Table Of ContentJets in d(p)-A Collisions: Color Transparency or Energy Conservation
Michael Kordell II and Abhijit Majumder
Department of Physics and Astronomy, Wayne State University, Detroit, MI 48201.
(Dated: February 1, 2016)
The production of jets, and high momentum hadrons from jets, produced in deuteron (d)-Au
collisions at the relativistic heavy-ion collider (RHIC) and proton (p)-Pb collisions at the large
hadron collider (LHC) are studied as a function of centrality, a measure of the impact parameter
of the collision. A modified version of the event generator PYTHIA, widely used to simulate p-
p collisions, is used in conjunction with a nuclear Monte-Carlo event generator which simulates
the locations of the nucleons within a large nucleus. We demonstrate how events with a hard jet
may be simulated, in such a way that the parton distribution function of the projectile is frozen
during its interaction with the extended nucleus. Using our approach, we demonstrate that the
6 puzzling enhancement seen in peripheral events at RHIC and the LHC, as well as the suppression
1 seenincentraleventsattheLHCaremainlyduetomis-binningofcentralandsemi-centralevents,
0 containingajet,asperipheralevents. Thisoccursduetothesuppressionofsoftparticleproduction
2 away from the jet, caused by the depletion of energy available in a nucleon of the deuteron (in
n d-AuatRHIC)orintheproton(inp-PbatLHC),aftertheproductionofahardjet. Weconclude
a thatpartoniccorrelationsbuiltoutofsimpleenergyconservationaremostlyresponsibleforsuchan
J effect.
8
PACSnumbers: 25.75.-q,13.87.-a,25.45.-z
2
]
h I. INTRODUCTION ments,bothbyPHENIX[4]atRHICandbyATLAS
t at the Large Hadron Collider (LHC), on the spec-
-
cl Inthecontextofhardprocessesinheavy-ioncolli- trum of high transverse momentum (high pT) jets
produced in d-Au [5] and p-Pb [6] collisions. The
u sions,maximallyasymmetriccollisions,suchasd-Au
n atRHICandp-PbattheLHC,haveservedthepur- measurements plot the centrality dependent nuclear
[ pose of baseline measurements: Quantifying initial modification factor RdAu of high pT jets: A ratio of
2 state nuclear effects without the presence of a hot- the detected yield of jets to that expected based on
an estimate of the number of nucleon-nucleon col-
v dense extended final state. Early measurements of
lisions in one p(d)-A collision. In both cases, one
5 suppressed back-to-back hadron correlations, with
9 momenta perpendicular to the colliding nuclei, at notices an enhancement in the RdAu in peripheral
5 events and a “suppression” in central collisions. In
the STAR detector at RHIC [1] for Au-Au colli-
2 a study of the rapidity dependence of the recon-
sions,comparedwithanulleffectind-Au(compared
0 structedjet,bytheATLAScollaboration,itwasob-
withp-p)establishedjetquenchingasafinalstateef-
.
1 fect that takes place primarily in the presence of an servedthatthisperipheralenhancementandcentral
0 suppression was muchmore prevalent in the p going
extended Quark-Gluon-Plasma (QGP). These jets
6 direction and vanishing in the Pb direction.
with momentum transverse to the incoming beams,
1
were quenched in Au-Au, but were minimally af- Theseresultsarerathercounterintuitive. Nuclear
:
v fected in d-Au collisions. effects, in particular those that involve jets and jet
i
X Thesewereconsistentwithmeasurementsofalack production, are expected to be dominant in cen-
of suppression in the expected yield of high trans- tral events where the initial state engenders several
r
a verse momentum (leading) hadrons in d-Au colli- nucleon-nucleon collisions, also the final out going
sions at the PHENIX detector [2]. In 2006, the partons have to traverse a more extended medium.
PHENIX collaboration, extended this analysis to Similar arguments may be ascribed to the rapidity
centrality (the experimental measure of impact pa- dependence of hard particle production, with hard
rameter) dependent suppression [3, 4]. This data partons traversing longer distances in the nucleus
demonstrated an odd enhancement in the yield of going direction than in the p or d going direction.
high momentum hadrons in peripheral d-Au events. In this paper we posit that events which lead to
While nuclear effects which modify the dynamics the production of a hard jet, requiring an initial
of jet production, were expected in central events, statepartonwithaconsiderablevalueofx,haveini-
where nucleons from the deuteron encounter several tial states with a fewer number of soft partons, due
collisions with the large nucleus, these were not ex- to the large amount of energy that has been drawn
pectedatallinperipheraleventswherethedeuteron away from the nucleon by the high-x parton. This
has fewer collisions with the large nucleus. effectismostpronouncedonthepartonsinthep(d)
Recentlytherehavebeenaseriesofnewmeasure- going direction, and much less on the A going di-
2
rection as the formation of a hard parton in a single of soft partons that arise after the hard parton has
nucleon(inanucleus)doesnoteffectthesoftparton been extracted.
