Study of the behavior of nuclear modification factor in freeze-out state

0.4 MB·English

by  M. Ajaz

Chinese Physics C
CPC(HEP&NP),2009,33(X):1—5 Vol.33,No.X, Xxx,2009
Study of the behavior of the nuclear modification factor
in freeze-out state
M. Ajaz1,2;1) M. K. Suleymanov1,3;2) K. H. Khan1 A. Zaman1
1 DepartmentofPhysics,COMSATSInstituteofInformationTechnology,44000,Islamabad,Pakistan
2 DepartmentofPhysics,AbdulWaliKhanUniversity,23200,Mardan,Pakistan
3
3 Veksler-BaldinLaboratoryofHighEnergy,JointInstituteforNuclearResearch,141980,Dubna,Russia
1
0
2 Abstract : Oneofthelatesttrendsintheadvancementofexperimentalhigh-energyphysicsistoidentifythe
n quark gluon plasma (QGP) predicted qualitatively by quantum chromodynamics (QCD). We discuss whether
a nucleartransparencyeffectwhichisconsideredanimportantphenomenon,connectedwithdynamicsofhadron-
J nuclear and nuclear-nuclear interactions could reflect some particular properties of the medium. FASTMC is

9 used for Au-Au collisioin at RHIC energies. Critical change in the transparency is considered a signal on the

appearance of new phases of strongly interacting matter and the QGP.
]
x
Key words : nuclear modification factror, nuclear transparency, strongly interacting matter, QGP
e
- PACS : 25.75.Ag 24.10.Lx 25.75.Nq 21.65.Qr
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c
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1 Introduction the nuclear wave-function carrying a small momen-
[
tum fraction x of the nuclear momentum [3]. Under-
1
standing the correct initial conditions therefore re-
v One of the latest trends in the advancement of
1 experimentalhigh-energyphysicsistosearchfornew quires the understanding of the properties of these
6 small x modes. A sophisticated effective field theory
states of strongly interacting matter and to identify
7
approach has been developed to describe the proper-
1 the quark gluon plasma (QGP) [1] predicted qualita-
. tivelybyquantumchromodynamics(QCD)[2]. QGP ties of partons at small x [4–6] forming a color glass
1
condensate (CGC) [4, 7, 8]. The CGC is charac-
0 is considered a state of strongly interacting matter
3 terized by a bulk scale Λ which grows with energy
under extreme conditions (high temperatures and/or s
1 and the size of the nuclei. For RHIC energies, Λ
: densities of the baryons). This can be brought about s
v is of the order of 1-2 GeV [9–12] provided Λ is a
under laboratory conditions during the collisions of s
i
X relativistic heavy nuclei by increasing the energies constant as for cylindrical nuclei. The field strengths
1
r andvaryingthemassesofcollidingnuclei. Thisleads in the saturation region behave as about : since
α
a s
to a continuing quest of leading research which cen- α (Λ ) << 1, the field strengths are large. Further-
s s
tersonhigh-energyphysicstocreatenewaccelerators more, the occupation number of saturated gluons is
1
of heavy nuclei and enhance the energies of existing also of the order of >> 1. For more details,
α
accelerators. Now to create the states of strongly s
the interested reader is referred to [13–15] where
interacting matter and the possible formation of a
the initial conditions for nuclear collisions are formu-
quarkgluonplasma(QGP),collisionsofnucleiatvery
latedintheCGC.Stronglyinteractingmattermaybe
high energies and high densities are required. Since
subject to a series of phase transitions with increas-
the collisions are very violent and the time scales in-
ing temperature and/or density of the baryon among
volvedareveryshort,theformationofQGPdepends
whichisthefirst-orderphasetransitionofrestoration
on the initial conditions for the matter produced in
of a specific symmetry of strong interactions—chiral
the collision. More precisely, it depends on the dis-
symmetry that is strongly violated at low tempera-
tributions of partons in the wavefunctions of the two
tures and/or densities of the baryon charge. How-
nuclei before the collision. Multi-particle production
ever, to create necessary laboratory conditions and
in high energy collisions is dominated by modes in
Received04May2012
1)E-mail:[email protected]
2)E-mail:mais [email protected]
(cid:13)c2009ChinesePhysicalSocietyandtheInstituteofHighEnergyPhysicsoftheChineseAcademyofSciencesandtheInstitute
