11

Theory and HPC Theory and HPC

EElenalena Bratkovskaya Bratkovskaya

Institut für Theoretische PhysikInstitut für Theoretische Physik & FIAS, & FIAS, Uni. FrankfurtUni. Frankfurt

HIC for FAIR Physics Day: HPC Computing,HIC for FAIR Physics Day: HPC Computing,FIAS, Frankfurt am MainFIAS, Frankfurt am Main

1111 NovemberNovember 2014 2014

The holy grail of heavy-ion physics:The holy grail of heavy-ion physics:

• Study of the Study of the phase phase transitiontransition from from

hadronic to partonic hadronic to partonic matter – matter –

Quark-Gluon-PlasmaQuark-Gluon-Plasma

• Search for the Search for the critical pointcritical point

• Study of the Study of the in-mediumin-medium properties of hadrons at high baryon density properties of hadrons at high baryon density and temperatureand temperature

The phase diagram of QCDThe phase diagram of QCD

Physics at FAIRPhysics at FAIR

FAIR energiesFAIR energies are well suited to study are well suited to studydense and hot nuclear matterdense and hot nuclear matter : :

a phase transition to QGP a phase transition to QGP in-medium effects of hadronsin-medium effects of hadrons chiral symmetry restoration chiral symmetry restoration

Way to study:Way to study:

Experimental Experimental energy scanenergy scan of different of different observables in order to find an observables in order to find an ‚anomalous‘‚anomalous‘ behavior by comparing behavior by comparing with theorywith theory

Dynamical models of HIC!Dynamical models of HIC!

4

Dynamical models for HICDynamical models for HIC

MacroscopicMacroscopic MicroscopicMicroscopic

‚‚Hybrid‘Hybrid‘ QGP phase: hydro with QGP EoS QGP phase: hydro with QGP EoS hadronic freeze-out: after burner - hadronic freeze-out: after burner - hadron-string transport modelhadron-string transport model (‚hybrid‘-UrQMD, EPOS, …)(‚hybrid‘-UrQMD, EPOS, …)

fireballfireball models: models: no explicit dynamics: no explicit dynamics: parametrized time parametrized time evolution evolution (TAMU)(TAMU)

idealideal(Jyväskylä,SHASTA,(Jyväskylä,SHASTA,TAMU, …) TAMU, …)

Non-equilibrium microscopic transport modelsNon-equilibrium microscopic transport models – – based on many-body theorybased on many-body theory

Hadron-string Hadron-string modelsmodels

(UrQMD, IQMD, HSD, (UrQMD, IQMD, HSD, QGSM …)QGSM …)

Partonic cascadesPartonic cascades pQCD basedpQCD based(Duke, BAMPS, …)(Duke, BAMPS, …)

Parton-hadron models:Parton-hadron models:

QGP: QGP: pQCDpQCD based cascade based cascade massless q, gmassless q, g hadronization: coalescencehadronization: coalescence (AMPT, HIJING)(AMPT, HIJING)

QGP: QGP: lQCD EoSlQCD EoS massive quasi-particlesmassive quasi-particles (q and g with spectral functions) (q and g with spectral functions) in self-generated mean-field in self-generated mean-field dynamical hadronizationdynamical hadronization HG: off-shell dynamicsHG: off-shell dynamics(applicable for strongly interacting (applicable for strongly interacting systems) systems)

viscousviscous(Romachkke,(2+1)D VISH2+1, (Romachkke,(2+1)D VISH2+1,

(3+1)D MUSIC,…)(3+1)D MUSIC,…)

hydro-models:hydro-models: description of QGP and hadronic phasedescription of QGP and hadronic phase by hydrodanamical equations for fluid by hydrodanamical equations for fluid assumption of local equilibriumassumption of local equilibrium EoS with phase transition from QGP to HGEoS with phase transition from QGP to HG initial conditions (e-b-e, fluctuating)initial conditions (e-b-e, fluctuating)

55

Theoretical description of ‘in-medium effects’Theoretical description of ‘in-medium effects’

Many-body theory:Many-body theory:Strong interaction Strong interaction large widthlarge width = short life-time = short life-time broad spectral function broad spectral function quantum objectquantum object

How to describe the How to describe the dynamics of dynamics of broadbroad strongly interacting quantum strongly interacting quantum statesstates in in transport theorytransport theory??