distribution in the remaining nucleons. The higher In the subsequent section we describe the event
the x required, the more the suppression in the soft generator that samples the location of the nucleons
particle production. Thus reactions with very high in the two incoming nuclei. In Sec. III, we outline
energyjetproductionprobethecorrelationbetween thechangesintroducedintothePYTHIAeventgen-
partons within a nucleon. This sensitivity to multi- erator. In Sec. IV we present comparisons with ex-
parton hard-soft correlations is unique to these ex- perimentaldataatRHICandLHC.Ourconclusions
periments,whichprobeahithertounmeasuredfacet are presented in Sec. V.
ofnucleonstructure: isthereastrongcorrelationbe-
tween the x values of the leading partons in a given
event and the total number of partons in the nu- II. SAMPLING THE NUCLEAR
cleon, in that event. By “strong” we are suggesting DISTRIBUTION
something more than the trivial correlation due to
straightforward energy conservation: is there a kind Maximally asymmetric collisions such as p-Pb or
of color transparency in the initial state, for events d-Au represent cases where the experimentally de-
with a hard jet in the final state? Our calculations termined centrality of the event appears to be in-
do not provide a clear answer to this second ques- fluenced by the production of a hard jet. In or-
tion. Beyondthis,anothergoalofthisworkistopro- der to simulate jet production in such systems, the
vide a reliable parameter free event generator which PYTHIA event generator was modified and exten-
may be used, with certain caveats, to reproduce at sively used. This modification of the event genera-
leastsomeportionofthesenewdataonp(d)-Acolli- tordepended onthenumberofnucleon-nucleoncol-
sions with jet production. The results of this paper lisionsinagivenp(d)-Aevent. Thisnumberofcolli-
willprovidedetailedinputtoamorededicatedevent sionswasdeterminedusingseveralmethods. Inthis
generator that will have to be constructed to study section we describe these methods.
such collisions in greater detail. Along with a description of our setup, we will ex-
plore and eliminate the most na¨ıve explanation of
In the remainder of this paper, we describe our
theobservedcorrelationbetweenjetproductionand
model and how soft particle production is affected
centrality: The deuteron due to its large size, of-
by the production of a hard jet. To make direct
ten has the proton and neutron far apart and thus
connectiontoexperiments, wesetouttomodifythe
caseswhereajetismostlikelytobeproduced,when
PYTHIA event generator [7] which is used exten-
eithernucleonstrikesthedensestpartoftheoncom-
sively to model p-p collisions. To date there have
ingnucleusmaycoincidewithcaseswheretheother
been several approaches which have attempted to
nucleon simply escapes without interaction leading
describethisnewstrikingphysicsresult. InRef.[8],
to reduced soft particle production. It should be
the authors have proposed a similar mechanism of
pointed out, in passing, that such a scenario is im-
enhancement in peripheral events and suppression
mediately ruled out by an almost identical correla-
in central events but not incorporated it in an event
tion between jet production and centrality in LHC
generator framework. In Ref. [9], the authors have
collisions, where there is only one proton colliding
proposedthatthewave-functionoftheprotoniscon-
with the large nucleus.
siderably modified in the presence of a hard par-
ton. In Ref. [10], the authors have attempted to
understand the effect of the energy depletion due
A. The Deuteron:
to jet formation using the HIJING event genera-
tor [11, 12]. In none of these calculations, could
CollisionsattheLHCalwaysinvolveaprotoncol-
the authors achieve widespread agreement with the
lidingwithaPbnucleus. However, attopRHICen-
data. The current effort has been constructed en-
ergies the collisions are usually that of a deuteron
tirelywithinthePYTHIAeventgenerator, bymod-
(d) on a Au nucleus. The deuteron is an extremely
ifying it. As such, we suffer from several constraints
well studied state in low energy nuclear physics.
whichareinbuiltwithinthisparticulareventgenera-
The wave-function of the deuteron is given by the
tor. Thereadermayquestionwhywedidnotusethe
Hulth´en form [13]:
HIJING event generator as in Ref. [10], the primary
reason behind this is the resampling of the parton e−ar−e−br
distributionfunctionbetweencollisions;thishasthe ψH(r)= r , (1)
effect of the proton (or nucleon in d-Au collisions)
changing its parton distribution function between where, a = 0.228/fm, b = 1.18/fm. The probability
successive collisions which changes the distribution distribution of a nucleon within a deuteron is given
3
as,
ρ(r)=|ψ (r)|2. (2)
H
This distribution is sampled to obtain the positions
of the two nucleons.