ofModernPhysicsoftheChineseAcademyofSciencesandIOPPublishingLtd
No.X M.Ajaz etal: Instructionfortypesettingmanuscripts 2
pick up a ”signal” of formation of the QGP phase, believedthattheearlyuniversewentthroughaQGP
oneneeds alotof intellectualandmaterial resources. phase as it expanded and cooled. Hadronization is
The well known time evolution of central heavy ion the next stage in the reaction setup where the relax-
collisions is shown in Fig. 1. Several phases of a typ- ation of the energy density takes place. The central
ical heavy ion collision can be identified. Here the system is undergoing expansion, thereby reducing its
five states are shown as: I. pre-interaction state; II. temperature and density. For symmetry reasons, the
parton-parton interaction one and the mixed phase; expansion is azimuthally symmetric for central colli-
III. QGP phase ; IV. hadranization and V. freezout. sions. The matter begins to expand collectively into
In the pre-interaction state, two nuclei are approach- transverse directions. The features of this process
ing each other with high velocity. their orientation may be understood at a qualitative level in terms
in space and the initial beam direction define the re- of the self-similar cylindrically symmetric hydrody-
action plane. The impact parameter b is located in namic expansion. In the self-similar expansion, the
the reaction plane which is a perpendicular distance velocity is proportional to the distance from symme-
between the center of the two colliding nuclei. In the try axis. The system will expand and cool until the
case of most central collision the value of b is equal energydensitiesandtemperaturesarenolongersuffi-
to zero. In the second stage when the two heavy cient to sustain a thermally equilibriated system. At
nuclei approach each other and start to overlap, the a temperature of about 15 fm/c, the momenta of the
parton-partoninteractionisexpectedbecauseofhigh particle will kinetically freeze-out and the particles
energyandcentrality,whichleadstothemixedphase willstreamfreelywithoutfurtherstronginteractions.
of the strongly interacting system. After the overlap Ineachstate, themattercanbecharacterizedbydif-
of the matter distributions of the two colliding nu- ferenttemperatureanddensity. Apartfromthesepa-
clei,thepropertiesofthenucleon-nucleoninteraction rameters, there could be another very interesting pa-
are not well known. Medium effect -the modifica- rameter, namely the transparency (Tr) of matter, to
tionofthepropertiesoftheconstituents,andathigh characterizethesestates. Webelievethattheappear-
energies the transition to the QGP occurs. The crit- anceandchangingofthetransparencycouldgivethe
ical value of temperature for the formation of such necessary information for the identification of QGP
plasma is of the order of 170 MeV. The idea of QGP formation. To extract the nuclear transparency, nu-
is illustrated with the following example. Consider clearmodificationfactor(R)isused. Intheliterature
a certain volume containing baryons. Experiments one can find two different ways of defining nuclear
have shown that baryons have non-zero spatial vol- modification factor denoted by R and R . The
AA CP
ume [16]. Thusclearlyacriticalvolumeexistswhere former is defined as the ratio of the particles yield in
baryonsfillthevolumecompletelyandatthiscritical nucleus-nucleus collision normalized to the number
volume it is assumed that the baryon structure van- of binary collisions to that of nucleon-nucleon colli-
ishes and forming the plasma of quarks and gluons. sions, whereas the latter is defined as the ratio of the
Here it is worth pointing out that the quarks are still particles yield in the central to peripheral collisions.
confined by the strong interaction but now instead Sometimes, due to the lack of appropriate pp data,
of being confined within hadrons they are confined which enables to calculate R , a ratio of central to
AA
within the allowed volume. Now the energy density peripheralspectraisused(R ),onthepremisethat
CP
ismuchhigherinthisvolumeunliketheenvironment ultra peripheral events look very much like elemen-
found inside nucleons. The matter inside the volume tary collisions. We use the latter one in the current
is proposed to be in a state known as a QGP. It is study.