Barcelona / Barcelona / Valencia Valencia groupgroup

(1783)N(1783)N-1-1 and and (1830)N(1830)N-1-1

exitationsexitations

semi-classical BUUsemi-classical BUU

generalized transport equationsgeneralized transport equations

first order gradient first order gradient expansion of quantum expansion of quantum Kadanoff-Baym equationsKadanoff-Baym equations

In-medium effects = changes of particle properties in the hot and In-medium effects = changes of particle properties in the hot and dense baryonic medium; example – vector mesons, strange mesonsdense baryonic medium; example – vector mesons, strange mesons

6666

Semi-classical BUU equationSemi-classical BUU equation

collprr t

f)t,p,r(f)t,r(U)t,p,r(f

m

p)t,p,r(f

t

Boltzmann-Uehling-Uhlenbeck equation Boltzmann-Uehling-Uhlenbeck equation (non-relativistic formulation)(non-relativistic formulation)- propagation of particles in the propagation of particles in the self-generated Hartree-Fock mean-field self-generated Hartree-Fock mean-field potential potential U(r,t)U(r,t) with an on-shellwith an on-shell collision term: collision term:

)termFock()t,p,r(f)t,rr(Vpdrd)2(

1)t,r(U 33

3occ

)t,p,r(f

is the is the single particle phase-space distribution function single particle phase-space distribution function - probability to find the particle at position - probability to find the particle at position rr with momentum with momentum pp at time at time tt

self-generated self-generated Hartree-Fock mean-field potential:Hartree-Fock mean-field potential:

Ludwig Boltzmann

collision term: collision term: elastic and elastic and inelastic reactionsinelastic reactions

P)4321(d

d)pppp(||dpdpd

)2(

4I 4321

3123

32

33coll

Probability includingProbability including Pauli blocking of fermions: Pauli blocking of fermions:

)f1)(f1(ff)f1)(f1(ffP 43212143

Gain term: 3+4Gain term: 3+41+21+2 Loss term: 1+2Loss term: 1+23+43+4

Collision termCollision term for 1+2for 1+23+4 (let‘s consider fermions) :3+4 (let‘s consider fermions) :

1

2

3

4

t

12

7777

Dynamical description of strongly interacting systemsDynamical description of strongly interacting systems

Semi-classical on-shell BUU:Semi-classical on-shell BUU: applies for small collisional width, i.e. for a weakly applies for small collisional width, i.e. for a weakly interacting systems of particlesinteracting systems of particles

Quantum field theory Quantum field theory Kadanoff-Baym dynamicsKadanoff-Baym dynamics for resummed single-particle Green functions Sfor resummed single-particle Green functions S<<

(1962)(1962)

Leo KadanoffLeo Kadanoff Gordon BaymGordon Baym

)M(S 20

xx

1x0

advancedSSSSS

retardedSSSSS

axyxyxy

cxy

advxy

axyxyxy

cxy

retxy

anticausal})y(Φ)x({ΦTiS

causal})y(Φ)x({ΦTiS

})x(Φ)y({ΦiS

})x(Φ)y({ΦηiS

aaxy

ccxy

xy

xy

Green functions SGreen functions S< < /self-energies /self-energies ::

operatororderingtime)anti()T(T

)fermions/bosons(1ca

Integration over the intermediate spacetimeIntegration over the intermediate spacetime

How to describeHow to describe strongly interacting systems?! strongly interacting systems?!

