Energy Systematics of Jet Tomography

0.11 MB·

by  A. Adil

Preprint submitted to
HEAVY ION
Acta Phys.Hung.A 22/1 (2005) 000–000
PHYSICS
Systematics of Jet Tomography at RHIC:
√s = 62.4 vs. 200 AGeV
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0 A. Adil1 and M. Gyulassy2
2
n 1,2 Columbia University,
a
538 West 120th Street, New York, NY, USA.
J

1
3
Received 1 January 2005

2
v
Abstract. The collision energy dependence of jet tomography is investigated
6
9 withintheGLVformalism. Weestimatesystematicuncertaintiesresultingfrom
0 the interplay of energy loss fluctuations and the rapid increase of the parton
0 transverse momentum slopes as √s decreases from 200 to 62.4 AGeV.
1
5
Keywords: Heavy Ion Collisions, Jet Quenching, Gluon Fluctuations, RHIC
0
PACS: 12.38.Mh;24.85.+p;25.75.-q
/
h
t
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l 1. Introduction
c
u
n We study the energy systematics of jet tomographyin nuclear collisions within the
:
v GLV formalism[ 1, 2] in the √s = 62.4 to 200 AGeV range. Jet tomography at
i √s= 62.4 AGeV data [ 3] tests the predicted √s decrease of the QGP density and
X
the predicted variation of the gluon/quark jet source. In this paper, we calculate
r
a the nuclear modification factor, RAA(pT,y =0,√s), for central Au Au collisions
−
at both √s=62.4, 200 AGeV for neutralpions. Previouspredictions for 62 AGeV
have been published by Wang[ 4] and Vitev[ 5].
We concentrate here on the role of energy loss fluctuations [ 2, 7] on the pre-
dictedsinglehadronattenuationpatterninordertogainanestimateofsomeofthe
systematic theoretical errors in the jet tomographic technique. To isolate the role
of fluctuations we neglect k smearing, the Cronin enhancement, gluon and quark
T
shadowing,and nonperturbative baryondynamicalcontributions that stronglydis-
tort the hadron spectra below p < 4 5 GeV[ 1]. So our results are valid for π0
T
−
spectra for p >4 5 GeV.
T
−
We test the influence of the shape of the energy loss fraction spectrum, P(ǫ,ǫ¯)
about the mean energy loss fraction, ǫ¯, which was first pointed out as important in
[ 8]. This sensitivity to the shape increases as the high p slopes increase at lower
T
2 A. Adil and M. Gyulassy
√s.
2. Calculation of Spectra and R
AA
The neutral pion cross section in pp can be calculated using collinear factorized
pQCD. In a dense QCD medium the induced radiative energy loss reduces the
initial p of the jet parton by a fraction ǫ before hadronization. In this paper we
T
calculate the π0 inclusive spectrum as the following.
E dσπ0(ǫ¯) =K dx dx dǫf (x ,Q2)f (x ,Q2)dσab→cdP(ǫ,¯ǫ)zc∗Dπ0/c(zc∗,Q2) ,
h d3p abcdZ 1 2 a/A 1 b/A 2 dtˆ zc πzc
X
(1)
where z = zc The inclusive number distribution is calculated by mutiplying
c∗ 1 ǫ
this invariant d−istribution with the the Glauber geometric binary collisions factor,
T (b). The functions f and D are the conventional MRS D- distribution
AA a/A h/c
functionandKKPfragmentationfunction,respectively. Gluonnumberfluctuations
are taken into account using the distribution P(ǫ,ǫ¯), where ǫ¯is interpreted as the
average fractional energy loss and is proportional the local gluon rapidity density.
We explore two simplified forms of fluctuation distributions to assess some of the
systematic uncertainties in the predicted quenching. One is a “uniform” model
that essentially reproduces the truncated Poisson of [ 2, 5]. The second is called
”squeezed” because it accumulates strength near the ǫ 1 opaque limit. This
≈
distribution is considered to take into account the alternative branching form of
implementing gluon fluctuations.
The “uniform” distribution takes the form,
θ(0<ǫ<2ǫ¯) if 0<¯ǫ<0.5
P(ǫ,ǫ)= 2ǫ¯ (2)
1 if 0.5<ǫ¯
(cid:26)
while the “squeezed” distributon is the following.
θ(0<ǫ<2ǫ¯) if 0<ǫ¯<0.5
P(ǫ,ǫ)= 2ǫ¯ (3)
( θ(2ǫ¯2−(11<ǫ¯ǫ)<1) if 0.5<ǫ¯
−
The factorsofK andQ2 arefittopp dataatthe requisiteCOMenergies. ǫ¯evolves
with √s according to the the multiplicity evolution. We assume that ǫ¯ (√s) =
c
Cc dNg(√s)/dy ǫ¯ (200)wherecisthepartontypeandC aretheQCDCasimirs.
