Scaling of nuclear modification factors for hadrons and light nuclei

0.3 MB·English

by  C. S. Zhou

EPJ manuscript No.
(will be inserted by the editor)
Scaling of nuclear modification factors for hadrons and light
nuclei
C. S. Zhou1,2, Y. G. Ma1,3 a, and S. Zhang1b
1 Shanghai Instituteof Applied Physics, Chinese Academy of Sciences, Shanghai201800, China
2 University of Chinese Academy of Sciences, Beijing 100049, China
3 ShanghaiTech University,Shanghai 200031, China
6
1
Received: date/ Revised version: date
0
2
Abstract. The number of constituent quarks (NCQ-) scaling of hadrons and the number of constituent
c
e nucleons(NCN-)scalingoflightnucleiareproposedfornuclearmodification factors(Rcp)ofhadronsand
D light nuclei, respectively, according to the experimental investigations in relativistic heavy-ion collisions.
Based on coalescence mechanism the scalings are performed for pions and protons in quark level, and
1 light nucleid(d¯) and 3Hefor nucleoniclevel, respectively,formed in Au+ Auand Pb +Pb collisions and
nice scaling behaviour emerges. NCQ or NCN scaling law of Rcp can be respectively taken as a probe for
] quarkornucleoncoalescencemechanismfortheformationofhadronorlightnucleiinrelativisticheavy-ion
h
collisions.
t
-
l
c PACS. PACS-key 25.75.Gz, 12.38.Mh, 24.85.+p
u
n
[ 1 Introduction tween nucleus-nucleus (AA) collisions and proton-proton

3 (pp) collision RAA or the one between the central col-
v Quark-gluon plasma (QGP) which was predicted by the lisions and peripheral collisions Rcp, can give quantita-
6 tive properties of the nuclear medium response when the
Quantum chromodynamics (QCD) [1] can be formed in
8 high speed jet transverses it. In high transverse momen-
ultra-relativistic heavy-ion collisions, at the Relativistic
3 tum (p ) region,NMF is suppressedowing to jet quench-
Heavy-Ion Collider (RHIC), Brookhaven National Labo- T
4
ingeffectinhot-densematter andthushasbecome oneof
ratory[2,3,4,5]andatthe LargeHadronCollider(LHC),
0
therobustevidencesontheexistenceoftheQuark-Gluon-
. CERN,andthe energydependence ofquarkmatterprop-
1 Plasma [2,3,4,5,26,27,28,29,30]. In lower p region, ra-
erties is thoughtas one of importantobservablesto study T
0 dialflowboostsortheCronineffect[31,32]competeswith
variousaspectsoftheQCDphasediagram[6,7,8,9,10,11,
5
the quenching effect and enhances the NMF, which has
12,13,14,15] in the beam energy scan program at RHIC
1
beenalsodemonstratedbytheRelativisticHeavy-IonCol-
: [16].ExtensiveexperimentalresultsinAu+Aucollisions,
v lider (RHIC) beam energy scan (BES) project [33]. Re-
including particle and anti-particle production and spec-
i cently, the study of nuclear modification factor was for
X tra, the nuclear modification factors (NMF) RAA or Rcp
the first time extended to intermediate-energy heavy-ion
r of hadrons and baryon-to-meson ratios at √sNN = 200
a GeV/chavebeenreported[2,3,4,5,17,18,19,20,21].Some collisions and the radial flow effect on proton NMF has
been quantitatively investigated by Ma’s group [34,35].
thermalparametersoftheQGPareextracted,forinstance
thechemicalfreeze-outtemperatureT ,thebaryonchem-
ch
ical potential µ and the strangeness chemical potential
B
µ etc [22,23], which helps us to understand the phase
S
structure at high temperature.
