Recent selected theory developments for NICA

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by  David Blaschke

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Recent selected theory developments for NICA
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b
DavidBlaschke1,2,3,(cid:63)
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1JointInstituteforNuclearResearch,Dubna,Russia
1 2UniversityofWroclaw,Wroclaw,Poland
3NationalResearchNuclearUniversity(MEPhI),Moscow,Russia

]
h
t Abstract.InthiscontributionIpresentafewselectedtopicsofrecenttheoreticaldevel-
-
l opmentsofrelevancefortheNICAfacilityunderconstruction. Inafirstpart,Idiscuss
c
u newaspectsoftheQCDphasediagramlikethepossibleexistenceofacriticalendpointof
n first-orderphasetransitionsfromtheperspectiveofgeneralizationsofthe3-flavorPNJL
[ model including the conjecture of a universal pressure for the onset of deconfinement

inheavy-ioncollisionsandastrophysics. Asecondpartisdevotedtofirstresultsofthe
1
newlyconstructedeventsimulator(THESEUS)whichisbasedontheparticlizationofthe
v
formerthree-fluidhydrodynamicscodebyIvanov,RusskikhandToneevthatallowsalso
9
tostudytheroleofhadronicfinalstateinteractions. Possiblesignalsofthemixedphase
2
1 accessibleatNICAareconsidered. Inparticular,therobustnessofthebaryon-stopping
0 signal of deconfinement and the occurrence of antiflow for protons have b√een investi-
0 gatedforAu+AucollisionsintherangeoftheNICA-MPDenergyscanfor s∼6...8
. GeV.Thissignalisreflectedalsointheflowpatternoflightnuclearclusters,inparticular
2 √
deuterons. ThesharppeakfortheK+/π+ ratioat s ∼ 8GeV(the"horn"effect)isnot
0
7 obtainedinthepresentversionofTHESEUSandcallsforimprovementoftheequation
1 ofstateinput. IreporttherecentprogressindevelopingageneralizedBeth-Uhlenbeck
: approachtoaunifieddescriptionofquark-hadronmatterwhichincludesnowstrangeness
v andrevealsanewmechanismforexplainingtheK+/π+ ratioduetothepronouncedoc-
i
X currenceofananomalousmodeintheK+atfinitebaryochemicalpotentials.
r
a
1 Introduction
TheWhitePaperon"ExploringStronglyInteractingMatteratHighDensities"attheNuclotron-based
IonColliderfAcility(NICA)hasrecentlyappearedasaTopicalIssueintheEuropeanPhysicalJournal
A[1]. Itcomprises56articlesrelatedtothemostprospectivephysicsaspectstobeexploredatthis
upcomingfacility. IshallpresentafewselectedtopicsofrecenttheoreticaldevelopmentsforNICA
inwhichIhavebeeninvolved.
First I consider key aspects of the QCD phase diagram like the possible existence of a critical
endpoint(CEP)offirst-orderphasetransitionsthathasbeenelaboratedin[2]fornonlocalPolyakov-
loopextendedNambu–Jona-Lasinio(PNJL)modelsconstrainedbylatticeQCDwithspecialempha-
sis on the role of a repulsive vector meanfield. The CEP is also discussed from the perspective of
generalizations of the color superconducting 3-flavor PNJL model [3] including the conjecture of a
(cid:63)e-mail:[email protected]
universal pressure for the onset of deconfinement in heavy-ion collisions and astrophysics [4]. In
thiscontextIfinditworthwhiletoquoteresultsofRef.[5]whereconsequencesfortheQCDphase
diagramhavebeendemonstratedofenforcingacoincidencebetweenchiralsymmetryrestorationand
deconfinementwithacorrespondinglyadjustedbagpressureontopofamodelwithdynamicalchiral
symmetryrestoration. TheseconsiderationsoftheQCDphasediagramindifferentdynamicalmodels
areimportantforthepreparationoftheNICAexperimentsastheycangivetheoreticalestimateson
theaccessibilityofcertainQCDphasesandwhateffectsonemayhopetodetectinthegivenenergy
range.