8888

From Kadanoff-Baym equations to From Kadanoff-Baym equations to generalized transport equationsgeneralized transport equations

After the After the first order gradient expansion of the Wigner transformed first order gradient expansion of the Wigner transformed Kadanoff-Baym Kadanoff-Baym equations and separation into the real and imaginary parts one gets:equations and separation into the real and imaginary parts one gets:

Backflow termBackflow term incorporates theincorporates the off-shelloff-shell behavior in the particle propagationbehavior in the particle propagation !! vanishes in the quasiparticle limit vanishes in the quasiparticle limit AAXPXP (p(p22-M-M22) )

Spectral function:Spectral function:

– – ‚‚widthwidth‘ of spectral function‘ of spectral function = = reaction ratereaction rate of particle (at space-time position X) of particle (at space-time position X)

4-dimentional generalizaton of the Poisson-bracket:4-dimentional generalizaton of the Poisson-bracket:

W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

GTE: GTE: Propagation of the Green‘s functionPropagation of the Green‘s function iiSS<<XPXP=A=AXPXPNNXPXP , , which carries which carries

information not only on the information not only on the number of particlesnumber of particles ( (NNXPXP)), but also on their , but also on their properties,properties, interactions and correlationsinteractions and correlations (via (via AAXPXP))

0retXPXP p2Im

drift termdrift term Vlasov termVlasov term collision term =collision term = ‚gain‘ ‚gain‘ - ‚loss‘ term - ‚loss‘ termbackflow termbackflow term

Generalized transport equations (GTE):Generalized transport equations (GTE):

c Life timeLife time

9999

General testparticle off-shell equations of motionGeneral testparticle off-shell equations of motion

EmployEmploy testparticle Ansatztestparticle Ansatz for the real valued quantityfor the real valued quantity ii S S<<XP XP --

insert in generalized transport equations and determine equations of motion !insert in generalized transport equations and determine equations of motion !

General testparticle off-shell equations of motion General testparticle off-shell equations of motion for the time-like particles:for the time-like particles:

with

W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

1010

Collision term in off-shell transport modelsCollision term in off-shell transport models

Collision termCollision term for reaction 1+2->3+4:for reaction 1+2->3+4:

withwith

The trace over particles 2,3,4 reads explicitlyThe trace over particles 2,3,4 reads explicitly for fermionsfor fermions for bosonsfor bosons

The transport approach and the particle spectral functions are The transport approach and the particle spectral functions are fully determined once thefully determined once the in-medium transition amplitudes Gin-medium transition amplitudes G

are known in theirare known in their off-shell dependence!off-shell dependence!

additional integrationadditional integration

‚‚loss‘ termloss‘ term ‚‚gain‘ termgain‘ term

In-medium transition rates: G-matrix approachIn-medium transition rates: G-matrix approach

Need to knowNeed to know in-medium transition amplitudes G and their off-shellin-medium transition amplitudes G and their off-shell dependencedependence

Coupled channel G-matrix approachCoupled channel G-matrix approach

Transition probability :Transition probability :

with G(p,with G(p,,T) -,T) - G-matrixG-matrix from the solution offrom the solution of coupled-channel equations:coupled-channel equations:

G

•Baryons: Pauli blocking Baryons: Pauli blocking and potential dressingand potential dressing

• Meson selfenergy and Meson selfenergy and spectral functionspectral function

For strangeness: For strangeness: D. Cabrera, L. Tolos, J. Aichelin, E.B., arXiv:1406.2570; W. Cassing, L. Tolos, E.B., A. Ramos, NPA727 (2003) 59D. Cabrera, L. Tolos, J. Aichelin, E.B., arXiv:1406.2570; W. Cassing, L. Tolos, E.B., A. Ramos, NPA727 (2003) 59

Collision width in off-shell transport modelCollision width in off-shell transport model

! ! Assumptions used in transport calculationsAssumptions used in transport calculations for V-mesons for V-mesons (to speed up calculations):(to speed up calculations):

• Collision width inCollision width in low density approximation:low density approximation:collcoll = = VNVNtottot

• replacereplace VNVNtottot by averaged value G=const:by averaged value G=const: collcoll = = GG

(Works well (Works well – – cf. low density approximation vs. the full dynamical calculation of cf. low density approximation vs. the full dynamical calculation of CollColl in Ref. in Ref.

