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Remnants of Initial Anisotropic High Energy Density Domains in Nucleus-Nucleus Collisions

a r X i v :n u c l -t h /9811006v 2 19 D e c 1998

Remnants of Initial Anisotropic High Energy Density Domains in

Nucleus-Nucleus Collisions

F.Wang a and H.Sorge b

(a)Nuclear Science Division,LBNL,Berkeley,CA 94720,USA (b)Department of Physics,SUNY at Stony Brook,NY 11794,USA

Abstract

Anisotropic high energy density domains may be formed at early stages of ultrarelativistic heavy ion collisions,e.g.due to phase transition dynamics or non-equilibrium phenomena like (mini-)jets.Here we investigate hadronic observables resulting from an initially created anisotropic high energy density domain.Based on our studies using a transport model we ?nd that the initial anisotropies are re?ected in the freeze-out multiplicity distribution of both pions and kaons due to secondary hadronic rescattering.The anisotropy appears to be stronger for particles at high transverse momenta.The overall kaon multiplicity increases with large ?uctuations of local energy densities,while no change has been found in the pion multiplicity.

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Under normal conditions,quarks and gluons are con?ned in hadrons.The situation is entirely di?erent at high densities as may have been created in the early universe shortly after the Big Bang or in today’s laboratory experiments in which two nuclei are colliding. It is impossible under such conditions that spatially separated hadrons be formed.Instead, formation of quark matter is expected[1–5].The primary goal of high energy heavy ion experiments is to create this new state of matter,the quark-gluon-plasma(QGP)in which quarks and gluons are no longer con?ned in individual hadrons.It is conceivable that a decon?ned matter may be formed at an early stage of a heavy ion collision only in a local-ized region in con?guration space,surrounded by hadronic matter.For example,Gyulassy et al.[6]argued that as a result of multiple mini-jet production at RHIC energy,the initial conditions of the QGP formed in ultrarelativistic nuclear collisions might be inhomogeneous, with large?uctuations of the local energy density.They showed that such initial conditions could result in azimuthal asymmetry in particle distributions.In contrast to mini-jet pro-duction,S.Mr′o wczy′n ski[7]argued that color?lamentation could also result in azimuthal asymmetry by a?ow of large number of particles with relatively small transverse momenta. Kapusta et al.[8]argued that the probability of a hard nucleon-nucleon collision that was able to nucleate a seed of QGP in the surrounding hot and dense hadronic matter in a central heavy ion collision may not be small even at AGS energy.In addition,disoriented chiral condensates(DCC)may be formed in heavy ion collisions by the restoration of chiral symmetry[9,10].The formation of DCC could result in a spectacular asymmetry in charged (and neutral)pion phase-space distributions[11].

Once created at early stage of a heavy ion collision,a QGP will undergo a phase transition from the decon?ned state to a normal hadonic state,followed by hadronic expansion.What are measured in experiments are the particle momenta long after these particles have ceased to interact(freeze-out).It remains an experimental and theoretical challenge to extract information on the initial conditions from the particle distributions at freeze-out.Early investigation by Pratt[12]showed that two particle correlations may be useful to search for these?uctuations in initial conditions.

Because of secondary particle interactions(hadronic rescattering),primordial quark-gluon distributions from a QGP may be completely altered during the hadronic expansion stage.On the other hand,an initial anisotropy from the quark-gluon stage in con?guration space may not be washed out but survive the hadronic stages.Non-isotropic energy densi-ties may leave their imprint on momentum spectra due to hadronic rescattering.Di?erent amounts of rescattering can result in variations of particle multiplicities along di?erent direc-tions.An interesting consequence may be that a non-spherical high energy density domain, which can be formed at an early stage of a heavy ion collision due to?uctuations in energy deposition,may produce an anisotropy in pion and kaon emission after freeze-out.It is the goal of the present work to study the possible magnitude of such an anisotropy,given the magnitude of the initial anisotropy in con?guration space.