Sect. 3 is devoted to the new event simulation program THESEUS. Within a collaboration in-
volving a team of 9 scientists from Germany, France, Italy, Poland, Russia, Ukraine and the United
States we have succeeded to create a startup version for a new Three-fluid Hydrodynamics-based
Event Simulator Extended by UrQMD final State interactions (THESEUS) and reported about its
performancein[7]. Inparticular,therobustnessofthebaryon-stoppingsignalofdeconfinement[8,9]
andtheoccurrenceofantiflowforprotonsforAu+AucollisionsintherangeoftheNICA-MPDen-
√
ergy scan for s ∼ 6...8 GeV [7] have been reconsidered in THESEUS. For the first time it was
possible to investigate the effect of hadronic rescattering on the results of the three-fluid hydrody-
namicssimulations. Tothisendtheultrarelativisticquantummoleculardynamics(UrQMD)program
has been implemented. The antiflow signal for a first order phase transition is reflected also in the
flowpatternoflightnuclearclusters, inparticularfordeuterons[10]. THESEUSanditsunderlying
three-fluid hydrodynamics model shall be developed further, in particular to be able to improve the
descriptionofthehadronizationprocessandcapturesubtleeffectslikethe"horn"effectfortheK+/π+
ratio. Amaingoalofongoingstudiesistoimprovetheequationofstate(EoS)input. Inthisrespect
recent progress in developing a generalized Beth-Uhlenbeck (GBU) approach [11–13] to a unified
descriptionofquark-hadronmatter[14]whichincludesnowstrangeness[15,16](seealso[17])has
shownremarkableresults. IthasrevealedanewmechanismforexplainingtheK+/π+ratioduetothe
pronounced occurrence of an anomalous mode in the K+ channel at finite baryochemical potentials
[16]. The GBU approach on the basis of a PNJL model utilizes a generalization of the Φ− deriv-
ableapproachthataccountsforaspectrumofhadronresonancesasboundstatesofquarkswhichget
dissolved into the quark-gluon plasma continuum by the Mott effect encoded in medium-dependent
hadronic phase shifts. It can describe the lattice QCD thermodynamics results on the temperature
axis of the QCD phase diagram [14] and should therefore next be extended to finite baryochemical
potentials.
2 The phase diagram as probed at NICA
This section selects a few aspects out of the rich thematics of the QCD phase diagram that have
recentlybeendiscussedinthecontextoftheupcomingNICAexperiments. Forageneralintroduction
totheQCDphasediagramonemayconsultthereviewbyFukushimaandHatsuda[18]andthemore
recentonebyFukushimaandSasaki[19].
Interesting aspects that have been spared out here concern inhomogeneous condensates [20] for
whichinsteadofaCEPaLifshitzpointoccursinthephasediagram.Anotherpointofinterestincluded
intheNICAWhitePaperisthebehaviorofscalarmesonsinthephasediagram[21]. Theirproperties
may trace the chiral restoration transition and provide a potentially observable signal in the two-
photon channel [22] if the background can be sufficiently suppressed. Promising progress has also
been made by the Functional Renormalization Group approach that provides spectral functions for
the quark-meson model phase diagram [23]. In near future one can expect interesting predictions
alsoforthepartofthephasediagramprobedatNICAprovidingtheapproachcanbegeneralizedto
includebaryons.
(cid:32)
0.7 (cid:50)(cid:52)(cid:48)
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(cid:32)(cid:32)
Figure 1. Left panel: Normalized dynamical masses for the different form factors under study (NJL, Set A
(cid:32)(cid:32)
- C) and wave function renormalization for Set B and Set C, fitted to lattice QCD data [28]. Middle panel:
(cid:32)(cid:32)
ComparisonbetweenSetCresultsfordifferentvaluesofthevectorcouplingparameterη andlatticeQCDdata
V
[32].Rightpanel:Phasediagramswith(pseudo)criticaltemperaturesT (µ)andcriticalpointsfornonlocalrank-
c
2PNJLmodel(SetC).Dashed(full)linescorrespondtocrossover(firstorder)transitions. Thecorresponding
dash-dottedanddottedlinesrepresentthedeconfinementtransitionrange,i.e.Φ=0.4andΦ=0.6,respectively.
ThehighlightedregiondenotestheCEPpositionfavoredbythepresentstudy.ThefiguresarefromRef.[2].