Asiswellknown,theHulth´enwave-functionleads
to a rather wide nuclear distribution. This is illus-
trated in Fig. 1, where we plot three representative
events, with both the Au nucleus and the deuteron
distributions projected on the z-axis which is the
axisofmomentumofthetwonuclei. Ascanbeseen
from Fig. 1. the nucleons in the deuteron may be
closetogether,aswellas,agoldradiusapart. Dueto
the large separation between the nucleons, excluded
volume corrections were unnecessary but were still
included.
FIG. 2: Color Online: The sampled Woods-Saxon dis-
tribution for a large nucleus (in this case Au with an
A=192.)
FIG.1: ColorOnline: ThesampledHulth´endistribution
for two nucleons in a deuteron.
B. The Large Nucleus (Au or Pb)
Moving to the nuclear state, there are several
methods that may be used to simulate the fluctu-
ating initial state represented by the large nucleus.
Inthiswork, wewillonlyfocusontheAuorPbnu-
cleus, as these are studied experimentally. In most
cases, we will use the Woods-Saxon density distri-
FIG. 3: Three separate events in d-Au collisions. Nu-
bution, given at a radial distance r as:
cleon distributions are projected onto the x-y plane.
ρ
ρ(r)= 0 , (3)
1+e(r−R)/a
Pb, a = 0.546fm, R = 6.62fm). The Woods-Saxon
where ρ is a constant related to the density at the distribution of Eq. (3) is a single particle distribu-
0
center of the nucleus, R is the radius of the nucleus, tion. On top of this we introduce a nucleon-nucleon
and a is the skin depth. These parameters are cho- correlation by hand: the excluded volume correc-
sentomatchthoseusedbytheexperimentsatRHIC tion. ThisisdonesimilartothemethodofRef.[14],
and LHC (for Au, a = 0.535fm, R = 6.38fm; for wherewegenerateasetof3randomnumberswhich
4
isolate the location of a nucleon. If this location is an artificial excess enhancement of the particle pro-
within an exclusion distance of d = 2R (twice the duction from each individual nucleon-nucleon colli-
p
protonradius)ofanothernucleon,thenthislocation sion. In this work, we will use the event genera-
isabandonedandanothergenerated. Theprocessis tor PYTHIA to simulate nucleon-nucleon collision.
continued until all A nucleons have been included. Within the PYTHIA event generator the cross sec-
At the end of this process the center-of-mass of the tion increases with energy. To counter the possible
nucleus is calculated and the nucleus is re-centered. artificialincreaseinparticleproductionwithenergy,
While only the Hulth´en form is used for the the full cross section generated by PYTHIA is used
deuteron, several probability distributions beyond with no change in the geometric size of the nucleon
Woods-Saxon were tried for the nucleon distribu- with the energy of the nuclear collision. In a future
tion in a large nucleus. These include distribu- effort,animpactparameterinnucleon-nucleoncolli-
tionsbasedonshell-modelwave-functionsbothwith sions will be used to generate particle production in
and without a modified delta interaction to account events where the two nucleons do not overlap com-
for the short range repulsion between nucleons in pletely.
a nucleus [15] (simple excluded volume). However, Once both nuclei have been generated, and cen-
none of these enhancements led to any noticeable ters of mass determined, the impact parameter b is
changes in the final results as compared to the simulated with a probability distribution dP/db2 =
Woods-Saxon distribution with a simple excluded 1/b2 ,andtheangleoftheimpactparameterisde-
Max
volume. It should be pointed out that in this ef- terminedrandomlybetween0and2π. Themaximal
fort, we have only considered p-A and d-A collisions impact parameter b is chosen such that no de-
Max
which only sample the single and two-nucleon dis- pendence is observed in minor changes of this quan-
tribution within a nucleus. It is entirely possible tity. There is no further reorienting of the nuclei.
that the collision of nuclei larger than a deuterium The number of binary collisions can now be deter-
with nuclei smaller than Au may lead to the greater mined by simply counting the number of nucleons
role for multi-particle correlations within a nucleus. in the Au side, whose centers are within a trans-
There is very little information in nuclear structure versedistanced=2R ofanucleoninthedeuteron.
p
on such multi particle correlations. We will not dis- There arise events where not a single collision takes
cuss this issue further in this effort, and only focus place, these events are dropped from the analysis.
on simulations using the Woods-Saxon distribution
Basedontheaboveconsiderations,wepresentthe
with an excluded volume.