Fig.1. Aschematicviewofthetimeevolutionofthecentralheavyioncollision. ImagepreparedbySteffen
Bass, Duke University
No.X M.Ajaz etal: Instructionfortypesettingmanuscripts 3
In Ref. [17] a signal on mixed phase formation is matter [20]asaresultoftheformationofpercolation
considered an important point to identify QGP be- cluster could stop the decrease of yields of heavy fla-
cause such a state must contain real particles which vors. Thus we expect to see the new structure in the
can interact with matter and therefore could be de- behavior of the particles yields as a function of the
tected. centrality which could connect with the percolation
cluster formation.
2 The nuclear modification factor
In this paper we discuss some ideas connected
with the identification of QGP using the information
comingfromthefreezoutstate. Themainideaisthat
the values of transparency (Tr) for different states
of time evolution of heavy ion collisions are different
(Tr , Tr and Tr ). To characterize the Tr it is
III IV V
convenienttousethenuclearmodificationfactor(R).
A comparison of yields in different ion systems by
using nuclear modification factors (involving central
and peripheral collisions) should provide information
on the hadronization [18] (see Fig. 2). R highlights
the particle type dependence at intermediate p as
T
was suggested by the coalescence models [19] leading
to the idea that hadrons result from the coalescence
n
of quarks in the dense medium. Using R = 1 (here
n
2
e.g., n and n could be heavy flavor particles yields
1 2
withfixedvaluesofp andη)asafunctionofcentral-
T
ity, the masses and energy it is possible to get nec-
essary information on the properties of the nuclear
matter. In such definition, the appearance of trans-
parency could be identified and detected using the
condition R=1. The data obtained by STAR RHIC Fig.2. Yieldsofsomebaryonsasafunctionof
BNL [18] on the behavior of the nuclear modifica- the centrality (expressed with the number of
participants) in Au+Au collisions normalized
tion factors of the strange particles as a function of
tothemostperipheralpointandtonumberof
the centrality in Au+Au- and p+p-collisions at 200
participant (N ) shown in the upper frame
GeV (see Fig.2) may help us to answer the questions part
and number of binary collisions (N ) shown
bin
on how the new phases of strongly interacting mat-
in the lower frame [18]. N and N are
part bin
ter form. To probe the processes governing this pro-
calculated in the framework of the Glauber
duction, yields of (anti-)strange particles have been
model. Differentmarkerswithdifferentcolors
normalized as a function of the number of partici- correspond to different baryons as shown.
pants N (usually related to soft processes) and
part
of the number of binary collisions N (supposed to
bin
describe hard processes) for Au-Au collisions as it is
shown in the upper and lower frames of Figure 2, re-
spectively. Strange particles deviate from the N
part
scalingandfollowabetterscalingwithN . Wemay
bin
expect a signal on the formation of the intermediate Fig. 3 shows the results of the PHENIX, RHIC on
nuclearsysteme.g.,nuclearcluster. Thestrangepar- the studies of J/ψ production from p+p to central
ticlescouldbeformedasaresultofquarkcoalescence Au+Au collisions. Results from PHENIX include
inhighdensitystronglyinteractingmatterandonthe R distributions for the Au+Au and Cu+Cu colli-
AA
otherhandtheycouldbecapturedbythissystemin- sions [21]. Thedatashowsanincreasingsuppression
tensively. So by increasing the centrality, the yields withN . AtcentralAu+Aucollisionsthesuppres-
part
of heavy flavors could decrease. The appearance of sion is larger than predicted by normal absorption in
superconducting property of the strongly interacting cold nuclear matter production [22, 23].