2.1 CEPinanonlocalPNJLmodelconstrainedbylatticeQCD
Dynamical models for quark hadron matter that have the potential to provide more insights to the
microphysics of the hadron-to-quark matter phase transition are based on the hierarchy of the QCD
DysonSchwingerequationswherehadronsappearasboundstatesofquarksduetotheirinteractions
via confining forces mediated by nonperturbative gluon propagators [24–26]. The key quantities of
this approach are the dynamical mass function and the wave function renormalization of the quark
propagatorthataredescribedinexcellentagreementwithlatticeQCDdata[27,28].
Asimilarqualityofthedescriptionofthequarkpropagatorisachievedwithinthenonlocalchiral
quark models that are defined by a covariant form factor which is calibrated with the same lattice
QCD data, see the left panel of Fig. 1. For their finite temperature extension, the coupling to the
Polyakovloopresultsinpredictionsofthepseudocriticaltemperaturethatareinexcellentagreement
withthelatticeQCDdata[29,30]. TheextensionofthesemodelstothewholeT −µplanehasbeen
accomplished in Ref. [31] with particular emphasis on the role that interactions in the Dirac vector
channel play for the position and the very existence of the CEP. This discussion has been extended
in [2] where the possibility of a very small or vanishing vector coupling at low chemical potentials
as obtained on the basis of lattice QCD results for the imaginary chemical potential technique has
beensuggestedasapossiblesolutionoftheproblemtodescribethelatticedataforthetemperature
dependenceofthepressuredifference∆P= P(T,µ)−P(T,0)atfiniteµ=T [32],seethemiddlepanel
c
ofFig.1. ThefavorablemodelisSetCwhichinthiscasepredictsacriticalendpointatT ∼ 130
√ CEP
MeVandµ = 225MeV.Thiscorrespondstochemicalfreeze-outparametersfor s ∼ 6GeV,
CEP NN
i.e. belowtherangeoftheRHICbeamenergyscanoftheSTARexperiment,butwellinreachforthe
plannedNICAenergyscan.
2.2 Universaltransitionpressureina3-flavorcolorsuperconductingPNJLmodel
For the first time, the phase diagram of a 3-flavor color superconducting PNJL model has been ob-
tained in [3], the results are shown in Fig. 2. The entropy per baryon isolines indicate paths for the
dynamicalevolutionofafireballatNICA/FAIRenergieswhereupmostline(s/n = 11)corresponds
√
to s ∼ 4.5 GeV (E ∼ 9 A GeV) [33]. The yellow region (n < 0) denotes an instability of
NN lab B
Figure2.Phasediagramofthe
three-flavorcolorsuperconducting
PNJLmodelforsymmetricquark
matterfrom[3].Fordetailsseetext
inSubsect.2.2.
thehomogeneousmeanfieldapproximationtoquarkmatterwhichiscuredwhenaphasetransitionto
hadronicmatterisinvokedwithauniversaltransitionpressureof80MeV/fm3[34]delimitingthegrey
region. Inthe rangeof temperaturesaccessiblein theenergyscan programsof heavy-ioncollisions
√
for s = 4−200 GeV this coincides with the phase equilibrium between the PNJL model and
NN
thehadronresonancegas(solidblueline). Thesolidredlinecorrespondstothecriticaltemperature
for2SCsuperconductivityinquarkmatter. Thegreen(blue)linescorrespondtoequallight(strange)
quarkmassesreducedrelativetothevacuumvaluebyafactorlabellingtheselines. Alongtheorange
linesthetracedPolyakovloophasthevaluethatlabelsthem.
2.3 Enforcingcoincidentchiralanddeconfinementtransitionsinthephasediagram
A challenging question is whether chiral restoration and quark deconfinement transitions coincide
in the QCD phase diagram or not. In lattice QCD simulations at low chemical potentials the peak
positions of chiral and Polyakov-loop susceptibilities are to good accuracy coincident, but this may
not be the case for high baryon densities, allowing for three alternatives: a massive quark matter
phase[35,36],aquarkyonicphase[37,38]withchiralquarksconfinedinbaryons(andmesons)and
thecasethatchiralrestorationanddeconfinementcoincideinthewholephasediagram.Thelattercase
isbasedontheQCDDyson-SchwingerequationswheretheKugo-Ojimaconfinementmechanismis
realizedbythedynamicalquarkmassfunctionwhichservesforchiralsymmetrybreakingandatthe
sametimeconspireswiththewavefunctionrenormalizationsoastoremovethequasiparticlepoleof
thequarkpropagator[39,40]. DexheimerandSchramm[41]haveconstructedamodelthatrealizes
coincidentchiralanddeconfinementphasetransitionviathecouplingofquarkandhadronmassesto
thePolyakovloop. ThepositionofthecriticalendpointandthecriticalchemicalpotentialatT = 0
is fixed by the behavior of the Polyakov-loop potential which they extend by adopting a chemical
potentialdependence.