Since we are going to study the translation of initial spatial anisotropies into?nal-state momentum anisotropies of kaons and pions due to hadronic rescattering,it is important that the model to be used contains the relevant dynamics and describes existing experimental data to a reasonable degree.One of the important physics results learned from current heavy ion experiments at the BNL AGS and the CERN SPS is that there is a large amount of secondary particle interactions in central collisions.Transport models[13–18]have been employed to

study the importance of these interactions for observables.For example,strangeness yields may change drastically due to the hadronic cascading[19–21].In fact,the systematics of the observed strangeness enhancement[22–25]–energy and mass dependence–can be described by the Relativistic Quantum Molecular Dynamics(RQMD)approach[26–28]rather well. In this paper,we use the RQMD approach to investigate the translation of initial spatial anisotropies into?nal-state momentum anisotropies of kaons and pions.One should note, however,that the excess of strange anti-baryons which has been observed[24,29,30]cannot be solely produced by hadronic collisions within the RQMD approach[31].More complicated mechanisms pointing to earlier and denser stages are required.For instance,formation of color ropes[20,31,32]which has been implemented in RQMD,density-dependent antibaryon masses[33]or quark coalescence[34,35]may be responsible.While the strange antibaryons may well be a very interesting probe of the matter deposition at early times in heavy ion collisions,it should be noted that they are very rare particles at presently accessible energies[36].Lack of statistics has prevented us to employ these species in the context discussed here of dynamically caused event-by-event?uctuations.

RQMD(version2.3)[15]was used to simulate head-on Pb+Pb collisions(impact param-eter b=0)at SPS energy(158GeV/nucleon).The in?uence of the hadronic rescattering on the inclusive yields has already been studied by one of the authors.By including rescattering in RQMD,pion multiplicity is reduced by8%and kaon multiplicity increases by over50% at SPS energy[15].

For the present work we did not attempt to include dynamical?uctuations in the local energy deposition other than given by the standard RQMD procedure.Instead,the initial conditions after hadronization as resulting from the model were modi?ed to create arti?cially anisotropic domains beyond the model’s intrinsic–dynamical and statistical–?uctuations. We feel this is justi?ed in view of the considerable uncertainties in the early-state dynamics which cannot be reliably calculated based on quantum chromodynamics(QCD).

In the following we specify our strategy to include additional?uctuations on an event-by-event basis:At t=1fm/c in the center of mass frame,a randomly chosen fraction of hadrons with rapidity|y|<1.5was moved into an elliptical area in the transverse plane,located around the center of the?reball,and the longitudinal position(z)was kept unchanged.The new(x,y)positions in the cylinder were randomly sampled from a homogeneous distribution. Size of the transverse cross-section of the cylinder was chosen as8fm(major axis)×2fm (minor axis).The total energy and momentum are conserved by this procedure.On the other side,the arti?cially induced?uctuations of the local hadron densities modify the subsequent collision dynamics.After the re-arrangement,RQMD is properly re-initialized and propagates the hadrons until freeze-out.

We have studied two cases:

1.10%of the hadrons(|y|<1.5)were moved.Approximately90hadrons representing a

total energy of120GeV were moved in each event.This resulted in a30%increase of total energy within the cylinder,and a20–30%increase in the total number of binary collisions.About11K events were studied for this case.

2.20%of the hadrons(|y|<1.5)were moved.Approximately180hadrons representing a

total energy of240GeV were moved in each event.This resulted in an60%increase of total energy within the cylinder,and a40–50%increase in the total number of binary

collisions.About10K events were studied for this case.

The left panel of Fig.1shows the projection of the particle density onto the z=0plane, resulting from the re-arrangement at t=1fm in the center of mass frame.The right panel of Fig.1shows the level of asymmetry in con?guration space due to the creation of a high energy density domain.Fig.2shows average energy density within the elliptical cylinder as a function of time in the center of mass frame for the second case.The solid curves are for energy summed over all particles/strings,and the dashed ones are those for particles/strings within|y|<1.5.Arti?cial creation of the high energy density domain is visible as the discontinuity at t=1fm.The bases are the time pro?le of the average energy density from a default RQMD event.Although the energy density in the central elliptical cylinder is arti?cially increased at the initial stage,the freeze-out density is similar to that from a default RQMD event,as shown in the?gure.This indicates that the freeze-out density is constant in RQMD over a wide range of initial conditions.

