What can we learn from the directed flow in heavy-ion collisions at BES RHIC energies?

0.3 MB·

by  Yu. B. Ivanov

EPJ manuscript No.
(will be inserted by the editor)
What can we learn from the directed flow in heavy-ion collisions
at BES RHIC energies?
Yu. B. Ivanov1,2 and A. A. Soldatov2
1 National Research Centre ”Kurchatov Institute” (NRC”Kurchatov Institute”),Moscow 123182, Russia
2 National Research Nuclear University ”MEPhI” (Moscow Engineering Physics Institute),Moscow 115409, Russia
6
1 Received: date/ Revised version: date
0
2
Abstract. Analysis of directed flow (v1) of protons, antiprotons and pions in heavy-ion collisions is per-

n formed in the range of collision energies √sNN = 2.7–39 GeV. Simulations have been done within a
a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS with
J deconfinement transitions: a first-orderphase transition and a smooth crossover transition. The crossover

5 EoS is unambiguously preferable for the description of the most part of experimental data in this energy
1 range. The directed flow indicates that the crossover deconfinement transition takes place in semicentral
Au+Aucollisions in awide range ofcollision energies 4<√sNN < 30 GeV.The obtained resultssuggest
] that the deconfinement EoS’s in the quark-gluon sector∼should b∼e stiffer at high baryon densities than
h
those used in thecalculation. The latter findingis in agreement with that discussed in astrophysics.
t
-
l
c PACS. 25.75.-q , 25.75.Nq, 24.10.Nz
u
n
[ 1 Introduction and the wiggle-like behavior of the excitation function of

1 themidrapidityv1slopewereputforwardasasignatureof
v Thedirectedflow[1]isoneofthekeyobservablesinheavy theQGPphasetransition.However,theQGPEoSisnota
2 ion collisions. Nowadays it is defined as the first coeffi- necessarily prerequisite for occurrence of the midrapidity
90 cient, v1, in the Fourier expansion of a particle distribu- v1 wiggle[13]:Acertaincombinationofspace-momentum
tion,d2N/dy dφ,inazimuthalangleφwithrespecttothe correlationsmay result in a negative slope in the rapidity
3
reaction plane [2,3] dependence of the directed flow in high-energy nucleus-
0
nucleus collisions.
.
1 d2N dN ∞ The directed flow of identified hadrons—protons, an-
0
= 1+ 2v (y)cos(nφ) , (1)
6 dy dφ dy n tiprotons, positive and negative pions—in Au+Au colli-
!
1 nX=1 sions was recently measured in the energy range √sNN
: =(7.7-39)GeVbytheSTARcollaborationwithintheframe-
v where y is the longitudinal rapidity of a particle. The di-
workofthebeamenergyscan(BES)programattheBNL
i rected flow is mainly formed at an early (compression)
X Relativistic Heavy Ion Collider (RHIC)[14]. These data
stage of the collisions and hence is sensitive to early pres-
r suregradientsintheevolvingnuclearmatter[4,5].Asthe havebeenalreadydiscussedinRefs.[15,16,17].TheFrank-
a furt group [15] did not succeed to describe the data and
EoS is harder, stronger pressure is developed. Thus the
to obtain conclusive results. Within a hybrid approach
directed flow probes the stiffness of the nuclear EoS at
[18], the authors found that there is no sensitivity of the
the early stage of nuclear collisions [6], which is of prime
directed flow on the EoSand, in particular,on the occur-
interest for heavy-ion research.
rence of a first-order phase transition. One of the possi-
In Refs. [7,8,9], a significant reduction of the directed
ble reasons of this result can be that the initial stage of
flow in the first-order phase transition to the quark-gluon
the collisionin allscenariosis describedwithin the Ultra-
phase(QGP)(theso-called”softest-point”effect)waspre-
relativistic Quantum Molecular Dynamics (UrQMD) [19]
dicted, which results from decreasing the pressure gradi-
in the hybrid approach. However, this initial stage does
ents in the mixed phase as compared to those in pure
not solely determine the final directed flow because the
hadronicandquark-gluonphases.Itwasfurtherpredicted
UrQMDresults stilldiffer fromthose obtainedwithin the
[10,11,12] that the directed flow as a function of rapid-
hybrid approach[18].