IntheircontributiontotheNICAWhitePaper,Fischer,KlähnandHempel[5]realizethecoinci-
denceofchiralrestorationanddeconfinementintheQCDphasediagrambyadoptingabagpressure
B , see also [6]. The hadronic phase is described by a generalized relativistic density functional
dc
modelwithlightclusters[42]andforthephasetransitionaMaxwellconstructionisapplied. InFig.3
Figure3. PhasediagramforaselectedchiralbagconstantB1/4 =152.7MeV,comparingthenewapproach[6,
χ
43](leftpanels)withthe"standard"NJLone(B =0,rightpanels).Toppanels:Dependenceonbaryochemical
dc
potential.Bottompanels:Dependenceonthebaryondensity(seetextfordefinitions).Solidgraylinesmarklines
ofconstantentropyperbaryoninunitsoftheBoltzmannconstantk .Typicaltrajectoriesofheavy-ioncollisions
B
intheNICAMPDexperimentwillliebetweenthelineslabelledby"10"and"20";forexplanationsseethetext.
FigurefromRef.[5].
thephasediagramforthismodel(leftpanels)iscontrastedtothecasewhere B = 0(rightpanels).
dc
It is remarkable for the upcoming NICA experiments that the upper limiting density for the mixed
√
phase is only about twice the nuclear saturation density for s ∼ 6 GeV where T ∼ 130 MeV
NN
whenenteringthemixedphaseandaftercompletionofthetransitionthematterisheateduptoabout
150MeV. Foran orientationinthat figure, considerthe rangeofentropy perbaryon s/n = 10−25
√
[33]thatwillbecoveredbytheNICAMPDcolliderexperiment,where s = 4...11GeV[44].
NN
ThisEoSfulfilsalsotheconstraintfromrecentprecisemassmeasurementsofpulsarswhichrequire
themaximummassofaneutronstarorhybridstarpredictedfortheEoStoreachatleast2M [43].
(cid:12)
2.4 High-masstwinstarssupporttheCEP
Startingfromthepossibleexistenceofathirdfamilyofcompacthybridstarsathighmassasindicators
ofastrongfirstorderphasetransitionincompactstarinteriors[45](highmasstwinstars[46])from
which the existence of a critical point in the QCD phase diagram follows, in the contribution [4] to
theNICAWhitePapertherelationbetweenthepressureattheonsetofthedeconfinementtransition
forstarswithM ∼2M andtheirradiushasbeenshownforthefirsttime,seeFig.4.Ifthemaximum
(cid:12)
star radius from observations turns out to be less than 14 km, e.g. in the range 13.6 - 14.0 km this
wouldindicatealimitingpressureofthehadronicphaseofmatterof74-90MeV/fm3,inexcellent
agreementwiththeanalysisofchemicalfreeze-outinheavy-ioncollisionsbyRafelski&Petran[34]
Figure4.Leftpanel:Mass-radiusrelationshipsforthreeexamplesofanewclassofhybridneutronstarequations
ofstatewithastrongfirstorderphasetransitionexhibitinganendpointofpurelyhadronicconfigurationsatabout
2 M andastablebranchofcompacthybridstars,disconnectedfromthehadronicones("thirdfamily"). Right
(cid:12)
panel: The radius R at the endpoint of the hadronic configurations (∼ 2 M ) for different classes of hybrid
(cid:12)
equationsofstateversusthecorrespondingpressureatthephasetransition p . Alltheseequationsofstate
trans
allowforathirdfamilyofstarsathighmass("high-masstwin"stars).FiguresfromRef.[4].
whichgave82±8MeV/fm3. Suchauniversalityofthelimitingpressureofthehadronicphaseinthe
QCDphasediagram,ifitexists,wouldbeofenormousheuristicvalueforinterdisciplinarystudiesof
theQCDphasediagraminheavy-ioncollisionsandinAstrophysics.