results of the nuclear Monte-Carlo simulations for a
d-Au collisions in Fig. 4. In Fig. 4, the distribu-
tion of events as a function of the number of binary
C. Transverse Size of Nucleons and Binary collisions is presented. Following this, events are di-
Collisions: vided into 4 bins (0-20%, 20-40%, 40-60%, 60-88%)
based on the fraction of the total number of events
The nuclear Monte-Carlo generator samples nu- contained in these bins. Each of these bins in the
cleons from the Au (or Pb) side and from the d side number of collisions represents a range of overlap-
and then projects these on the x-y plane as shown ping impact parameters. While this represents the
in Fig. 3. In the work presented in this paper, the standard method of determining centrality in theo-
transversesizeofthenucleonshasnotbeenmodified retical calculations or simulations, we will show, in
with the energy of the collision. The inelastic cross a later section, that this method of determining the
section for nucleon-nucleon scattering is known to centrality of the event leads to results that are not
grow with collision energy. While centrality selec- consistent with experimental results for high trans-
tion at the nuclear level is one of the major issues verse momentum (high-pT) pion, charged particle,
dealt with in this effort, no centrality selection is andjetproductionatbothRHICandLHCenergies.
imposed on the individual nucleon-nucleon encoun- In this section we have focussed mostly on d-Au
ters. As a result, when a proton from the d overlaps collisionswherebothincomingnucleihavetobesim-
withanotherfromtheAuside,nomatterhowsmall ulated. In subsequent sections we will also present
the overlap, the entire parton distribution function results for p-Pb collisions where only one nucleus
(PDF) of either nucleon is enacted in the collision, needs to be simulated. There are no other consider-
i.e., nucleon-nucleon collisions are not expected to ations concerning p-Pb that need to be made other
have any centrality dependence. than the location of the p is set by the impact pa-
Glancing at Fig. 3, it becomes clear that if the rameter b. As pointed out above, no explicit change
transverse size of the nucleons is increased with in- in the transverse size with energy has been used in
creasing energy then this will lead to an increase in this first attempt to understand the behavior of jets
thenumberofbinarycollisions and that willleadto inp(d)-Acollisions. Wealsomentionthatinallsim-
5
ulations,wekeeptrackoftheisospinofthenucleons. lision with a similar parton in the oncoming nucleus
will produce back to back jets at mid-rapidity. The
presence of a parton with such a large energy will
C e n t r a lit y B in n in g w it h N u m b e r o f C o llis io n s lead to less energy being available for the produc-
in0 .1 1 tion of other softer partons. As a result, there will
b
N0 .1 0 8 8 -1 0 0 % be a depletion in the number of soft partons in the
/dnt0 .0 9 6 0 -8 8 % proton in p-Pb (or projectile nucleon in d-Au) col-
ve 4 0 -6 0 % lisions. A similar situation will occur in one of the
e0 .0 8 nucleons within the large nucleus. As a result, an
N 2 0 -4 0 %
d0 .0 7 event with a jet will lead to the production of fewer
0 -2 0 %
0 .0 6 charged particles.
0 .0 5 To simulate this effect, we treat the collision of
the p (or any of the nucleons in d) with a string
0 .0 4
of n nucleons in the large nucleus as a single colli-
0 .0 3
sion between a nucleon and an object with a larger
0 .0 2 (modified) PDF. As a result, the PDF of the pro-
0 .0 1 jectile nucleon is sampled only once. To be clear,
there are several methods to carry this out, we will
0 .0 0
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 only focus on the most expeditious method. In the
remainder of this paper, we will refer to the collec-
N
b in tion of n nucleons struck as a single entity by the
projectile nucleon as a “super”-nucleon.
FIG. 4: Color Online: The event distribution in d-Au
As a first step to simulate the super-nucleon, we
collisionsasafunctionofthenumberofbinarycollisions
enhancethePDFofoneoftheincomingnucleonsas
andthedivisionofeventsinthefourdifferentcentrality
bins. FS(x)=npFp(x)+nnFn(x). Where, np and nn are
the number of protons and neutrons struck by the
projectilenucleon. Alongwiththistheenergyofthe
super-nucleonisalsoenhancedasE =(n +n )E,
S p n
III. THE MODIFIED PARTON whereE istheenergyoftheprojectilenucleoninthe
DISTRIBUTION FUNCTION lab frame. This prescription turns out to produce a
very faithful description of the soft particle produc-
Using the nuclear collision event generator, the tion in d-Au (or p-Pb) collisions. This is illustrated
number of nucleon-nucleon collisions in each event by the increase in the yield of soft particles with in-
may be determined. Each nucleon in the deuteron, creasing enhancement of the super-proton shown in
in a d-Au collision at RHIC, or the proton in p-Pb Fig.5. Onenotesbothanincreaseinthemeanvalue
collisions at the LHC, will potentially engender sev- ofchargedparticleproduction,aswellasanincrease
eralcollisionswithnucleonsinthelargenucleus. At in the event-by-event fluctuation in charged particle
RHIC the relativistic γ factor is about a 100 while production, as expected.