In the viewpoint of experimental probes, the nuclear It will be of very interesting to check if the Rcp of π
modification factor (NMF) R is a very useful observ- and p can be scaled together by a number of constituent
cp
able for studying the feature of QGP [24,25]. Extensive quark(NCQ)scalinglawasellipticflow’sNCQ-scaling[6,
studies have been carried out both experimentally and 21,36]. On the other hand, Rcp of light nuclei is not yet
theoretically.Thesestudies indicatethattheNMF,which addressedinrelativisticheavyioncollisions.Inthepresent
can be represented either by the modification factor be- study,apparentdifferencesbetweentheRcp oflightnuclei
are found for different nucleon number. With the help of
Send offprint requests to: thecoalescencemodel[37],wealsofoundawaytofitthem
a Email: [email protected] byanumberofconstituentnucleon(NCN)scaling.Inthe
b Email: [email protected] following texts, we will discuss these phenomena.
2 C. S. Zhou et al.: Scaling of nuclearmodification factors for hadronsand light nuclei
2 Number of constituent quark (NCQ)
scaling of hadron’s R 2 Au+Au @ 200 GeV π, p
cp
20-40%/40-80% ,
Inrelativisticheavyioncollisionstheproductionofhadrons 0-12%/60-80% ,
atintermediatetransversemomentumcanbedescribedby 0-12%/40-80% ,
coalescence mechanism [38], i.e.
p
Rc 1
d3N d3N nq
h q
E =B E , (1)
hd3P nq(cid:18) qd3P (cid:19)
h q
where n is the number of constituent quarks of a hadron
q
and the coefficient B is the probabilities for n quarks
to hadron coalescencne.q From the coalescence meqchanism 0
0 2 4 6 8
it was found that elliptic flow of hadrons can be scaled
to the number of constituent quark [6,21,36]. And the p (GeV/c)
T
nuclear modification factor R is defined as [24,25],
cp
Fig. 1. (Color online) Rcp for pions and protons in Au+Au
[d2N/pTdydpT/ Nbin ]central collision at √sNN = 200 GeV. Original data of Rcp are taken
Rcp(pT)= [d2N/p dydp / Nh ]iperipheral, (2) from ref. [41].
T T bin
h i
where N is the average number of binary nucleon-
bin 0.8
nucleonhcolliisions per event. The ratio of Nbin central to Au+Au @ 200 GeV π, p
N peripharal canbefoundindata[17]fohrAu+iAucolli-
bin 20-40%/40-80% , /0.83
h i
sionsat√sNN =200GeVandindata[39,40]forPb+Pb 0.6 0-12%/60-80% , /0.66
collisions at √s = 2760 GeV. The jets and high p
NN T 0-12%/40-80% , /0.73
particles created in the early stage will lose most energy
throughinteractionsintheevolutionofthesystemincen- * cp0.4
~R
tral A+A collisions and it is confirmed by suppression of
R at high p in experiments in relativistic heavy-ion
cp T
collisions. Figure 1 displays Rcp for pions and protons in 0.2
three central-peripheralpairs,where the originaldata are
from ref. [41]. Of course, obvious differences between pi-
ons and protons are observed. In this paper, however, we 0
will focus on another topic, i.e. if there is number of con- 0 1 2 3
stituent quarkscaling ofRcp for hadronsas that for ellip- p /nq (GeV/c)
tic flow [21,6,36] at intermediate transverse momentum. T
From eq. (1) and eq. (2), it can be deduced, Fig.2. (Coloronline)Numberofconstituentquarkscalingof
Rcp for pion and proton in Au+Au collision at √sNN = 200
R∗ (p )= Bnq,central −1/nq(R (n p ))1/nq GeV.Original data of Rcp are taken from ref. [41].
cp T (cid:18)B (cid:19) cp q· T
nq,peripheral
N c 1/nq−1 ∗
h bini , (3) fig.2,whichcanscalepionandprotonRcptogether.Itcan
×(cid:18) Nbin p(cid:19) be seen from the listed factor which shows the difference
h i ∗ e
between pion’s R and protons is a constant factor with
R∗ is the scaled nuclear modification factor to scale me- cp
cp centrality dependence.