E.B., NPA696 (2001) 761) E.B., NPA696 (2001) 761)

Collision width is defined by all possible interactions in the local cellCollision width is defined by all possible interactions in the local cell

Example:Example: Collision width Collision width collcoll for 1+2->3+4 process – defined from the for 1+2->3+4 process – defined from the loss termloss term of the collision integral of the collision integral IIcollcoll::

2MPX

2collcoll )N,MP(X,Γ)loss(I

244

233

222 MPXMPXMPX432

)4(2S

244

233

222

2

244

233

222

2432

2coll

ffN)PPPP(|))M,P()M,P()M,P()M,P((G|

)M,P,X(A)M,P,X(A)M,P,X(A)M,P,X(ATrTrTr)M,P,X(

0retXPXP p2Im

Total widthTotal widthcollision widthcollision widthdecay widthdecay width= = collcoll++decdec

In the In the vacuumvacuum: : = = decdec

(similar for the n<->m reactions!)(similar for the n<->m reactions!)

Mean-field potential in off-shell transport modelMean-field potential in off-shell transport model

0retXPXP p2Im

Interacting relativistic particles have a Interacting relativistic particles have a complex self-energy:complex self-energy:

retXP

retXP

retXP ImiRe

By By dispersion relationdispersion relation we get a contribution to the we get a contribution to the real part of self-energyreal part of self-energy::

)pq(

)q(Imdq)p(Re

0

retXP

0

0retXP

that givesthat gives a mean-field potential U a mean-field potential UXP XP via:via: XP00retXP Up2)p(Re

Many-body theory:Many-body theory:

to the inverse livetime of the particleto the inverse livetime of the particle~1/~1/. .

The The collision widthcollision width coll coll is determined from the is determined from the loss termloss term of the collision integral of the collision integral IIcollcoll

= = collcoll++decdecThe neg. imaginary partThe neg. imaginary part is related viais related via

thethe complex self-energy complex self-energy relatesrelates in a self-consistent way to the self-generated in a self-consistent way to the self-generated mean-field potential and collision width (inverse lifetime)mean-field potential and collision width (inverse lifetime)

14141414

Detailed balance on the level of 2<->n: Detailed balance on the level of 2<->n: treatment of multi-particle collisions in transport approachestreatment of multi-particle collisions in transport approaches

W. Cassing, NPA 700 (2002) 618W. Cassing, NPA 700 (2002) 618

Generalized collision integralGeneralized collision integral for for n <->mn <->m reactions:reactions:

is Pauli-blocking or Bose-enhancement factors; is Pauli-blocking or Bose-enhancement factors; =1 for bosons and =1 for bosons and =-1 for fermions=-1 for fermions

is a is a transition probabilitytransition probability huge CPU!huge CPU!

15151515

Antibaryon production in heavy-ion reactionsAntibaryon production in heavy-ion reactions

0 2 4 6 8 1010

0

101

102

Pb+Pb, 160 A GeVcentral

__

BB->X

__

3 mesons -> BB

dN

/dt

[arb

. un

its]

t [fm/c]

W. Cassing, NPA 700 (2002) 618W. Cassing, NPA 700 (2002) 618Multi-meson fusionMulti-meson fusion reactionsreactions mm11+m+m22+...+m+...+mnn B+Bbar B+Bbar(m=(m=

important for antiproton, antilambda important for antiproton, antilambda dynamics !dynamics ! 2<->32<->3

approximate equilibrium of annihilation and recreationapproximate equilibrium of annihilation and recreation

1616

From hadrons to partonsFrom hadrons to partons

In order to study the In order to study the phase transitionphase transition from from hadronic to partonic matter – hadronic to partonic matter – Quark-Gluon-PlasmaQuark-Gluon-Plasma – – we we need need a a consistent non-equilibrium (transport) model withconsistent non-equilibrium (transport) model withexplicit explicit parton-parton interactionsparton-parton interactions (i.e. between quarks and gluons) (i.e. between quarks and gluons) beyond strings!beyond strings!explicit explicit phase transitionphase transition from hadronic to partonic degrees of freedom from hadronic to partonic degrees of freedomlQCD EoS lQCD EoS for partonic phasefor partonic phase

PParton-arton-HHadron-adron-SString-tring-DDynamics (ynamics (PHSDPHSD))

QGP phase QGP phase described bydescribed by

DDynamical ynamical QQuasiuasiPParticle article MModel odel (DQPMDQPM)