it is close to 2750 at the LHC. At such large boosts, Yet another feature of this formula for the super-
the parton distribution function within the nucleon nucleon is that it also gives a rather faithful repre-
istimedilatedtodistanceswellbeyondthelengthof sentation of the pseudo-rapidity distribution of the
the large nucleus. As a result, the parton distribu- produced charged particles. This distribution for
tionofthenucleonsindeuteron(inad-Au)collision, minimum bias events, plotted in Fig. 6, shows the
or that in the proton in p-Pb collisions is “static” “classic” asymmetric double humped structure of
(frozen) as it progresses through the large nucleus. the pseudo-rapidity distribution for d-Au collisions
We use the word static to indicate that the parton at RHIC energies. The overall normalization is less
distribution, though being continuously depleted by than that measured in actual experiments. How-
collisionswithpartonsinthenucleonsfromthelarge ever, one should recall that we are generating this
nucleus, is itself not undergoing any intrinsic fluctu- by modifying PYTHIA where only the interactions
ation in the course of its passage through the large between the projectile nucleon and the column of
nucleus. struck nucleons is included. No re-interaction of the
Thisbringsthediscussiontotheprimarypointof producedparticleswiththeremainderofthenucleus
thispaper: Considerthecase,where,inthecourseof is included, and this leads to an obvious depletion
fluctuations of the PDF, the proton in p-Pb (or one in overall particle production. The assumption be-
ofthenucleonsind-Au)hasfocussedalargeamount ing made in comparing these results to experimen-
ofenergywithinasingleparton. Thisparton,incol- tal data is that even though the overall number of
6
4 .0
1 .2 M h
ents nn == 12 0 E -e n h /dent3 .5
ev1 .0 M ev
N3 .0
N d
g
0 .8 M ch2 .5
N
0 .6 M 2 .0
1 .5
0 .4 M
1 .0
0 .2 M
0 .5
0 .0 M 0 .0
1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 -9 -6 -3 0 3 6 9
h
N
c h g
FIG.5: ColorOnline: Themultiplicityofchargedparti- FIG. 6: Color Online: The pseudo-rapidity distribution
clesinasimulatedd-AucollisionwiththeAusidesimu- ofchargedparticlesinasimulatedd-Aucollisionwiththe
latedasasuper-nucleonwithapartondistributionfunc- Ausidesimulatedasasuper-nucleonwithapartondis-
tion given as F (x) = n F (x)+n F (x), and energy tributionfunctiongivenasF (x)=n F (x)+n F (x),
S p p n n S p p n n
enhancedasE =(n +n )E. Intheaboveplotn =10, and energy enhanced as E =(n +n )E.
S p n p S p n
and n =10.
n
this cannot be plotted in the manner of Fig. 7.
charged particles (or transverse energy) produced is Due to this large enhancement in the hard por-
notmatchedbetweenthesimulationsandtheexper- tion of the PDF, this straightforward enhancement
iment, the relative distribution between centrality of the PDF for a super-nucleon cannot be used.
bins will be the same as in the experiment. Since the primary focus of the simulations reported
in this paper has to do with jet production and its
In spite of the success in soft particle production
ensuing effect on soft particle production due to en-
using the prescription of enhancing both the PDF
ergy conservation, we will insist on keeping the jet
andthetheenergyofanucleoninthetargetnucleus,
production cross section as close to the reality as
this procedure leads to an uncontrollable modifica-
possible, and not enhance the energy of the super-
tion to the high momentum (large-x) portion of the
nucleon. For comparison with experiment, we will
PDF. This is to be expected, as the super-nucleon
useamorecomplicatedenhancementformulaforthe
nowhasn=n +n timestheenergyofasinglenu-
p n
super-nucleon, where the soft portion of the PDF is
cleon, and can thus produce hard partons of higher
modified by a shadowing function, and an enhance-
energy(highereventhanthekinematicboundof100
ment by the number of collisions n = n +n , but
GeVatRHIC,or2.75TeVattheLHC)withoutthe p n
no energy enhancement. We will also use a shadow-
penalty of a rapidly falling PDF. As an illustration
ing function which modifies the super-nucleon PDF
of this effect, we plot the ratio of a gluon spectrum
event-by-event, depending on the number of nucle-
from a super-nucleon to that from a regular nucleon
ons struck by the projectile nucleon. In the case of
as a function of the ratio of the energy of the gluon
a d-Au collision, both nucleons may strike multiple
to that of the projectile nucleon (un-enhanced nu-
nucleons and thus both collisions would be modeled
cleon).
as a nucleon super-nucleon collision. The formula
It is interesting to note that the soft gluon (x <
use for this is given as,
0.1) production in enhanced in the super-nucleon
as a function of the total enhancement coefficient N
n = n +n . There is no enhancement for inter- S(x)=1+(R(x)−1) coll , (4)
p n (cid:104)N (cid:105)
coll
mediate energy gluons x ∼ 0.1, and then an almost
nindependentenhancementforhigherenergygluon where N is the number of collisions encountered
coll
withx>0.1. Notethatthiswillofcoursebebroken byasingleprojectilenucleonasitpassesthroughthe
as one moves past the x≥n, however, since the de- target nucleus in a given event. The mean number
nominator of the ratio plotted in Fig. 7 will vanish, ofcollisionsperprojectilenucleonisgivenas(cid:104)N (cid:105).