son’s and baryon’s R together. Unfortunately the coef- e
cp Similarly,R ofpionsandprotonsforthePb+Pbcol-
ficient B can not be determined experimentally. So we cp
can try tnoqscale hadron’s R by the following formula, lisions at √sNN = 2760 GeV are plotted as a function of
cp p in fig. 3 for different central-peripheralpair combina-
T
N c 1/nq−1 tion. Again, significant differences are observed between
R∗ (p )= (R (n p ))1/nq h bini , pionsandprotons.After the number ofconstituentquark
cp T cp q· T (cid:18) Nbin p(cid:19) scaling for R , we plot fig. 4 for demonstration of R∗
Re∗ (p ) Rc∗p(pT) h. i (4) of pion and pcproton, where the original data of Rcp earcpe
cp T ≡ Bnq,central −1/nq from [39,40,42,43]. The scaled factor of Rc∗p for proton is
e (cid:16)Bnq,peripheral(cid:17) increasing∗with the increasing of the centerality of numer-
ator of R , which takes similar centrality dependence in
∗ cp
Figure2presentsRcp ofpionandprotonasafunction LHC as in RHIC energy.So it implies that the number of
oftransversemomentueminAu+Aucollisionsat√sNN = constitueent quark scaling of Rcp for hadron supports the
200GeV,wheretheoriginaldataofRcp arefromref.[41]. viewpointofquarkcoalescencemechanismforhadronfor-
∗
ThevalueofR ofprotonisscaledbyafactorlistedinthe mation in the intermediate transverse momentum range
cp
e
C. S. Zhou et al.: Scaling of nuclearmodification factors for hadronsand light nuclei 3
(a) 0-5% (b) 5-10% (c) 10-20% (d) 20-30%
Pb+Pb @ 2760 GeV
π
X/70-80%) 1 p X/70-80%) 1 X/70-80%) 1 X/70-80%) 1
(Rcp 0.5 (Rcp 0.5 (Rcp 0.5 (Rcp 0.5
0 0 0 0
0 2 4 0 2 4 0 2 4 0 2 4
p (GeV/c) p (GeV/c) p (GeV/c) p (GeV/c)
T T T T
(e) 30-40% (f) 40-50% (g) 50-60% 4 (h) 60-70%
2 2
(X/70-80%)Rcp 1.51 (X/70-80%)Rcp 1.51 (X/70-80%)Rcp 21 (X/70-80%)Rcp 23
0.5 0.5 1
0 0 0 0
0 2 4 0 2 4 0 2 4 0 2 4
p (GeV/c) p (GeV/c) p (GeV/c) p (GeV/c)
T T T T
Fig. 3. (Color online) Rcp forpionandprotoninPb+Pbcollision at √sNN =2760 GeV.Original dataofRcp aretakenfrom
refs. [39,40,42,43].
(a) 0-5%, p/0.54 (b) 5-10%, p/0.55 (c) 10-20%, p/0.58 (d) 20-30%, p/0.62
Pb+Pb @ 2760 GeV
π
X/70-80%) 0.2 p X/70-80%) 0.2 X/70-80%) 0.2 X/70-80%) 0.2
~*R(cp 0.1 ~*(Rcp 0.1 ~*R(cp 0.1 ~*(Rcp 0.1
0 0 0 0
0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5
p /n (GeV/c) p /n (GeV/c) p /n (GeV/c) p /n (GeV/c)
T q T q T q T q
(e) 30-40%, p/0.67 (f) 40-50%, p/0.73 (g) 50-60%, p/0.80 0.8 (h) 60-70%, p/0.88
0.4 0.4
~*R(X/70-80%)cp 000...231 ~*(X/70-80%)Rcp 000...231 ~*R(X/70-80%)cp 00..24 ~*(X/70-80%)Rcp 000...246
0 0 0 0
0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1 1.5
p /n (GeV/c) p /n (GeV/c) p /n (GeV/c) p /n (GeV/c)
T q T q T q T q
Fig. 4. (Color online) Number of constituent quark scaling of Rcp for pion and proton in Pb+Pb collision at √sNN = 2760
GeV. Original data of Rcp are taken from refs. [39,40,42,43].
for relativistic heavy-ion collisions and the difference of d3N A
n
= B E , (5)
the scaled Rcp between pions and protons keeps a con- A(cid:18) nd3Pn(cid:19)
stant factor which displays a centrality dependence.