ity exhibits a wiggle near the midrapidity with a nega-
tive slope near the midrapidity, when the incident energy In Refs. [16,17] the new STAR data were analyzed
is in the range corresponding to onset of the first-order within two complementary approaches: kinetic transport
phase transition. Thus, the wiggle near the midrapidity approachesoftheparton-hadronstringdynamics(PHSD)
2 Yu.B. Ivanov,A.A. Soldatov: What can we learn from thedirected flow
[20] and its purely hadronic version (HSD) [21]), and a present in a local space-time region. The freeze-out pro-
hydrodynamic approach of the relativistic three-fluid dy- cedure starts if ε < ε . The freeze-out energy density
tot frz
namics(3FD)[22,23].Incontrasttootherobservables,the ε = 0.4 GeV/fm3 was chosen mostly on the condition
frz
directed flow was found to be very sensitive to the accu- of the best reproduction of secondary particle yields.
racy settings of the numerical scheme. Accurate calcula- DifferentEoS’scanbeimplementedinthe3FDmodel.
tions require a very high memory and computation time. A key point is that the 3FD model is able to treat a de-
Due to this reason in Refs. [16,17] we failed to perform confinement transition at the early nonequilibrium stage
calculations for energies above √sNN = 30 GeV within of the collision, when the directed flow is mainly formed.
the 3FD model. In this workwe apply a purely hadronic EoS[26], an EoS
Inthepresentpaperweextendtheanalysisperformed withacrossovertransitionasconstructedinRef. [27]and
in Refs. [16,17] within the 3FD model. We succeeded to an EoS with a first-order phase transition into the QGP
perform simulations at √sNN = 39 GeV, which allow us [27]. These are illustrated in Fig. 1. Note that an onset
to strengthen conclusions on the relevance of used EoS’s, ofdeconfinementinthe 2-phaseEoStakesplace atrather
in particular, on the stiffness of the EoS at high baryon high baryon densities, above n 8 n . In EoS’s compati-
0
densities in the QGP sector and outline the range of the ble with constraints on the occu∼rrence of the quark mat-
crossover transition to the QGP in terms of collision en- ter phase in massive neutron stars, the phase coexistence
ergy. starts at about 4 n [28]. As it will be seen below, this
0
excessive softness of the deconfinement EoS’s of Ref. [27]
isanobstacleforproperreproductionofthe directedflow
2 The 3FD model at high collision energies.
The 3FDapproximationis aminimal wayto simulate the
early-stage nonequilibrium state of the colliding nuclei at 20
high incident energies. The 3FD model [22] describes a T=10, 100, 200 MeV
nuclearcollisionfromthe stageof the incident coldnuclei crossover EoS
approachingeachother,tothefinalfreeze-outstage.Con- 15 2-phase EoS
trary to the conventional one-fluid dynamics, where a lo- hadr. EoS
)
calinstantaneousstoppingofmatterofthecollidingnuclei N
m
is assumed, the 3FD considers inter-penetrating counter-
010
streamingflowsofleadingbaryon-richmatter,whichgrad- n
(
ually decelerate each other due to mutual friction. The P/
basic idea of a 3FD approximationto heavy-ioncollisions
5
is that a generally nonequilibrium distribution of baryon-
rich matter at each space-time point can be represented
as a sum of two distinct contributions initially associated
0
with constituent nucleons of the projectile and target nu-
0 4 8 12 16 20
clei.Inaddition,newlyproducedparticles,populatingpre-
n/n
dominantly the midrapidity region, are attributed to a 0
third, so-called fireball fluid that is governed by the net- Fig.1. Pressurescaledbytheproductofnormalnuclearden-
baryon-free sector of the EoS. sity (n0 = 0.15 fm−3) and nucleon mass (mN) versus baryon
Atthefinalstageofthecollisionthep-andt-fluidsare density (scaled by n0) for three considered EoS’s. Results are
eitherspatiallyseparatedormutuallystoppedandunified, presentedforthreedifferenttemperaturesT =10,100and200
while the f-fluid, predominantly located in the midrapid- MeV (bottom-up for corresponding curves).