3 Three-fluid hydrodynamics based simulations and mixed phase signals
3.1 Baryonstoppingsignal
InFig.5weshowtheNICAenergyscanforthecurvatureCyofthenetprotonrapiditydistribution
atmidrapidityforcentralAu+Aucollisionswithimpactparameterb=2fm(leftpanels), b=6fm
(middlepanels)andb=11fm(rightpanels). Wecomparethe3FHmodelresult(blacksolidlines)
with THESEUS (blue short-dashed lines) and THESEUS without UrQMD (red long-dashed lines).
Theresultsforthetwo-phaseEoS(upperrowofpanels)arecomparedtothoseforthecrossoverEoS
(lowerrowofpanels).Fornoncentralcollisionsthecurvaturepatternisshiftedtowardspositivevalues
whilethe "wiggle"asa characteristicfeaturefor theEoS withafirst orderphasetransition [47,48]
remainsratherrobust[8,9]. Fordetails,see[7].
3.2 Antiflowoflightclusters
Among the suggested signatures of a first order phase transition in heavy-ion collision experiments
is the antiflow of nucleons, i.e., a negative slope for the rapidity dependence of the directed flow v
1
atmidrapidity[49]. Ithasbeenshowninhydrodynamiccalculationsalreadyin[50]thatthisfeature
is relatedto the softestpoint of theequation of state. Naturally, this sensitivityto the EoScould be
nicely demonstrated within the three-fluid hydrodynamics approach [51, 52]. The proton antiflow
feature has been obtained also in different transport theory based simulations that implement a first
orderphasetransition,forinstancethehybridapproach[53]whichusesahydrodynamicdescription
22--pphhaassee EEooSS,, bb == 22 ffmm 22--pphhaassee EEooSS,, bb == 66 ffmm 22--pphhaassee EEooSS,, bb == 1111 ffmm
15 15 15
10 10 10
5 5 5
Cy 0 Cy 0 Cy 0
- 5 - 5 - 5
- 10 - 10 - 10
(a) (b) (c)
- 15 - 15 - 15
2 3 4 5 6 7 8 9 101112 2 3 4 5 6 7 8 9 101112 2 3 4 5 6 7 8 9 101112
s [GeV] s [GeV] s [GeV]
NN NN NN
ccrroossssoovveerr EEooSS,, bb == 22 ffmm ccrroossssoovveerr EEooSS,, bb == 66 ffmm ccrroossssoovveerr EEooSS,, bb == 1111 ffmm
15 THESEUS 15 15
THESEUS w/o UrQMD
10 3FH 10 10
E866, E895, E917
5 NA49, Pb+Pb 5 5
Cy 0 Cy 0 Cy 0
- 5 - 5 - 5
- 10 - 10 - 10
(d) (e) (f)
- 15 - 15 - 15
2 3 4 5 6 7 8 9 101112 2 3 4 5 6 7 8 9 101112 2 3 4 5 6 7 8 9 101112
s [GeV] s [GeV] s [GeV]
NN NN NN
Figure 5. Energy scan for the curvature Cy of the net proton rapidity distribution at midrapidity for central
Au+Aucollisionswithimpactparameterb=2fm(panels(a)and(d)),b=6fm(panels(b)and(e))andb=11
fm(panels(c)and(f)).Wecomparethe3FHmodelresult(blacksolidlines)withTHESEUS(blueshort-dashed
lines)andTHESEUSwithoutUrQMD(redlong-dashedlines).Theresultsforthetwo-phaseEoS(panels(a)-(c))
arecomparedtothoseforthecrossoverEoS(panels(d)-(f)). Fornoncentralcollisionsthecurvaturepatternis
shiftedtowardspositivevalueswhilethe"wiggle"asacharacteristicfeaturefortheEoSwithafirstorderphase
transitionremainsratherrobust.FigurefromRef.[7].
ofthephasetransitionsandwichedbyUrQMDmodelingofinitialandfinalstages,andthetransport
theoreticalmodelJAM[54,55].