Tosummarisethissection,wefindthattheconstituent where
quark scaling holds for the nuclear modification factor of
hadrons. It indicates the energy loss of hadrons is essen- Pp =Pn =PA/A, (6)
tially originated from the partonic stage which leads to
the same energy loss factor per constituent quark, which and the coefficient BA (1/V)A−1 is related to the fire-
∼
is consistent with the concept of quark-gluonplasma. ball volume in coordinate space and depends on momen-
tum [37,44,45]. The coefficient B can be extracted from
A
dataorcalculatedbycoalescencemechanism[44,45].The
3 Number of constituent nucleon (NCN) number of constituent nucleon (NCN) scaling of light nu-
scaling for R of light nuclei clei’s Rcp can be obtained through replacing nq by A in
cp
eq. (3).
While the collision system reaches a kinetic freeze-out If there exists a similar scaling of Rcp for light nu-
stage, nucleons could be coalesced to light nuclei. In this clei as that for elliptic flow [46,47,48], it certainly sup-
case,thecoalescencemechanismfortheformationoflight ports the coalescence mechanism for formation of light
nuclei is similar to formula (1) with considering the same nuclei at kinetic freeze-out stage. Our earlier prediction
distribution of protons and neutrons, on number-of-nucleon scaling of elliptic flow [46,47] was
recentlysupportedbytheSTARdatafromAu+Aucolli-
d3N d3N Z d3N A−Z sions[48].Eventhoughtheenergydomainishugedifferent
A p n
E =B E E ,
Ad3P A(cid:18) pd3P (cid:19) (cid:18) nd3P (cid:19) between our prediction [46,47] and the STAR data [48],
A p n
4 C. S. Zhou et al.: Scaling of nuclearmodification factors for hadronsand light nuclei
8
(a)NA49, [email protected] GeV (b)PHENIX, Au+Au@200 GeV (c)ALICE, Pb+Pb@2760 GeV
%/33-100%) 46 dp %/20-92%) 23 pdpd (C/P) 435 3pdpH,,CCe//PP==00--1200%%//6200--8800%%
(0-12Rcp 2 (0-20Rcp 1 Rcp 21
0
0 0.5 1 1.5 2 1 2 3 4 0 2 4 6
p (GeV/c) p (GeV/c) p (GeV/c)
T T T
Fig. 5. (Color online) Rcp of light nuclei of (a) Pb + Pb at 17.2 GeV, (b) Au + Au at 200 GeV, and (c) Pb + Pb at 2760
GeV, respectively . Original data are taken from the NA49 Collaboration [51] for Pb+Pb collisions at √sNN = 17.2 GeV, the
PHENIX Collaboration [52,53] for Au+Au collisions at √sNN = 200 GeV and the ALICE collaboration [39,40,42,43,54] for
Pb+Pb collisions at √sNN = 2760 GeV.
5 (a)NA49, [email protected] GeV (b)PHENIX, Au+Au@200 GeV (c)ALICE, Pb+Pb@2760 GeV
%/33-100%) 43 dp/0.40 %/20-92%)1.51 pddp//00..4400 (C/P)1.51 3pdpH,/,C0Ce.//2/PP08==.4001--1200%%//6200--8800%%
~*(0-12Rcp 21 ~*(0-20Rcp0.5 ~*Rcp0.5
0
0 0.5 1 0.5 1 1.5 2 0 0.5 1 1.5 2
p /A (GeV/c) p /A (GeV/c) p /A (GeV/c)
T T T
Fig. 6. (Color online) Numberof constituent nucleon (NCN) scalings for Rcp of light nuclei of (a) Pb + Pb at 17.2 GeV, (b)
Au + Au at 200 GeV, and (c) Pb + Pb at 2760 GeV, respectively . Original data are taken from theNA49 Collaboration [51]
forPb+Pbcollisions at √sNN =17.2 GeV,thePHENIXCollaboration [52,53]forAu+Aucollisions at√sNN =200 GeVand
theALICE collaboration [39,40,42,43,54] for Pb+Pb collisions at √sNN = 2760 GeV.