Cg dNg(200)/dy g c/g
Thu(cid:16)s, the free p(cid:17)arameter is ǫ¯ (200) which is set to fit PHENIX [ 9] π0 data at 200
g
AGeV.
Once the spectra for the A A and p p reactions at the requisite energies
− −
havebeen calculated,the nuclearmodification factorR is just the ratiobetween
AA
them. Thisgivesarangeofvaluesforeachdistribution(“uniform”and“squeezed”)
determined by the errors of the data. For the “squeezed” distribution, the deter-
mined range is 0.65 < ǫ¯ (200) < 0.76 while the “uniform” distribution can be fit
g
Energy Systematics: 200 vs. 62.4 AGeV 3
to R data with the range 0.70 < ǫ¯ (200) < 0.80. The “squeezed” distribution
AA g
needsaloweraverageopacityasthedistributionitselfisbiasedtowardsǫ 1when
→
ǫ¯>0.5.
1 1
Red Lines s1/2 = 200 GeV, Average Quench 0.65-0.76 Red Lines s1/2 = 200 GeV, Average Quench 0.70-0.80
Blue Solid Lines s1/2 = 62.4 GeV, Average Quench 0.50-0.59 Blue Solid Lines s1/2 = 62.4 GeV, Average Quench 0.54-0.62
0.8 Blue Dashed Lines s1/2 = 62.4 GeV, Average Quench 0.42-0.49 0.8 Blue Dashed Lines s1/2 = 62.4 GeV, Average Quench 0.46-0.52
0.6 0.6
RAA dNg/dy = 650 RAA
0.4 dNg/dy = 770 0.4 ddNNgg//ddyy == 675700
0.2
0.2
0
Fig4. 1. Plo6ts of tpTh (G8eeV)predic10ted ban12ds of RAA(p0T4 ) at √s6=62.4pT (G8AeV)GeV fo10r both t12he
“squeezed”and“uniform”distributions. The figure onthe left showsthe predicted
R for the “squeezed” distribution while the figure on the right shows R for
AA AA
the “uniform” distribution.
ThepredictedR at62.4AGeVisobtainedusingthemultiplicitysystematics
AA
from PHOBOS [ 10] that suggests the value dN /dy(√s = 62.4) 650 770. We
g
≈ −
expect from hadron gluon duality arguments that this multiplicity is reduced from
about 1000 at 200 AGeV. Therefore, we expect that ǫ¯(62.4) (0.65 0.77)ǫ¯(200).
≈ −
Thebandsfoundbyfittingto200AGeVPHENIXdatacannowbeextrapolatedto
further bands at 62.4 AGeV. The predicted R (p ) for both distributions can be
AA T
seeninFig. 1. Usingourmultiplicityextrapolationswefindthatforthe“squeezed”
distribution and dN /dy(62.4) 650(770), 0.42(0.50) < ǫ¯ (62.4) < 0.49(0.59).
g g
≈
Similarly,forthe“uniform”distributionanddN /dy(62.4) 650(770),0.46(0.54)<
g
≈
ǫ¯ (62.4)<0.52(0.62). One of the things to note is that the “uniform” distribution
g
prediction is significantly flatter over p than its “squeezed” counterpart. This is
T
because once ǫ¯ > 1 the two distributions treat quenching very differently. The
2
“uniform” distribution saturates to a uniform distribution over0<ǫ<1 while the
“squeezed” distribution piles up closer to ǫ 1 and causing a larger variation in
→
the quench. The calculations for the nuclear modification at √s = 62.4 AGeV are
consistentwithVitev [5]. Any deviationsbetweenthe spectracanbe attributedto
the inclusionofmodelsforCronininteractionsaswellasinitialpartonk smearing
T
in [ 5] which are not included in the current calculations.
Note that the predicted R (p ,√s=62.4) (Fig. 1) have a negative p slope
AA T T
compared to the generally flat R at 200 AGeV. This higher slope is caused by
AA
the earlier set in of the kinematic limits of the problem at lower energies. The
“kinematic suppression” can be more robustly seen by calculating the observable
R (s)= RAA(s) seeninFig. 2. TheR curveshaveadistinctdownwardsslopedue
s RAA(200) s
to the increasing power of the initial parton distributions. R is perhaps a better
s
observable to use than R to observe the energy dependence of jet quenching as
AA
4 A. Adil and M. Gyulassy
3
Solid Lines indicate dNg/dy = 770
1 Dashed Lines indicate dNg/dy = 650
2
2
Rs
3
4
1
1,3 denote Squeezed Distribution
2,4 denote Uniform Distribution
04 6 8 10 12 14 16
Fig.2. TheratioforR at62.4AGeVtopT (tGehV)atat200AGeV.Curvesfor“squeezed”
AA
distributions are generally higher than curves for “uniform” distributions.
the uncertainty in the multiplicity extrapolationsget canceledin the ratio. R also
s
able to differentiate between the two types of fluctuation distributions (see Fig. 2).
References
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