coll
7
Q 2 = ( 2 7 . 5 G e V ) 2
io1 0 0
t
a n = 4
R
n = 9
n = 1 6
1 0
1
0 .0 1 0 .1 1
x
FIG.7: ColorOnline: Theratioofthegluondistribution FIG. 8: Color Online: The distribution of charged par-
inasuper-nucleontothatinanucleonasafunctionofx, ticles produced in a p-Pb collision, as a function of the
theenergyfractionofthegluon,relativetotheprojectile number of collisions suffered by the projectile proton.
nucleon.
C e n t r a lit y B in n in g w it h N u m b e r o f C h a r g e d P a r t ic le s
The shadowing factor of R(x) which depends on x
0 .1 0
and the mass number of the target nucleus A, is g
ch 8 8 -1 0 0 %
taken from Ref. [16]. For the case of a quark it has 0 .0 9
N 6 0 -8 8 %
a rather involved form: /dnt0 .0 8 4 0 -6 0 %
e
RA = 1+1.19log1/6A(x3−1.2x2+0.21x) (5) ev0 .0 7 2 0 -4 0 %
q
√ N0 .0 6 0 -2 0 %
− 0.1(A1/3−1)0.6(1−3.5 x)exp(−x2/0.01). d
0 .0 5
Without the enhancement in energy of the super-
0 .0 4
nucleon one does not get the asymmetric distribu-
0 .0 3
tionofproducedchargedparticlesasshowninFig.6.
However, there is still an enhancement in the pro- 0 .0 2
duction of charged particles with increasing number
0 .0 1
of collisions. This is illustrated for p-Pb collisions
in Fig. 8 where the distribution of the number of 0 .0 0
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4
charged particles per event is plotted for different
N
number of collisions encountered by the proton. We c h g
present this plot for p-Pb at LHC energies as the ef-
fect of our modifications to the super-nucleon PDF FIG.9: ColorOnline: Thedistributionofthenumberof
has a smaller effect at these energies (the shift is chargedparticlesproducedandthedivisionoftheevents
proportionately larger at RHIC). in the four different centrality bins.
No doubt, this enhancement is proportionately
lessthanthatinFig.5,however,itissufficienttoal-
lowustobinincentrality. Wepointoutonceagain, section being unchanged in PYTHIA, while assum-
that in this process of simulating d-Au collisions at ing that the reduced soft particle production in this
RHIC energies, or p-Pb collisions at LHC energies, model, as a function of the deduced centrality, is
the soft particle production is in no way commensu- proportionaltotheparticleproductioninarealcol-
rate with that in a real d-Au or p-Pb collision. We lision.
are carrying out this exercise to demonstrate the ef- To illustrate this issue, we plot the distribution
fect of a shift in centrality due to the production of of the number of events as a function of the num-
a hard jet. We insist on the jet production cross berofproducedchargedparticlesinoursimulations
8
for d-Au collisions at RHIC energies. As is clearly
2 .2
demonstrated by this figure, there are clear, non-
u p
vanishing ranges of particle production, which can dA2 .0 0 R d A u , 0 - 1 0 0 %
beclearlydemarcatedascentralitybins. Thesesim- R1 .8
ulations are all done using the Hard-QCD switch 1 .6
of PYTHIA. This is the case both for the particle
1 .4
production in general and for particle production in
1 .2
addition to the production of a hard jet. This is
1 .0
donesothatthemechanismsthatleadtosoftparti-
cle production both in the presence and absence of 0 .8
S im u la t io n
a hard jet remain the same in the simulation. 0 .6
In what follows, we will consider jet and leading 0 .4 P H E N I X
(cid:214)
hadron production at high-pT and compare the ef- 0 .2 d + A u , s = 2 0 0 A G e V
fect of this on soft particle production. This will
0 .0
be done both for RHIC and LHC energies, for jet
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2
production at central rapidities. Charged particle
p ( G e V )
detection,whichleadstoacentralitydetermination, T
will be carried out at all rapidities, i.e., over the en-
FIG. 10: Color Online: The nuclear modification factor
tire collision. In actual experiments, charged parti- for neutral pions for minimum bias d-Au collisions at
clesaredetectedatrapiditiesfarfromwherethejets RHIC. Experimental data are taken from Ref. [17]
are produced, in an effort to remove any correlation
between the two processes. Since, in our simulated
collisions, the number of particles produced is far
fewer than an actual experiment, we collect charged
particles at all rapidities, to allow to distinguish be- 2 .2
tween different centralities with higher statistics. u p
dA2 .0 0 R d A u , 0 - 2 0 %
R1 .8
1 .6
IV. COMPARISON WITH EXPERIMENT
1 .4
1 .2
Intheproceedingsections,themodelusedtosim-
ulatejet(andhighp particle)productionasafunc- 1 .0
T
tion of centrality in d-Au collisions at RHIC and 0 .8
p-Pb collisions at the LHC, was described in de- 0 .6 S im u la t io n
tail. As stated before, our primary goal is two fold: P H E N I X 0 -2 0 %
0 .4
(cid:214)
to set up an event generator that may be used to 0 .2 d + A u , s = 2 0 0 A G e V
faithfully represent the experimental data on hard
0 .0
softcorrelationsinasymmetriccollisions,albeitwith
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2
some caveats, as well as to understand the underly-
p ( G e V )
ing cause of the starting results in such correlations T
using this new event generator.