∗
the scaling phenomenonis the same,whichindicates that the NA49 collaboration[51].Figure 6 (b) givesthe R of
cp
theproductionoflightnucleistemsfromthenucleonicco- (anti-)proton and (anti)deuteron in Au+Au collisions at
e
alescence mechanism rather than quark coalescence even √sNN = 200 GeV and the data are from PHENIX col-
in ultra-relativistic energy. The same concept of number- ∗
laboration[52,53].Andfig.6(c)showsthe R ofproton,
of-nucleon scaling of elliptic flow was also followed by a cp
dynamical model [49] as well as a multiphase transport deuteron and 3He in Pb + Pb collisions at √esNN = 2760
GeV and the data are from ALICE collaboration [39,40,
(AMPT) model [50].
42,43,54].Fromtheseplots,itwasfoundthenuclearmod-
ificationfactor(R )ofdeuteronand3Hecanbescaledto
Here we consider the coalescence mechanism for light cp
proton’s R after performing the number of constituent
nuclei by Eq. (5). As the yields of p(p¯) and n(n¯) are simi- cp
∗
nucleon(NCN) scaling.There is a constantfactor for R
lar,wehavetheyieldsoflightnucleiwithA-massnumber cp
oflightnucleito thatofprotons.Althoughthe NCN scal-
obey the Eq. (5). Before the scaling, we show the R of
cp e
ing for R of light nuclei is studied at three different col-
lightnucleiofPb+Pbat17.2GeV [51],Au+Auat200 cp
GeV [52,53] , and Pb + Pb at 2760 GeV [54,42,43,39, lision energy √sNN from 17.2 GeV to 2760 GeV, there
needs more experimental results of energy and centrality
40],respectively.Again,thecurvesfordifferentlightnuclei
dependence of light nuclei production to explore the con-
are not collapsed together. After the scaling for nucleon
∗
number, fig. 6 shows the number of constituent nucleon stant factor for Rcp of light nuclei which is related to the
on(NCN)scalingforR oflightnuclei,R∗ .Figure6(a) coalescence parameter from eq. (4).
cp cp e
∗ ∗
representstheR ofprotonanddeuteroninPb+Pbcol- In light of this study, we can investigate the R for
cp e cp
lisions at √sNN = 17.2 GeV and the data are takenfrom light nuclei experimentally to distinguish their formation
e e
C. S. Zhou et al.: Scaling of nuclearmodification factors for hadronsand light nuclei 5
mechanism in heavy ion collisions. Current data support inChinaunderContractNo.2014CB845400,theNational
that the (anti-) light nuclei are coalesced by the (anti-) NaturalScience FoundationofChinaunder contractNos.
nucleons. In fact, the constituent nucleon number scaling 11421505,11220101005,11105207andU1232206,andthe
of elliptic flow for light nuclei which was firstly proposed CAS Project Grant No. QYZDJSSW-SLH002.
in intermediate-energy heavy-ion collisions [46,47,55,56]
alsosupportsthecoalescencemechanismfortheformation
of light nuclei at kinetic freeze-out stage in the reaction References
system.Actually,atRHIC,theellipticflowof(anti-)light
nucleidataofAu+Auat200GeV[48]givestheevidence
1. F. Karsch, Nucl. Phys.A 698, 199c (2002).
ofthe nucleon-number scalingas proposedby Ma’s group 2. I. Arsene et al. (BRAHMS Collaboration), Nucl. Phys. A
[46].Furthermore,theobservationofanti-hypertriton[19] 757, 1 (2005).
and anti-helium 4 [20] at STAR also indicates that the 3. B. B. Back et al. (PHOBOS Collaboration), Nucl. Phys.A
anti-nucleon coalescence is responsible for their produc- 757, 28 (2005).
tion yield in the basis of attractive interaction between 4. J.Adamesetal.(STARCollaboration),Nucl.Phys.A757,
anti-nucleons [57,58]. 102 (2005).