As discussed at the beginning,the purpose of the study is to investigate possible signa-tures of high energy density domains at initial stages of heavy ion collisions in the azimuthal distributions of particles at freeze-out.The resulting freeze-out charged pion distribution is displayed in Fig.3,for the?rst case in the upper panel and for the second case in the bottom panel.As clearly seen from the?gure,the distributions are azimuthally asymmetric.There are fewer pions emitted along the major axis of the ellipse,in agreement with the picture that pion yield is reduced by rescattering[15].It should be noted that this result qualitatively agrees with the result that the elliptic?ow is in-plane at SPS energy for medium impact parameters[37]where the initial geometry is similar to the high energy density domain studied here.Only particles with rapidities|y|<2are plotted in the?gure.No anisotropy was found for particles with rapidity of more than2units away from mid-rapidity.This is presumably due to that only particles within|y|<1.5were modi?ed.

The azimuthal multiplicity distributions can be described by the functional form

dN

The azimuthal distributions of K+(left panel)and K?(right panel)multiplicities are shown in Fig.5for the second case.A cut of|y|<2is also applied in all plots.The top two plots are the distributions for kaons including all p⊥,whereas the other plots have various p⊥cuts.As can be seen from the plots,the kaon multiplicity is anisotropic as well.The ?ts to the functional form(1)are superimposed on the?gure as the solid curves.The?t results of the anisotropy are tabulated in Table I.The magnitude of the anisotropy in the kaon multiplicity is similar to the pions.This indicates that absorption of pions and kaons is similar in the?reball.

However,compared to the kaon multiplicity from the default RQMD events,the overall kaon multiplicity is increased.The?tted average to the kaon multiplicity(|y|<2)from default RQMD events is shown as the straight line on each plot in Fig.5.The relative increase in K?is larger than in K+,whereas the absolute increase is similar.For reference, the magnitudes of the absolute and relative increases in kaon multiplicity are tabulated in Tables II and III,respectively.To demonstrate this point more clearly,the azimuthal distributions of the di?erence in K+and K?multiplicities are computed and plotted in the top panel of Fig.6.The solid curves are?ts to the functional form(1),and the dotted lines are the?tted average to the corresponding distributions from default RQMD events. As can be seen from the plots,the increase in this quantity from default RQMD events is minor.Presumably,the slight increase in this quantity from default RQMD events is due to the excess in K+production(over K?)through associate production together withΛ’s. To illustrate this point,azimuthal distributions ofΛmultiplicity are plotted in the bottom panel of Fig.6.The distributions of N K+?N K?andΛare indeed similar.

The following picture emerges from the above results.More pions are absorbed along the major axis of the elliptical high energy density domain.Kaons are absorbed in the same manner as pions.The increase in number of binary collisions,presumably,enhances particle production including both pions and https://www.doczj.com/doc/e316026602.html,rge fraction of these pions,however,are destroyed by rescattering producing additional kaons.These kaons are produced dominantly through pair production mechanism.There are slight excess in K+over K?from associate production of K+together withΛ’s,mainly in the high p⊥region.

In summary,we have quantitatively studied,in the framework of RQMD model,the remnants of non-spherical,high energy density domains in particle emissions at freeze-out. Such domains can produce anisotropy in charged pion and kaon emission at freeze-out due to particle rescattering;the anisotropy persists more in high p⊥particles.For a27%asymmetry in the initial con?guration distribution(for the second case),a0.7%anisotropy was found in the pion distribution at freeze-out.This anisotropy increased from0.4%for pions with p⊥<0.5GeV/c to2.2%for pions with p⊥>0.8GeV/c.The factor how the initial asymmetry in con?guration space translates into?nal momentum space appears to be rather small.Depending on the transverse momentum window it varies between1.5and8percent. The anisotropy shows similar strength in kaon distributions.The addition of the high energy density domain resulted in enhanced kaon multiplicity at freeze-out,while there was essentially no change in the overall pion multiplicity.The increase in kaon multiplicity is mainly due to increased pair production.