Transport theoryTransport theory: off-shell Kadanoff-Baym equations for the : off-shell Kadanoff-Baym equations for the Green-functions SGreen-functions S<<

hh(x,p) in phase-space representation for the(x,p) in phase-space representation for the

partonic partonic andand hadronic phase hadronic phase

A. A. Peshier, W. Cassing, PRL 94 (2005) 172301;Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;NPA831 (2009) 215; NPA831 (2009) 215;

W. Cassing, W. Cassing, EEPJ ST PJ ST 168168 (2009) (2009) 33

1717

DQPM DQPM describes describes QCDQCD properties in terms ofproperties in terms of ‚‚resummedresummed‘‘ single-particle Green‘s single-particle Green‘s functionsfunctions – in the sense of a two-particle irreducible (– in the sense of a two-particle irreducible (2PI2PI) approach:) approach:

A. A. Peshier, W. Cassing, PRL 94 (2005) 172301;Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

Dynamical QuasiParticle Model (DQPM) - Dynamical QuasiParticle Model (DQPM) - Basic ideas:Basic ideas:

the resummed properties are specified by the resummed properties are specified by complex self-energiescomplex self-energies which depend which depend on temperatureon temperature:: ---- the the real part of self-energies real part of self-energies ((ΣΣqq,, Π)Π) describes a describes a dynamically generateddynamically generated massmass

((MMqq,M,Mgg));; -- -- the the imaginary part imaginary part describes thedescribes the interaction widthinteraction width of partonsof partons ( (qq,, gg))

space-like part of energy-momentum tensor space-like part of energy-momentum tensor TTdefines the potential energy defines the potential energy density and the density and the mean-field potentialmean-field potential (1PI) for quarks and gluons (1PI) for quarks and gluons (U (Uqq, U, Ugg))

2PI frame2PI framewwork ork guarantguarantiies a consistent description of the systemes a consistent description of the system in- and out-ofin- and out-off f equilibriumequilibrium on the basis ofon the basis of Kadanoff-Baym equations Kadanoff-Baym equations with proper states in with proper states in equilibriumequilibrium

Gluon propagator:Gluon propagator: ΔΔ-1-1 =P =P22 - Π - Π gluon self-energy:gluon self-energy: Π=MΠ=Mgg22-i2-i2ggωω

Quark propagator:Quark propagator: SSqq-1-1 = P = P22 - Σ - Σqq quark self-energy:quark self-energy: ΣΣqq=M=Mqq

22-i2-i2qqωω

1818

The Dynamical QuasiParticle Model (DQPM)The Dynamical QuasiParticle Model (DQPM)

PropertiesProperties of of interacting quasi-particles:interacting quasi-particles: massive quarks and gluonsmassive quarks and gluons (g, q, q(g, q, qbarbar))

withwith Lorentzian spectral functions :Lorentzian spectral functions :

DQPM: Peshier, Cassing, PRL 94 (2005) 172301;DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

with 3 parameters: with 3 parameters: TTss/T/Tcc=0.46; =0.46; c c=28.8; =28.8; =2.42=2.42

(for pure glue N(for pure glue Nff=0)=0)

fit to lattice (lQCD) results fit to lattice (lQCD) results (e.g. entropy density)(e.g. entropy density)

(T)ω4(T)Mpω

(T)ω4)T,(ρ

2i

222i

22

ii

)g,q,qi(

running couplingrunning coupling (pure glue):(pure glue):

NNcc = 3, N = 3, Nff=3=3

mass:mass:

width:width:

gluons:gluons: quarks:quarks:

lQCD: pure gluelQCD: pure glue

Modeling of the quark/gluon masses and widths Modeling of the quark/gluon masses and widths HTL limit at high T HTL limit at high T

1919

The Dynamical QuasiParticle Model (DQPM)The Dynamical QuasiParticle Model (DQPM)

Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)

Quasiparticle properties:Quasiparticle properties: large width and mass for gluons and quarks large width and mass for gluons and quarks

•DQPMDQPM matches well matches well lattice QCDlattice QCD

•DQPMDQPM provides provides mean-fields (1PI) for gluons and quarksmean-fields (1PI) for gluons and quarks as well as as well as effective 2-body interactions (2PI)effective 2-body interactions (2PI)