Tosummarisethissection,wefindthattheconstituent 5. S. S. Adler et al. (PHENIX Collaboration), Nucl. Phys. A
quark scaling holds for the nuclear modification factor of 757, 184 (2005).
light nuclei in relativistic heavy-ion collision. It indicates 6. J.Tian,J.H.Chen,Y.G.Ma,X.Z.Cai,F.Jin,G.L.Ma,
the energy modification of light nuclei is essentially origi- S. Zhang and C. Zhong, Phys. Rev.C 79, 067901 (2009).
natedfromthehadronicstageratherthanprotonicstage, 7. N.Yu,F. Liu, K. Wu,Phys.Rev.C 90, 024913 (2014).
whichleadstothesameenergylossfactorperconstituent 8. G.Y.Shao,M.Colonna, M.DiToro, Y.Liu,B. Liu,Nucl.
nucleons.Ontheotherhand,incontrasttothescalingbe- Sci. Techniques 24, 050523 (2013).
9. F. M. Liu, Nucl. Sci. Techniques24, 050524 (2013).
haviorofR for hadrons,the scaledR displaysa rising
cp cp
10. Y.Hu,Z.Su,W.Zhang,Nucl.Sci.Techniques24,050522
dependence as a function of p , which could stem from
T
(2013).
the larger radial flow or multiple nucleon scattering for
11. H.Wang,Z.Hou,X.Sun,Nucl.Sci.Techniques25,040502
(anti-) light nuclei as demonstrated in refs. [34,35].
(2014).
12. C. M. Ko, L. W. Chen, V. Greco, F. Li, Z. W. Lin, S.
Plumari,T.SongandJ.Xu,Nucl.Sci.Techniques24,050525
4 Conclusion
(2013).
13. C.M.KoandF.Li,Nucl.Sci.Techniques27,140(2016).
We propose, for the first time, that the number of con-
14. Y.J.Ye,J.H.Chen,Y.G.Ma,S.Zhang,C.Zhong,Phys.
stituentquark(NCQ-)scalingofhadronsandthenumber
Rev. C 93, 044904 (2016).
of constituent nucleons (NCN-) scaling of light nuclei for
15. Y. F. Xu,Y. J. Ye, J. H. Chen,Y. G. Ma, S. Zhang, C.
nuclearmodificationfactorR ,respectively,inthiswork.
cp Zhong, Nucl. Sci. Techniques27, 87 (2016).
TheNCQ-scalingofR ofhadronswasappliedtothe re-
cp 16. B.Mohanty(fortheSTARCollaboration), J.Phys.G38,
sults inAu+ Aucollisionsat√s =200GeVfromthe
NN 124023 (2011).
RHIC-STAR and in Pb+Pb collisions at √sNN = 2760 17. B.I. Abelev et al. (STAR Collaboration), Phys. Lett. B
GeV from the LHC-ALICE. The scaled R presents a
cp 655, 104 (2007).
constantdifferencebetweenpionsandprotonsatinterme- 18. G.Agakishievetal.,Phys.Rev.Lett.108,072301(2012).
diate transverse momentum and the constant difference 19. B.I.Abelevet al.(STARCollaboration), Science328,58
factorshowsa centralitydependence trend.This is asup- (2010).
plement for number of constituent quark scaling besides 20. H. Agakishiev et al. (STAR Collaboration), Nature 473,
ellipticflowwhichsupportsthecoalescencemechanismfor 353 (2011).
formationofhadrons.Itisalsoconsistentwiththeforma- 21. J. Adams et al. (STAR Collaboration), Phys. Rev. Lett.
tionofquark-gluonplasma inAu+Au collisionsat√sNN 92 , 052302 (2004).
= 200 GeV. 22. B.I. Abelev (STAR Collaboration), Phys. Rev. C 79,
Basedonthecoalescencemodel,thescalingofR has 034909 (2009).
cp
also been tested for light nuclei where the number of con- 23. P. Braun-Munzinger, J. Stachel, Nature 448, 302 (2007).
stituentnucleon(NCN-)scalingistakenintoaccount.The 24. J. Adams et al. (STAR Collaboration), Phys. Rev. Lett.
results display that the R spectra of different light nu- 91, 072304 (2003).
cp
clei become the one as protons after the scaling.This im- 25. J. Adams et al. (STAR Collaboration), Phys. Rev. Lett.
plies that the scaling factor for R of light nuclei should 91, 172302 (2003).
cp
26. J.D.Bjorken,FERMILAB-PUB-82-59-THYandErratum
be a constant value and would not be distorted for the
(unpublished).
structureofR .Thisscalingbehaviourcanbetakenasa
cp 27. X. N. Wang and M. Gyulassy, Phys. Rev. Lett. 68, 1480
nucleon coalescence mechanism of light nuclei, and illus-
(1992).
trates that those (anti-) light nuclei are originated from
28. E.Wang,X.N.Wang,Phys.Rev.Lett.87,142301(2001).
the hadronic stage.