ity region, keeps its identity and still overlaps with the
baryon-richfluids to a lesser (at high energies) or greater
(at lower energies) extent. In particular, the friction be- Inrecentpapers[23,29,30,31,32,33,34]alargevariety
tween the baryon-rich and net-baryon-free fluids is the of bulk observables has been analyzed with these three
only source of dissipation at this final stage because each EoS’s:thebaryonstopping[23,31],yieldsofdifferenthadrons,
separate fluid is described by equations of the ideal hy- theirrapidityandtransversemomentumdistributions[29,
drodynamicswiththe right-handsidescontainingfriction 30,32], the elliptic flow of various species [33,34]. This
with other fluids. All the observables in the 3FD model analysishasbeendoneinthesamerangeofincidentener-
are composed of contributions from all three fluids. Of gies as that in the present paper. Comparison with avail-
course,relativefractionsofthesecontributionsdependon able data indicated a definite advantage of the deconfine-
multiple factors, in particular, on the rapidity range.The ment scenarios over the purely hadronic one especially at
freeze-out is performed accordingly to the procedure de- high collision energies. As an example, excitation func-
scribedinRef.[22]andinmoredetailinRefs.[24,25].This tionsofaveragetransversemasses( m m)ofprotons,
T
h i−
is a so-call modified Milekhin scheme that conserves the antiprotons and pions are presented in Fig. 2. This quan-
energy, momentum and baryon number. The freeze-out tity characterizes the transverse radial flow in the reac-
criterionisbasedonalocalenergydensity,ε ,definedas tion and hence is relevant to the directed flow discussed
tot
a sum of contributions fromall (p-, t- and f-) fluids being here. In Fig. 2 the 3FD results on m are confronted
T
h i
Yu.B. Ivanov,A.A. Soldatov: What can we learn from thedirected flow 3
0.5 3 Results
] p
V
0.4
e
G The3FDsimulationswereperformedformid-centralAu+Au
[
m 0.3 collisions, i.e. at impact parameter b = 6 fm. In Ref. [45]
- hadronic the values of the impact parameter corresponding to the
〉T0.2 1st order tr. experimentalrangeof10–40%mostcentralcollisionswere
m
obtained using a Monte-Carlo Glauber calculation. The
〈 crossover
rangeofb 4.7–9.4fm was found. This rangemanifested
0.1 ≈
p very weak collision-energy dependence. The mean value
]
V of this range is b 7 fm, which is usually used for
e0.4 h i ≈
G representative calculations for this centrality bin, see e.g.
m [0.3 PHSD/HSD calculations in Ref. [16]. The Glauber cal-
culation [45] was based on a Woods-Saxon density profile
-
〉 withthediffusenessparameter 0.5fmandresultedinthe
mT0.2 AGS/SPS total hadronic cross-section for≈Au+Au collisions σ
〈 STAR AA ≃
720 barns. Within the 3FD model the initial nuclei are
0.1
representedby sharp-edgedspheres,i.e.with zero diffuse-
p
] ness.Thisisdoneforstabilityoftheincidentnucleibefore
V0.3
e collision[22].Underthisapproximationthetotalhadronic
G
m [ TAhue+rAefuorec,rowses-hseacvteiotnotaucrcnosrdoiuntgltyoscbaeleσtA3hFAeDm≃ea5n80vablaurenosf.