•DQPMDQPM gives gives transition ratestransition rates for the formation of hadrons for the formation of hadrons PHSDPHSD

fit to lattice (lQCD) resultsfit to lattice (lQCD) results (e.g. entropy density)(e.g. entropy density)

* BMW lQCD data S. Borsanyi et al., JHEP 1009 (2010) 073* BMW lQCD data S. Borsanyi et al., JHEP 1009 (2010) 073

TTCC=158 MeV=158 MeV

CC=0.5 GeV/fm=0.5 GeV/fm33

19

2020

Initial A+A collisionsInitial A+A collisions:: - - stringstring formation in primary NN collisions formation in primary NN collisions -- strings decay to strings decay to pre-hadronspre-hadrons ( (BB - baryons, - baryons, mm – mesons) – mesons)

Formation of QGP stage Formation of QGP stage by dissolution of pre-hadronsby dissolution of pre-hadrons intointo massive colored quarks + mean-field energy massive colored quarks + mean-field energy based on the based on the Dynamical Quasi-Particle Model (DQPM)Dynamical Quasi-Particle Model (DQPM) which defines which defines quark spectral functions, quark spectral functions, masses masses MMqq(()) and widths and widths qq (()) + + mean-field potential mean-field potential UUqq at givenat given – local energy density – local energy density ( related by lQCD EoS to ( related by lQCD EoS to T T - temperature in the local cell)- temperature in the local cell)

Parton Hadron String DynamicsParton Hadron String Dynamics

I. I. From hadrons to QGP:From hadrons to QGP: QGP phase:QGP phase: > > criticalcritical

II. II. Partonic Partonic phasephase - QGP: - QGP: quarks and gluons (= quarks and gluons (= ‚dynamical quasiparticles‘)‚dynamical quasiparticles‘)

withwith off-shell spectral functionsoff-shell spectral functions (width, mass) defined by the DQPM(width, mass) defined by the DQPM in in self-generated mean-field potential self-generated mean-field potential for quarks and gluonsfor quarks and gluons UUqq, U, Ug g

EoS of partonic phase: EoS of partonic phase: ‚crossover‘ from lattice QCD ‚crossover‘ from lattice QCD (fitted by DQPM)(fitted by DQPM) (quasi-) elastic and inelastic (quasi-) elastic and inelastic parton-parton interactions:parton-parton interactions:

using the effective cross sections from the DQPM using the effective cross sections from the DQPM

IV. IV. Hadronic phase:Hadronic phase: hadron-string interactions – hadron-string interactions – off-shell HSDoff-shell HSD

massive, off-shell (anti-)quarks massive, off-shell (anti-)quarks with broad spectral functions with broad spectral functions hadronize to hadronize to off-shell mesons and baryons or color neutral excited states -off-shell mesons and baryons or color neutral excited states - ‚strings‘ ‚strings‘ (strings act as ‚doorway states‘ for hadrons) (strings act as ‚doorway states‘ for hadrons)

III. III. Hadronization:Hadronization: based on DQPM based on DQPM

W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;NPA831 (2009) 215; NPA831 (2009) 215; EEPJ ST PJ ST 168168 (2009) (2009) 33; ; NNPPA856A856 (2011) (2011) 162162..

PHSD – ‚femto‘ acceleratorPHSD – ‚femto‘ accelerator

2222

PHSD code: structurePHSD code: structure

over B, ISUBSover B, ISUBS

NUMNUM

NUMNUM

NUMNUM

NUMNUM

PHSD is the parallel ensembles code!!!PHSD is the parallel ensembles code!!!

loop over loop over NUM – parallel ensembles or ‚events‘:NUM – parallel ensembles or ‚events‘: needed for the smooth description of the mean-field needed for the smooth description of the mean-field properties as energy density or baryon densityproperties as energy density or baryon density

possible parallelizationpossible parallelization

HSD modeHSD mode

2323

PHSD running time PHSD running time HPC HPC

PHSDPHSD mode mode: : Au+Au/Pb+Pb, central, t Au+Au/Pb+Pb, central, tfinalfinal = 40 fm/c  = 40 fm/c 