FIG. 11: Color Online: The nuclear modification factor
Viewed in the lab or center-of-mass frame, it be-
forneutralpionsfor0-20%mostcentrald-Aucollisions
came clear that the nucleon PDF from both the at RHIC. The simulation is carried out by binning in
projectile and the target are time dilated, and as centrality according to the number of binary collisions
such, cannot fluctuate in the short duration of the (prescriptionA:seetextfordetails). Simulationsinclude
collision. This led us to abandon HIJING [11, 12], shadowing and no energy loss. Experimental data are
and design a new event generator by modifying the taken from Ref. [17]
PDF of one of the nucleons in a PYTHIA nucleon-
nucleon collision. The effects of different modifica-
tions within PYTHIA and the overarching nuclear
event generator were highlighted in the preceding
sections. In the following, we demonstrate the suc- results were also historically the first to show the
cesses and shortcomings of this new event generator odd effect of an enhancement in peripheral events
when compared with actual experimental data. and a mild suppression in central collisions. The
The first comparisons are carried out for d-Au data in question are the centrality, p and rapidity
T
collisions at RHIC energies. These experimental (orpseudo-rapidity)dependentnuclearmodification
9
factor R , defined as, case in our model (as well as seen in the experimen-
dAu
tal data), an unmodified minimum bias R is by
dA
bm(cid:82)axd2b d4NdAu no means a trivial outcome. This is the first hint
d2pTdyd2b that the enhancement in peripheral events is being
R = bmin , (6)
dAu (cid:104)N (b ,b )(cid:105) d3Npp balanced by the suppression in central events.
bin min max d2pTdy
where N denotes the yield of leading hadrons or 2 .2
jiteyt.s, Ibnintnheed ninumtrearantsovrerosef tmhoemaebnotvuemf,oramndular,apoinde- dAu2 .0 p 0 R d A u , 4 0 - 6 0 %
R1 .8
also integrates over a range of impact parameter
1 .6
b, which in d-Au refers to the 2-D vector from the
center of mass of the large nucleus to the center of 1 .4
mass of the deuteron (in Fig. 3 for example). The 1 .2
(cid:104)Nbin(bmin,bmax)(cid:105)intheaboveformulareferstothe 1 .0
mean number of binary nucleon-nucleon collisions
0 .8
per nuclear collision.
S im u la t io n
0 .6
P H E N I X 4 0 -6 0 %
0 .4
(cid:214)
2 .2 0 .2 d + A u , s = 2 0 0 A G e V
p
dAu2 .0 0 R d A u , 2 0 - 4 0 % 0 .0
R1 .8 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2
1 .6 p ( G e V )
T
1 .4
FIG. 13: Color Online: Same as Fig. 11, except for 40-
1 .2
60% centrality.
1 .0
0 .8 The next step is to bin in centrality. Our first at-
S im u la t io n
0 .6 tempt will follow convention and utilize the number
P H E N I X 2 0 -4 0 % of binary nucleon-nucleon collisions as an indicator
0 .4
(cid:214)
d + A u , s = 2 0 0 A G e V of centrality. One runs the nuclear event genera-
0 .2
tor, and collects events, classifying them according
0 .0 to the number of binary collisions. One then bins
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 theeventaccordingtowhereN liesinFig.4. One
bin
p ( G e V )
T should point out that while, on average, an increas-
ing b(≡ |(cid:126)b|) leads to an decrease in N , any value
FIG. 12: Color Online: Same as Fig. 11, except for 20- bin
ofbcorrespondstoarangeofbinarycollisions. This
40% centrality.