The current study used RQMD events simulated with exact zero impact parameter to avoid possible anisotropy in the freeze-out particle multiplicity distribution arising from ?nite impact parameter.The magnitude of such anisotropy in central collisions at small

?nite impact parameters has not been studied in details.The current study assumed that the high energy density domain was present in every event at the center and had the same size and shape.It remains a future task to study the dependence of the anisotropy as functions of location,size and shape of the high energy density domain.In the present work,the anisotropy in particle emission is studied only inclusively.It remains a challenge to study the e?ect on an event-by-event basis,given the relative weakness of the e?ect as shown by the present work.

One of the authors(FW)thanks Dr.P.Jacobs,Dr.A.M.Poskanzer,Dr.H.G.Ritter and Dr.N.Xu for valuable discussions.He also thanks the Institute for Nuclear Theory where part of this work was carried out.This work was supported by the U.S.Department of Energy under contracts DE-AC03-76SF00098and DE-FG02-88ER40388.This research used resources of the National Energy Research Scienti?c Computing Center.

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TABLE I.Pion and kaon emission anisotropy at freeze-out,α,resulting from the initial anisotropic high energy density domain in central Pb+Pb collisions(impact parameter b=0 fm)at158GeV/nucleon simulated by RQMD.

particle p⊥<0.5p⊥>0.8π0.2% 1.0% case10.3%0.4%

K?0.0%0.7%

π0.4% 2.2% case2 1.1% 1.2%

K?0.3% 2.0%

all p⊥p⊥>0.5

?0.3%?0.1%

K+ 3.4%8.0%

6.7%8.2%

?0.7%0.2%

K+ 1.8%9.0%

5.4%

6.8%

TABLE III.Absolute increase in kaon multiplicity due to the initial anisotropic high energy density domain from default RQMD events.

particle p⊥<0.5p⊥>0.8

K+0.320.30

0.680.24

case20.720.21

K?0.080.27

FIG.1.RQMD simulation of central Pb+Pb collisions(impact parameter b=0fm)at158 GeV/nucleon:a high density domain is created at an initial stage(t=1fm in the center of mass frame)by moving10%(case1)or20%(case2)hadrons into an elliptical cylinder at the center of the?reball.Particle density at t=1fm projected on the z=0plane is shown at the left.The high energy density domain is shown in the sketched ellipse.Anisotropy in con?guration space is shown at right for the two initial conditions studied.

FIG.2.Average energy density in the cylinder(in a typical event)as a function of time in the center of mass frame.The solid curves are energy density calculated from all particles.The dashed curves are energy density calculated from particles with rapidity|y|<1.5.The lower solid curve and the lower dashed curve are the corresponding energy density from a default RQMD event. The increase in the energy density at t=1fm corresponds to creation of the high energy density domain(case2).

FIG.3.Azimuthal distribution of charged pion multiplicity at freeze-out for case1(top)and case2(bottom).Only pions with rapidity|y|<2are included.φ=0corresponds to the major axis(+x in Fig.1)of the ellipse of the high energy density domain.The solid curve is a?t to the functional form(1).The dotted line is the average charged pion multiplicity in default RQMD events.

FIG.4.Azimuthal distribution of charged pion multiplicity at freeze-out in rapidity|y|<2for various p⊥cuts for case2.

FIG.5.Azimuthal distribution of K+(left)and K?(right)multiplicity at freeze-out in rapidity |y|<2for various p⊥cuts for case2.

FIG.6.Azimuthal distribution of the di?erence between K+and K?multiplicities(top)and Λmultiplicity(bottom)at freeze-out in rapidity|y|<2for case2.

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Case 1: 10%Case 2: 20%

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