〉m- T0.2 p - ftmhe. iTmhpisacjtusptaifiraems oetuerrcahsohicbe3FoDfit≈hehbrei(pσrA3eFsAeDn/tσaAtiAve)1/b2. F≈ol6-
〈 p + lowing the experimental conditions, the acceptance p <
T
0.1 2 GeV/c for transverse momentum (p ) of the produced
2 5 10 20 50 T
particlesisappliedtoallconsideredhadrons.Thedirected
(cid:214) s [GeV] flow v (y) as a function of rapidity y at BES-RHIC bom-
NN 1
barding energies is presented in Fig. 3 for pions, protons
Fig. 2. Average transverse mass (minus particle mass) at
and antiprotons.
midrapidityofprotons(p),antiprotons(p¯)andpions(π)from
central(b=2fm)Au+Aucollisionsasfunctionsofthecollision Asseen,thefirst-order-transitionscenariogivesresults
energy. Experimental data are taken from Refs. [35,36,37,38, for the proton v1 which strongly differ from those in the
39] for AGS, [40,41,42,43] for SPS and [44] for BES-RHIC crossover scenario at √sNN = 7.7 and 19.6 GeV. This
energies. is in contrast to other bulk observables analyzed so far
[23,29,30,31,32,33,34]. At √sNN = 39 GeV the directed
flowofallconsideredspeciespracticallycoincidencewithin
thefirst-order-transitionandcrossoverscenarios.Itmeans
to old AGS/SPS data [35,36,37,38,39,40,41,42,43] and
thatthe crossovertransitionto the QGP has been practi-
also compared with new data from the STAR collabora-
callycompleted at√sNN = 39 GeV.It alsosuggeststhat
tion[44].Ontheaverage,thecrossoverscenariostilllooks
the region 7.7 √s 30 GeV, where the crossover
NN
preferable, though these new STAR data are somewhat ≤ ≤
EoSprovidesthebest(althoughnotperfect)overallrepro-
below those from SPS (for protons and antiprotons). It
duction of the STAR data, is the region of the crossover
could seem that the crossover and hadronic scenarios re-
transition.
produce (or fail to reproduce) the antiproton STAR data
The crossover EoS is definitely the best in reproduc-
to the same extent. However, the slope of the crossover
curve is definitely more adequate to the data. The first- tionoftheprotonv1(y)at√sNN ≤20GeV.However,sur-
prisinglythe hadronicscenariobecomespreferableforthe
order-transition scenario certainly fails for protons in the
energyregionwhereonsetofdeconfinementtakesplacein protonv1(y)at√sNN >20GeV.Asimilarsituationtakes
placeinthePHSD/HSDtransportapproach.Indeed,pre-
thisEoS.Theobservedstep-likebehaviorofthe m exci-
h Ti dictions of the HSD model (i.e. without the deconfine-
tationfunctionsoriginatesfrompeculiaritiesofthefreeze-
ment transition) for the proton v (y) become preferable
outin the 3FD model,as itis discussedin Ref.[30]inde- 1
at√s > 30 GeV [16], i.e. atsomewhat higher energies
tail.Thephysicalpatternbehindthisfreeze-outresembles NN
thaninthe3FDmodel.Moreover,theprotonv predicted
the process ofexpansionof compressedand heatedclassi- 1
bythe UrQMDmodel,ascited inthe experimentalpaper
cal fluid into vacuum, mechanisms of which were studied
[14] and in the recent theoretical work [15], better repro-
both experimentally and theoretically. The freeze-out is
ducestheprotonv (y)dataathighcollisionenergiesthan
associated with evaporation from the surface of the ex- 1
the PHSD and 3FD-deconfinement models do. Note that
panding fluid and sometimes with the explosive transfor-
theUrQMDmodelisbasedonthehadronicdynamics.All
mation of the strongly superheated fluid to the gas.
theseobservationscouldbeconsideredasanevidenceofa
The physical input of the present 3FD calculations is problemintheQGPsectorofaEoS.Atthesametimethe
described in detail in Ref. [23]. antiprotondirectedflowat√sNN >10GeVdefinitely in-
4 Yu.B. Ivanov,A.A. Soldatov: What can we learn from thedirected flow
00..0024 prSoTtoAnRs anStiTpArRotons SSpTTioAAnRRs pp-+ a√gsrNeeNm=ent39–GweitVh.inItthiseefinrcsotu-orardgeinr-gtrbaencsaituisoenastcezneraorioneatt-
baryon density the QGP sector of the EoS’s is fitted to
v1 0
the lattice QCD data and therefore can be trusted. The
-0.02 39 GeV crossoverscenario,aswellasallotherscenarios,definitely
fails to reproduce the antiproton v (y) data at 7.7 GeV.