also modifies the numerator of Eq. (6), to
simAuslaatfiiornstisntepcoimnsptaurdisyoinngwthitehreesxupltesriomfetnhteacludrraetnat, NA=(cid:88)dd22NpddAyuθ(Nbin−Nbminin)θ(Nbminax−Nbin),(7)
T
weplotthenuclearmodificationfactorforminimum Nbin
bias collisions. Here no division in centrality bins is where, Nmin and Nmax are set by the central-
carried out and thus there is no discussion of deter- bin bin
ity bin that we are interested in. The factor of
mining centrality by number of binary collisions or
(cid:104)N (b ,b )(cid:105) is simply replaced by (cid:104)N (cid:105) for
bin min max bin
number of charged particles produced. This serves
the bin in question, and can be calculated from
as a first test of the simulation, which performs ex-
Fig. 4. This is referred to as prescription A for nu-
tremely well in comparison to the data. The exper-
merically realizing the numerator of Eq. (6).
imental data have been taken from Ref. [17]. Both
An alternate prescription is to classify events ac-
the simulation and the experimental data show a
cordingtothenumberofproducedchargedparticles,
similar trend: A p independent near lack of mod-
T utilizingFig.9todivideeventsintodifferentcentral-
ification, with the possibility for a minor enhance-
itybins. Inthiscasethenumeratorisreplacedwith,
ment between 4 and 16 GeV. This is entirely to be
expected, high energy jets are mostly unmodified N =(cid:88)d2NdAuθ(N −Nmin)θ(Nmax−N ),(8)
in cold nuclear matter, and the minor enhancement B d2p dy ch ch ch ch
T
can be attributed to the anti-shadowing peak (near Nch
x (cid:39) 0.1). We would further add that in the case of where, Nmin and Nmax are the minimum and max-
ch ch
a large centrality dependent modification, as is the imum values for charged particles produced, set by
10
tal method of determining centrality. We first show
2 .2
the results of simulating the centrality dependence
p
dAu2 .0 0 R d A u , 6 0 - 8 8 % of the pion RdA using prescription A or using the
R1 .8 number of binary collisions.
1 .6
1 .4
2 .2
1 .2 p
1 .0 dAu2 .0 0 R d A u , 2 0 - 4 0 %
R1 .8
0 .8
1 .6
S im u la t io n
0 .6
1 .4
P H E N I X 6 0 -8 8 %
0 .4
(cid:214) 1 .2
0 .2 d + A u , s = 2 0 0 A G e V
1 .0
0 .0
0 .8
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 S im u la t io n
p T ( G e V ) 0 .6 P H E N I X 2 0 -4 0 %
0 .4
(cid:214)
FIG. 14: Color Online: Same as Fig. 11, except for 60- d + A u , s = 2 0 0 A G e V
0 .2
88% centrality.
0 .0
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2
p ( G e V )
T
the centrality bin that we are interested in. The
factor of (cid:104)Nbin(cid:105) in the denominator of Eq. (6), now FIG. 16: Color Online: Same as Fig. 15, except for 20-
has to be calculated from the collection of events 40% centrality.
that constitute each centrality bin. We denote this
method of calculating the R as prescription B.
dA In Fig. 11, the R for the top 0-20% most cen-
dA
tral collisions are plotted. One immediately notes
an enhancement in the simulation, but no such en-
2 .2
u p hancement in the experimental data, which seem to
dA2 .0 0 R d A u , 0 - 2 0 % be consistent with unity. The simulation does not
R1 .8 explain the experimental data. The enhancement
1 .6 in central events such as demonstrated by the sim-
1 .4 ulation, is entirely expected based on the shadow-
ing function that has been used to generate events.
1 .2
Within this framework, the complete lack of any
1 .0
modification in the experimental data is rather sur-
0 .8 prising; central event should present the maximal
S im u la t io n
0 .6 nuclear modification.
P H E N I X 0 -2 0 %
0 .4 As one moves up in centrality, from most central
(cid:214)
0 .2 d + A u , s = 2 0 0 A G e V to peripheral events, the enhancement seen in the
simulation tends to reduce progressively. There is
0 .0
less enhancement in the 20-40% events, even less in
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2
the 40-60% simulations, with no modification at all
p ( G e V )
T
in the 60-88% events. This behavior of the simula-
FIG. 15: Color Online: The nuclear modification factor tionisentirelyexpected,aswemovefromcaseswith
forneutralpionsfor0-20%mostcentrald-Aucollisions the largest expected nuclear density modification to
at RHIC. The simulation is carried out by binning in cases with little density and hence no modification
centrality according to the number of charged particles at all in the R . The experimental data, however,
dA
produced (prescription B: see text for details). Simula- show an entirely different trend: with no modifica-
tionsincludeshadowingandnoenergyloss. Experimen-
tioninthecentraleventandtheR risingwithcen-
dA
tal data are taken from Ref. [17].
trality from most central to most peripheral events.
The fact that the simulation results with prescrip-
As most readers are aware, prescription A, is the tion A match some of those from the experiment is
usual theoretical method of calculating the central- entirely coincidental. The simulation for the R
dA
ity dependence of the nuclear modification factor, drops as one transitions from central to peripheral
whereas prescription B is closer to the experimen- while the data trend in the opposite direction.
