +Au collisions as
[24] using the 4-particle cumulant moments method [25] compared to the STAR data [4]. The same energy
whichis supposedto reducenon-geometricaleffects such loss that is used to calculate single hadron suppres-
as inherent two-particle correlations from di-jet produc- sion and azimuthal anisotropy can also describe well the
tion[26]. Theenergylossextractedfromhigh-pT hadron observed away-side hadron suppression and its central-
spectrasuppressioncanalsoaccountfortheobservedaz- ity dependence. In the data, a background B(p )[1 +
T
imuthalanisotropyatlargepT. Iftheremainingv2 atin- 2v22(pT)cos(2∆φ)] from uncorrelated hadrons and az-
termediatepT ismadeupbykaonsandbaryonsfromthe imuthal anisotropy has been subtracted. The value of
soft component, one find that they must have v2 ≈ 0.23 v2(pT) is measured independently while B(pT) is deter-
(0.11) for 20-50%(0-10%) collisions. The total v2(pT) is mined by fitting the observed correlation in the region
shown by the solid lines. 0.75< φ <2.24 rad [4].
| |
0.3
0.25 00..11
0.2 00..0055
0.15 00
0.1
00..11
0.05
00..0055
0
0 2 4 6 8 10
00
FIG.2. AzimuthalanisotropyinAu+Aucollisionsascom-
pared tothe STAR[24] 4-particle cumulant result. 00..11
In the same LO pQCD parton model, one can also 00..0055
calculate di-hadron spectra,
00
dσh1h2 K
E E AB = d2bd2rdx dx d2k d2k 000...444 000...666 000...888 111 000...666 000...888 111
1 2d3p1d3p2 2 aXbcdZ a b aT bT
FIG.3. Back-to-backcorrelationsforchargedhadronswith
dzcdzdtA(r)tB(b r)gA(kaT,r)gA(kbT, b r) ptTrig > pT > 2 GeV/c, ptTrig = 4−6 GeV/c and |y| < 0.7 in
Z | − | | − |
Au+Au(lowercurves)andp+p(uppercurves)collisions as
fa/A(xa,Q2,r)fb/B(xb,Q2, b r) compared to theSTAR[4] data.
| − |
D (z ,Q2,∆E )D (z ,Q2,∆E )
h/c c c h/d d d
sˆ dσ
(ab cd)δ4(p +p p p ), (6) Since most of jets produced in the central core of the
2πzc2zd2 dtˆ → a b− c− d colliding volume are suppressed, the triggered high-pT
fortwoback-to-backhadronsfromindependentfragmen- hadrons mainly come from jets produced near the sur-
tationoftheback-to-backjets. Setp =ptrig,wedefine face traveling away from the dense core. These jets are
T1 T
a hadron-triggered FF as the back-to-back correlation notquenched,asobservedinSTARdata[4]. Mostaway-
with respect to the triggered hadron: side jets, however,will be suppressedas they go through
the dense core, except those that are propagating in di-
Dh1h2(z ,φ,ptrig)=ptrigdσAh1Ah2/d2ptTrigdpTdφ, (7) rections tangent to the surface. This leads to a much
T T T dσh1 /d2ptrig smaller azimuthal anisotropy of the away-side suppres-
AA T
3
sion. On the average, both the magnitude of the away- I would like to thank D. Hardtke, P. Jacobs and J.
sidesuppressionandthecentralitydependenceshouldbe Klay for helpful discussions. This work was supported
similar to the single hadron suppression, as seen in the by DOE under Contract No. DE-AC03-76SF00098.
data. Contrary to another study [27], we find that the
p broadening associated with energy loss has no sig-
T
nificant effect on the observedback-to-backcorrelations,
sincethosejetsthathavelargefinal-statebroadeningalso
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4