No.X M.Ajaz etal: Instructionfortypesettingmanuscripts 4
state R is almost a linearly increasing function of the
T independent of the types of particles and the sec-
th
ondregionisastraightline,whichhasnodependence
on T , it can be regarded as a regime change. Now
th
onecanseethatthestudyofthenuclearmodification
factorasafunctionofthermalfreeze-outtemperature
shows a critical change and saturation at a tempera-
ture about 150 MeV. This critical change in R is ac-
tually due to the critical change in the transparency
of the medium, which shows the changing properties
of the medium.
Fig. 3. Nuclear modification factor as a func-
tion of a number of participants (N ) for
part
Au+Au and Cu+Cu collisions [21].
It is supposed that Tr ∼R . To restore the
III−V III−V
time scale we are going to use the values of tempera-
ture because they must be different for III-V states.
If the states of III-Vl appear critically, the regime
change will have to be observed in the behavior of R
as a function of temperature. Fig. 4. The behavior of the nuclear modifi-
cation factor is shown as a function of ther-
mal freeze-out temperature. Different colors
3 Results
in the figure correspond to the ratio of differ-
ent particles/anti-particles yield produced in
To confirm the above idea we use data coming
centralAu+Aucollisionstothatofthecorre-
from different heavy ion generators and experiments. sponding particles/anti-particles yield in pe-
Fig. 4 shows the result of the study of the behav- ripheralAu+Aucollisions. ThebehaviorofR
ior of R function defined as ratio of the yields of is independent of the type of particle used.
different particles at central to peripheral collision
as a function of the thermal freeze-out temperature
4 Summary
(T ) produced in Au-Au collisions at RHIC ener-
th
gies. Different colors in Fig. 4 correspond to differ-
ent particles/anti-particles. The behavior of nuclear Wehavediscussedthattheappearanceofthecrit-
modificationfactorisstudiedforalltheoctetbaryons ical nuclear transparency, as a function of different
and a few octet pseudo scalar mesons as well as for kinematical parameter of nucleus-nucleus collision
their corresponding anti-particles. The results show is considered a signal of phase transition in nuclear
thatthebehaviorisindependentofthetypeofparti- mater. FASTMCisusedforAu-AucollisionatRHIC
cleused. ThedataissimulatedusingtheFastHadron energies. Thismodelofhadrongenerationallowsone
Freezout Generater (FASTMC) [24]. The FASTMC to study and analyze various observables for stable
hadron generation allows one to study and analyze hadrons and hadron resonances produced in ultra-
variousobservablesforstablehadronsandhadronres- relativistic heavy ion collisions. The behavior of R
onances produced in the ultra-relativistic heavy ion functionisstudiedasafunctionofthermalfreeze-out
collisions. Particlescanbegeneratedonthechemical temperature. Critical change in the transparency is
or thermal freeze-out hyper surface represented by a considered a signal on the appearance of new phases
parametrization or a numerical solution of relativis- of strongly interacting matter and the QGP. Nuclear
tic hydrodynamics with given initial conditions and modification factror is used to extract the informa-
equation of state [24]. There are two regions in the tiononnucleartransparencyeffect. Acriticalchange
behavior of R as a function of the T (see Fig. 4). in the behavior of R function at a temperature of
th
In the first region one can see that in the freeze-out about 150 MeV is observed.
No.X M.Ajaz etal: Instructionfortypesettingmanuscripts 5
11 KharzeevD.NardiM.Phys.Lett.B,2001507: 121.
12 TeaneyD.VenugopalanR.Phys.Lett.B,2002,539: 53.
References 13 KovnerA.McLerranL.WeigertH.Phys.RevD,1995,52:
3809; Kovner A. McLerran L. Weigert H. Phys. Rev D,
1 Jeon S. Koch V. Review for Quark-Gluon Plasma 3. eds.
1995,52: 6231.