29. G. L. Ma, Y.G. Ma, S. Zhang et al., Phys. Lett. B 647,
122 (2007).
Acknowledgement: This work was supported in part 30. M. Nie and G. Ma, Nucl. Techniques (in Chinese) 37,
bytheMajorStateBasicResearchDevelopmentProgram 100519 (2014).
6 C. S. Zhou et al.: Scaling of nuclearmodification factors for hadronsand light nuclei
31. J. W. Cronin et al.,Phys. Rev.Lett. 31, 1426 (1973).
32. J. W. Cronin et al.,Phys. Rev.D 11, 3105 (1975).
33. S. P. Horvat et al. (STAR Collaboration), J. Phys.: Conf.
Ser. 446, 012017 (2013).
34. M. Lv, Y. G. Ma, G. Q. Zhang, J. H. Chen, D. Q. Fang,
Phys.Lett. B 733, 105 (2014).
35. M. Lv, Y. G. Ma, G. Q. Zhang, J. H. Chen, D. Q. Fang,
Nucl.Techniques (in Chinese), 37, 100517 (2014).
36. S.A. Voloshin, Nucl. Phys.A 715, 379c (2003).
37. R.Scheibland U.Heinz, Phys. Rev.C 59, 1585 (1999).
38. L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C
93, 021903(R) (2016).
39. B.Abelevetal.(ALICECollaboration),Phys.Rev.C88,
044909 (2013).
40. B. Abelev et al. (ALICE Collaboration), Phys. Lett. B
720, 52 (2013).
41. B.I.Abelevet al.(STARCollaboration), Phys.Rev.Lett.
97, 152301 (2006).
42. B. Abelev et al. (ALICECollaboration), Phys. Rev.Lett.
109, 252301 (2012).
43. B.Abelevetal.(ALICECollaboration),Phys.Rev.C88,
044910 (2013).
44. L.Xue,Y.G.Ma,J.H.Chen,S.Zhang,Phys.Rev.C85,
064912 (2012).
45. N.Shah, Y. G. Ma, J. H. Chen, S. Zhang, Phys. Lett. B
754, 6 (2016).
46. T. Z. Yan, Y. G. Ma, Z. Z. Cai et al., Phys. Lett. B 638,
50 (2006).
47. Y.G. Ma et al.,Nucl. Phys.A 787, 611c (2007).
48. L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C
94, 034908 (2016).
49. YongseokOhandCheMingKo,Phys.Rev.C76,054910
(2007).
50. Lilin Zhu, Che Ming Ko, Xuejiao Yin, Phys. Rev. C 92,
064911 (2015).
51. T. Anticic et al. (NA49 Collaboration), Phys. Rev. C 69,
024902 (2004).
52. S. S. Adler et al. (PHENIX Collaboration), Phys. Rev. C
69, 034909 (2004).
53. S. S. Adler et al. (PHENIX Collaboration), Phys. Rev.
Lett. 94, 122302 (2005).
54. J. Adam et al. (ALICE Collaboration), Phys. Rev. C 93,
024917 (2016).
55. J.Wang,Y.G.Ma,G.Q.Zhang,W.Q.Shen,Phys.Rev.
C 90, 054601 (2014).
56. J. Wang, Y. G. Ma, G. Q. Zhang, W. Q. Shen, Nucl. Sci.
Techniques24, 030501 (2013).
57. L. Adamczyk et al. (STAR Collaboration), Nature 527,
345 (2015).
58. Z. Q. Zhang, Y. G. Ma, Nucl. Sci. Techniques 27, 152
(2016).