InRef.[10]ithasbeenconjecturedthattheflowoflightclusterssuchasdeuteronsmaytracethe
early flow at the hadronisation transition since by their inertia the heavier particles are less affected
by hadronic rescattering effects. This has been checked with the THESEUS code and indeed, the
antiflowofprotonsobtainedinthisprogramforthe2-phaseEoSasasignatureofthefirstorderphase
√
transition in this EoS in the energy range s ∼ 6−7 GeV is reflected also in the deuteron flow
NN
forthesameEoSwhilethecrossoverandpurehadronicEoSdonotshowtheantiflowsignature,see
Fig.6.
As for the proton antiflow, it would be premature to predict quantitatively the deuteron antiflow
duetopresentambiguitiesinthedeuteronformationmechanismbycoalescenceandintheusedEoS.
Inparticular,the2-phaseEoSistoosoftathighdensitiesandhasanunrealisticallyhighonsetdensity
of the phase transition. With an improved EoS, the antiflow signature of the phase transition could
√
occurinthebeamenergyrange4.7GeV < s < 7.7GeV,wherenoexperimentaldataexistyet
NN
butwheretheNICAMPDexperimentwillbeoperating[44].
Figure6.Energyscanoftheslope
ofthedirectedflowforprotons(left
panel)andfordeuterons(right
panel).Acomparisonofresults
fromTHESEUSsimulationswitha
2-phaseEoSthatpossessesastrong
first-orderphasetransitiontoresults
foracrossover(orpurelyhadronic)
EoSdemonstratesthatadipat
√
energiesof s =6−8GeV
NN
couldberegardedasaphase
transitionsignal.Such"antiflow"
signalisexpectedforprotonsas
wellaslightclusters.Forfurther
details,seeRef.[10];thefiguresare
takenfromthatpaper.
3.3 Marek’shorn
In previous chapters we have praised the advantages of the new THESEUS simulation program for
heavy-ioncollisionsintheNICA/FAIRenergyrange,wherethetransitionfromthebaryonstopping
to the transparency regime is expected. Promising signatures of a first order phase transition have
beendiscussed. However,the"horn"effectwhichisobservedintheenergyscanofthe K+/π+ ratio
(for the data see, e.g., Fig. 11 of Ref. [56], partly displayed here in the left and middle panels of
Fig. 7) is not reproduced in the present version of THESEUS and with the present EoS. This effect
has been suggested by Marek Gazdzicki and Mark Gorenstein as a signature of the mixed phase in
hadron-to-quarkmatterphasetransition[57]. Itsquantitativedescriptioninsimulationsofheavy-ion
collisionsisanotoriouslydifficultproblem. Recently,inanupgradeofthePHSDprogramwithchiral
symmetryrestorationeffects, asatisfactorydescriptionofthe"horn"effectcouldbegiven[58]. We
advocate another possibility to solve the "horn" puzzle. In a recent work on the Mott dissociation
ofpionsandkaonsinhot,densequarkmatter[16]whichextendstheGBUapproach[11–13]tothe
strangenesssector,wehavefoundthatastablemodeoftheK+ mesonoccursinthephasediagramat
finiteT andµduetothecompositenessandunequalmassesofthequarkconstituents.Thisin-medium
boundstateisagoodcandidateforcausingtheenhancementofthe K+/π+ ratioinacertaindomain
oftheenergyscanwhiletheK−/π−ratioremainsunaffected,seetherightpanelofFig.7. Weplanto
implementthecorrespondingEoSintoanupgradeoftheTHESEUSprogram.
4 Conclusions
In this contribution I have discussed a few selected theoretical developments of relevance for the
NICA facility under construction. First, I have picked new aspects of the QCD phase diagram like
0,4
0,3
ratio0,2
K+/+ - with anomalous
0,1 K-/- - with anomalous
K+/+
K-/-
0,0
1 10 100 1000
s1N/N2, [GeV]
Figure 7. Energy scan for the particle ratio K+/π+ in the NICA energy range for central Au+Au collisions
(impactparameterb=2fm)with(bluedottedlines)andwithout(reddashedlines)theUrQMDhadronicrescat-
tering. The calculation with a first order phase transition in the EoS (left panel) is compared to that with the
crossoverEoS(middlepanel). Forcomparisonweshowinboththesepanelstheresultswithoutparticlization
andUrQMDrescattering(blacksolidlines)andexperimentaldata,takenfromFig. 11ofRef.[56]. Datafrom
AGSexperiments(E802,E866,E895)areshownbyfilledcircles,datafromNA49byfilledsquares.Intheright
panelwedemonstratetheeffectoftheanomalousmodesontheK+/π+andK−/π−ratios(thicklines),compared
tothe"normal"casewithoutthesemodes(thinlines),from[16].UponimplementationofthiseffectintotheEoS
usedintheTHESEUSsimulationadecentimprovementofthedescriptionofthe"horn"effectwillbeachieved.