1
The reason is low multiplicity of produced antiprotons.
0.02
The antiproton multiplicity in the mid-central (b= 6 fm)
v1 0 Au+Aucollisionat7.7Gevis 1withinthedeconfinement
-0.02 27 GeV scenarios and 3 within the hadronic scenario. Therefore,
the hydrodynamicalapproachbasedonthe grandcanoni-
19.6 GeV calensembleiscertainlyinapplicabletotheantiprotonsin
0.02
this case. The grand canonical ensemble, with respect to
v1 0 conservationlaws,givesasatisfactorydescriptionofabun-
hadronic dantparticle production in heavyion collisions.However,
-0.02
crossover
whenapplyingthestatisticaltreatmenttorareprobesone
1st-order tr.
needs to treat the conservation laws exactly, that is the
0.02 11.5 GeV canonical approach. The exact conservation of quantum
v1 0 numbers is known to reduce the phase space available for
particle production due to additional constraints appear-
-0.02
ing through requirements of local quantum number con-
servation.Anexampleofapplyingthecanonicalapproach
0.02 7.7 GeV to the strangenessproduction canbe found in [46] anref-
erences therein.
v1 0
-0.02 Thepionsareproducedfromallfluids:nearmidrapid-
ity 60% from the baryon-rich fluids and 40% from
-0.04 ∼ ∼
-1 0 1 -1 0 1 -1 0 1 the net-baryon-free one at √sNN > 20 GeV. Hence, the
y y y
disagreement of the pion v with data, resulting from re-
1
Fig. 3. The directed flow v1(y) for protons, antiprotons dundantsoftnessoftheQGPEoSathighbaryondensities,
and pions from mid-central (b = 6 fm) Au+Au collisions at is moderate at √sNN > 20 GeV. In general, the pion v1
√sNN = 7.7–39 GeV calculated with different EoS’s. Experi- islesssensitivetothe EoSascomparedtothe protonand
mental data are from the STARcollaboration [14]. antiproton ones. As seen from Fig. 3, the deconfinement
scenarios are definitely preferable for the pion v (y) at
1
√sNN < 20 GeV. Though, the hadronic-scenario results
dicates a preference of the crossover scenario within both are not too far from the experimental data. At √sNN =
the PHSD/HSD and 3FD approaches. 39GeVthe hadronicscenariogiveseventhe best descrip-
This puzzle has a natural resolution within the 3FD tion of the pion data because of a higher stiffness of the
model. The the QGP sector of the EoS’s with deconfine- hadronic EoS at high baryondensities, as compared with
ment [27] was fitted to the lattice QCD data at zero net- that in the considered versions of the QGP EoS.
baryon density and just extrapolated to nonzero baryon
Thus,allthe analyzeddatatestify infavorofaharder
densities. The protons mainly originate from baryon-rich
QGPEoSathigh baryondensities than those used inthe
fluids that are governed by the EoS at finite baryon den-
simulations, i.e. the desired QGP EoS should be closer to
sities.Thetoostrongprotonantiflowwithinthecrossover
the used hadronic EoS at the same baryon densities (see
scenario at √sNN > 20 GeV is a sign of too soft QGP Fig. 1). At the same time, a moderate softenning of the
EoS at high baryon densities. In general, the antiflow or
QGP EoS at moderately high baryon densities is agree-
a weak flow indicates softness of an EoS [6,7,8,9,10,11,
12,13]. Predictions of the first-order-transition EoS, the ment with data at 7.7 <√sNN < 20 GeV.