Hwa R C and Wang X-N, Singapore: World Scientific,
14 Kovchegov Y V. Rischke D H. Phys. Rev. C, 1997, 56:
2004.
1084; Matinyan S G. Muller B. Rischke D H. Phys. Rev.
2 Greiner W. Schafer A. Quantum Chromodynamics.
C,1997,56: 2191;MatinyanSG.MullerB.RischkeDH.
Springer,1994.
Phys. Rev. C, 1998, 57: 1927; Guo Xiao-feng. Phys. Rev.
3 Gribov L V. Levin E M. Ryskin M G. Phys. Repts, 1983
D,1999,59: 094017.
100: 1; Mueller A H. QiuJ-W. Nucl. Phys. B, 1986, 268:
15 GyulassyM.McLerranL.Phys.Rev.C,1997,56: 2219.
427; Blaizot J P. Mueller A H. Nucl. Phys. B, 1987, 289:
16 Povh B. Rith K. Scholz C. et al. Particles And Nuclei,
847.
Springer-Verlag2004.
4 McLerranL.VenugopalanR.Phys.Rev.D,1994,49: 2233;
17 Sissakian A N. Sorin A S. Suleymanov M K. et al.
McLerranL.VenugopalanR.Phys.Rev.D,1994,49: 3352;
Phys.Part.Nucl.Lett.,2008,5: 1.
McLerranL.VenugopalanR.Phys.Rev.D,1994,50: 2225.
18 Roy Christelle. for the STAR Collaboration, POS
5 JalilianMarianJ.KovnerA.McLerranL.etal.Phys.Rev.
(HEP2005)141;RoyChristelle.SpecificitiesofRHICheavy
D, 1997, 55: 5414; Kovchegov Y. V. Phys. Rev. D, 1996,
ioncollisionsprobedbystrangeparticles.In: International
54: 5463;AyalaA.Jalilian-MarianJ.McLerranLD.etal.
EurophysicsConferenceinHighEnergyPhysics(EPS)Lis-
Phys. Rev. D, 1995 52: 2935; Ayala A. Jalilian-Marian J.
boa,Portugal,2005.
McLerranLD.etal.Phys.Rev.D,1996,53: 458.
19 MolnarD.etal.,Phys.Rev.Lett.,2003.91: 092301.
6 Jalilian-MarianJ.KovnerA.LeonidovA.etal.Nucl.Phys.
20 Satz H. Nucl. Phys. A, 1998 642: 130; Satz H. hep-
B,1997,504: 415;Jalilian-MarianJ.KovnerA.WeigertH.
ph/0007069,2000;BaymG.,PhysicaA,1979,96: 131
Phys.Rev.D,199959: 014015;McLerranL.Venugopalan
21 Cassagnac R G de. Eur.Phys.J.C, 2007, 49: 365; Pereira
R. Phys. Rev. D, 1999, 59: 094002; Iancu E. McLerran L
daCostaH.Nucl.Phys.A,2006,774: 747.
D. Phys. Lett. B, 2001, 510: 145; Iancu E. Leonidov A.
22 VogtR.ActaPhys.Hung.A,2006,25: 97.
McLerran L D. Nucl. Phys. A, 2001, 692: 583; Iancu E.
23 Suaide A A P. Brazilian Journal of Physics, 2007 37(2C):
LeonidovA.McLerranLD.Phys.Lett.B,2001,510: 133.
731.
7 McLerranLD.ActaPhys.Polon.B,1999,30: 3707.
24 Amelin N S. Lednicky R. Pocheptsov T A. et al. Yu M.
8 GavaiRV.VenugopalanR.Phys.Rev.D,1996,54: 5795.
Phys.Rev.C,2006,74: 064901;AmelinNS.LednickyR.
9 MuellerAH.Nucl.Phys.B,2000,572: 227.
LokhtinIP.etal.arXiv:0711.0835,2007.
10 VenugopalanR.ActaPhys.Polon.B,1999,30: 3731.