the possible existence of a critical endpoint of first-order phase transitions from the perspective of
a nonlocal chiral quark model calibrated with lattice QCD simulations that strongly suggests a low
orvanishingvectorcouplingatlowchemicalpotentials; generalizationsofthe3-flavorPNJLmodel
includingtheconjectureofauniversalpressurefortheonsetofdeconfinementinheavy-ioncollisions
and astrophysics; and a new model that enforces the coincidence of chiral and deconfinement tran-
sitions predicting a low critical density, accessible already at NICA fixed target experiments. Next,
IhavediscussedfirstresultsofthenewlyconstructedeventsimulatorTHESEUSwhichisbasedon
the particlization of the three-fluid hydrodynamics model by Ivanov, Russkikh and Toneev that al-
lows also to study the role of hadronic final state interactions. Possible signals of the mixed phase
accessible at NICA are considered. In particular, the robustness of the baryon-stopping signal of
deconfinement and the occurrence of antiflow for protons and deuterons have been investigated for
Au+Au collisions in the range of the NICA-MPD energy scan. The sharp peak for the K+/π+ ratio
√
at s ∼ 8GeV(the"horn"effect)isnotobtainedinthepresentversionofTHESEUSandcallsfor
improvementoftheequationofstateinput. Inthiscontext,Ihavepointedoutrecentprogressinde-
velopingageneralizedBeth-Uhlenbeckapproachtoaunifieddescriptionofquark-hadronmatterthat
revealsanewmechanismforexplainingtheK+/π+ratio. Onemaylookforwardtofurtherinteresting
developments of theory and simulations of heavy-ion collisions in the NICA energy range directed
towardsthediscoveryofamixedphaseintheQCDphasediagram.
Acknowledgements
I would like to thank the members of the board of guest editors for the EPJA Topical Issue on the
"NICA White Paper", Jörg Aichelin, Elena Bratkovskaya, Volker Friese, Marek Gazdzicki, Jørgen
Randrup, Oleg Rogachevsky, Oleg Teryaev and Vyacheslav Toneev, for their excellent work and
indispensablehelpinmakingthisvolumeappear. Iamgratefultoallmycollaboratorsintheresearch
reported here, in particular, David Alvarez-Castillo, Alexander Ayriyan, Niels-Uwe Bastian, Pavel
Batyuk, Sanjin Benic, Jens Berdermann, Marcus Bleicher, Gustavo Contrera, Pedro Costa, Pawel
Danielewicz, Aleksandr Dubinin, Tobias Fischer, Hovik Grigorian, Gabriela Grunfeld, Sophia Han,
Yuri Ivanov, Iuriy Karpenko,Thomas Klähn, Sergey Merts, Marlene Nahrgang, Hannah Petersen,
AndreyRadzhabov,GerdRöpke,OlegRogachevsky,LudwikTurko,DmitriVoskresensky,Agnieszka
WergielukandHermannWolter. Finally,Iwouldliketoacknowledgenumerousfruitfuldiscussions
with my colleagues at JINR Dubna, especially: Valery Burov, Alexandra Friesen, Yuri Kalinovsky,
SergeyNedelko,AlexanderSorin,OlegTeryaev,SlavaToneevandattheUniversityofWroclaw:Pasi
Huovinen,JakubJankowski,AlaksiejKachanovich,PokManLo,KrzysztofRedlich,ChihiroSasaki
andJanSobczyk. ThisworkhasbeensupportedbytheMEPhIAcademicExcellenceProjectunder
contractNo. 02.a03.21.0005andbythePolishNCNundergrantNo. UMO-2011/02/A/ST2/00306.
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