∼ ∼
QGP sector of which is constructed in the same way as Here it is appropriate to mention a discussion on the
that of the crossover one, fail even at lower collision en- QGPEoSinastrophysics.InRef.[47]itwasdemonstrated
ergies, when the QGP starts to dominate in the collision that the QGP EoS can be almost indistinguishable from
dynamics,i.e.at√sNN >15GeV.Thisfactalsosupports thehadronicEoSathighbaryondensitiesrelevanttoneu-
the conjecture on a too∼soft QGP sector at high baryon tronstars.Inparticular,thisgivesapossibility toexplain
densities in the used EoS’s. hybridstarswithmassesuptoabout2solarmasses(M⊙),
At the same time, the net-baryon-free (fireball) fluid in such a way that “hybrid stars masquerade as neutron
is governed by the EoS at zero net-baryon density. This stars” [47]. The discussion of such a possibility has been
fluidisamainsourceofantiprotons(morethan80%near revived after measurements on two binary pulsars PSR
midrapidity at √sNN > 20 GeV and b = 6 fm), v1(y) J1614-2230[48] and PSR J0348+0432[49] resulted in the
of which is in good agreement with the data at √sNN > pulsar masses of (1.97 0.04)M⊙ and (2.01 0.04)M⊙, re-
± ±
20 GeV within the crossover scenario and even in perfect spectively. The obtained results on the directed flow give
Yu.B. Ivanov,A.A. Soldatov: What can we learn from thedirected flow 5
us anotherindicationof arequiredhardeningofthe QGP reproductionoftheantiprotondv /dy whilethoseathigh
1
EoS at high baryon densities. baryondensities(protonslope)shouldbestifferinorderto
achieve better description of proton dv /dy. A combined
1
effect of this excessive softness of the QGP EoS and the
0.4
reducing baryonstopping results in more and more nega-
protons
NA49 tiveprotonslopesathighcollisionenergies.Thisisinline
=0 0.2 E895 with the mechanism discussed in Ref. [13]. The pion flow
y STAR
|y partially follows the proton pattern, as discussed above.
d Therefore, the pion v slope also becomes more negative
/1 1
v 0 with energy rise.As for the poor reproduction ofthe pro-
d
ton v1 slope at low energies (√sNN < 5 GeV), it is still
questionable because the same data but in terms of the
-0.2
transversein-planemomentum, P ,arealmostperfectly
0 h xi
reproduced by the crossover scenario [17]. It is difficult
0 to indicate the beginning of the crossover transition be-
=
|yy-0.1 hadronic cause the crossover results become preferable beginning
dv/d1 -0.2 c1rsot sosrodveer rtr. wHiotwhevreelra,ttivheelybelgoiwnncinolglisoifotnheencerrogsiseosve(r√tsrNanNsit>ion3cGaneVb)e.
antiprotons approximately pointed out as √sNN 4 GeV.
≃
Of course, the 3FD model does not include all factors
-0.3
0.15 determining the directed flow. Initial-state fluctuations,
pions which in particular make the directed flow to be nonzero
0 0.1 STAR p+ even at midrapidity, are out of the scope of the 3FD ap-
y= STAR p- proach. Apparently, these fluctuations can essentially af-
|
y
d 0.05 fect the directed flow at high collision energies, when the
v/1 experimental flow itself is very weak. Another point is
d 0 so-called afterburner, i.e. the kinetic evolution after the
thehydrodynamicalfreeze-out.Thisstageisabsentinthe
-0.05
conventional version of the 3FD. Recently Iu. Karpenko
2 4 6 8 10 20 40
constructed an event generator based on the output of
(cid:214) s [GeV] the 3FD model. Thus constructed particle ensemble can
NN
befurtherevolvedwithintheUrQMDmodel.Preliminary
Fig.4. Thebeamenergydependenceofthedirectedflowslope
results[52]showthat suchkind ofthe afterburnermainly
at midrapidity for protons, antiprotons and pions from mid-
central (b = 6 fm) Au+Au collisions calculated with different affects the pion v1 at peripheral rapidities. At √sNN < 5
GeV,themidrapidityregionofthepionv isalsoaffected.
EoS’s. The experimental data are from Refs. [14,51,50]. 1
The slopeofthe directedflowatthe midrapidityis of- 4 Conclusions
tenusedtoquantifyvariationofthedirectedflowwithcol-
lisionenergy.Theexcitationfunctionsfortheslopesofthe Inconclusion,the crossoverEoSis unambiguously prefer-
v distributions at midrapidity are summarized in Fig. 4, ableforthethemostpartofexperimentaldatainthecon-
1
where earlier experimental results from the AGS [50] and sidered energy range, though this description is not per-
SPS [51] are also presented. As noted above, the best fect. Based onthe crossoverEoSof Ref. [27], the directed
reproduction of the data is achieved with the crossover flow in semicentral Au+Au collisions indicates that the
EoS. The proton dv /dy within the first-order-transition crossoverdeconfinementtransitiontakesplaceinthewide
1
scenario exhibits a wiggle earlier predicted in Refs. [8,9, rangeincidentenergies4<√s <30GeV.Inpart,this
NN
11,12]. The first-order-transition results demonstrate the wide range could be a co∼nsequenc∼e of that the crossover
worst agreement with the proton and antiproton data on transition constructed in Ref. [27] is very smooth. In this
dv /dy. The discrepancies between experiment and the respect,thisversionofthecrossoverEoScertainlycontra-
1
3FD predictions are smaller for the purely hadronic EoS, dicts results of the lattice QCD calculations,where a fast
however,the agreementfor the crossoverEoSis definitely crossover, at least at zero chemical potential, was found
better though it is far from being perfect. As seen from [53].
Fig. 4, the rising transparency of colliding nuclei makes Athighestcomputedenergiesof√sNN >20GeV,the
the proton v slope to be close to zero even for compara- obtained results indicate that the deconfinement EoS’s in
1
tively hard hadronic EoS. the QGP sector should be stiffer at high baryon densities
Theabovediscussedproblemsofthecrossoverscenario than those used in the calculation, i.e. more similar to
reveal themselves also in the dv /dy plot. At high en- thepurelyhadronicEoS.Thisobservationisinagreement
1
ergies (√s > 20 GeV), the slopes also indicate that with that discussed in astrophysics.
NN
the used deconfinement EoS’s in the quark-gluon sector In view of this similarity of the QGP and hadronic
at zero baryon chemical potential are quite suitable for EoS’s at high baryon densities a question arises if we can
6 Yu.B. Ivanov,A.A. Soldatov: What can we learn from thedirected flow
use the directed flow to detect the deconfinement tran- 22. Yu. B. Ivanov, V. N. Russkikh, and V. D. Toneev, Phys.
sition. Qualitatively, a wiggle in the excitation function Rev. C 73, 044904 (2006).
of the net-proton v slope could be a signal of the QGP 23. Yu.B. Ivanov,Phys. Rev.C 87, 064904 (2013).
1
formation. This signal is unavoidable because of the EoS 24. V. N. Russkikh and Yu. B. Ivanov, Phys. Rev. C 76,
softening in the transition range from hadronic phase to 054907 (2007).
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STARdata[14].However,thissignalisstillambiguousbe- 1238 (2009).
cause the corresponding antiflow can be of pure hadronic 26. V. M. Galitsky and I. N. Mishustin, Sov. J. Nucl. Phys.
29, 181 (1979).
nature, as it was pointed out in Ref. [13]. Therefore, we
27. A.S.Khvorostukhin,V.V.Skokov,K.Redlich,andV.D.
are left with a routine way of comparing predictions of
Toneev, Eur. Phys. J. C48, 531 (2006).
various EoS’s (with and without deconfinement) with the
28. T. Kla¨hn, R. L astowiecki and D. B. Blaschke, Phys. Rev.
v1experimentaldata.Thiswillhopefullygiveusareliable
D 88, no. 8, 085001 (2013).
evidence on the QGP formation.
29. Yu.B. Ivanov,Phys. Rev.C 87, 064905 (2013).
Fruitful discussions with D. Blaschke, W. Cassing, V.
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