Elab, Elab, AGeVAGeV SS1/21/2, GeV, GeV CPU time, CPU time,

hhNUMNUM CPU CPU

time/NUMtime/NUM

10.710.7 4.864.86 0.20.2 5050 14.4sec14.4sec

4040 8.868.86 0.750.75 100100 27sec27sec

8080 12.412.4 1.151.15 100100 41.4sec41.4sec

158158 17.317.3 0.80.8 5050 57.6sec57.6sec

2130021300 200200 1.751.75 1515 7min7min

40600004060000 27602760 1.81.8 55 21.6min21.6min

NUM – the number of parallel ensembles/eventsNUM – the number of parallel ensembles/events

PHSD is the open source code for the FAIR experiments:PHSD is the open source code for the FAIR experiments:http://fias.uni-frankfurt.de/~brat/PHSD/index4.html

CPU time per event grows with energy CPU time per event grows with energy PHSD mode (for RHIC, LHC) – more time consuming than HSDPHSD mode (for RHIC, LHC) – more time consuming than HSD

from V. Konchakovski

2424

0 100 200 300 4000.00

0.01

0.02

0.03

0.04

0.05

0.06

0 100 200 300 4000.000

0.002

0.004

0.006

0.008

0.010

NA57NA49

HSD PHSD

+0

NwoundN

wound

Pb+Pb, 158 A GeV, mid-rapidity _ _

dN/d

y | y=

0 / N

wou

nd

PHSD for HIC (highlights)PHSD for HIC (highlights)

PHSD PHSD provides a provides a consistent description of consistent description of p+A and HIC dynamicsp+A and HIC dynamics

2525

The most CPU costly observablesThe most CPU costly observables(some examples)(some examples)

(Multi-)strange particles in Au+Au(Multi-)strange particles in Au+Au

27

Multi-strange baryon productionMulti-strange baryon production

Multi-strange hyperons (Multi-strange hyperons (Ξ, ΩΞ, Ω) are promising probes ) are promising probes to study:to study:

• in-medium effects at low bombarding energy in-medium effects at low bombarding energy

• QGP properties at high energy densityQGP properties at high energy density

Elementary productionElementary production::

In In heavy-ion reactionsheavy-ion reactions: sub-threshold channels, : sub-threshold channels, e.g.e.g.

Production through these channels highly Production through these channels highly depends on baryon density (and it‘s depends on baryon density (and it‘s fluctuations)fluctuations)

pKKKpp 0

(E(Ebeambeam > 3.7 GeV) > 3.7 GeV)

(E(Ebeambeam > 7.0 GeV) > 7.0 GeV)

p n

p K K p p

pKpp CBMCBM

Centrality dependence of (multi-)strange (anti-)baryonsCentrality dependence of (multi-)strange (anti-)baryons

enhanced production of (multi-) strange antibaryons in PHSDenhanced production of (multi-) strange antibaryons in PHSD

strange strange antibaryonsantibaryons

_ __ _++00

multi-strange multi-strange antibaryonantibaryon

__++

0 100 200 300 4000.00

0.01

0.02

0.03

0.04

0.05

0.06

0 100 200 300 4000.000

0.002

0.004

0.006

0.008

0.010

NA57NA49

HSD PHSD

+0

NwoundN

wound

Pb+Pb, 158 A GeV, mid-rapidity _ _

dN/d

y | y=

0 / N

wou

nd

0 100 200 300 40010-4

10-3

10-2

0 100 200 300 400

10-4

10-3

HSD PHSD

NA57 NA49

dN

/dy

| y=0 /

Nw

ound

Pb+Pb, 158 A GeV, mid-rapidity

Nwound

Nwound

multi-strange multi-strange baryonbaryon

--

strange strange baryonsbaryons++00

Cassing & Bratkovskaya, NPA 831 (2009) 215Cassing & Bratkovskaya, NPA 831 (2009) 215

Exitation function of (multi-)strange (anti-)baryonsExitation function of (multi-)strange (anti-)baryons

Collective flow:Collective flow:anisotropy coefficients (vanisotropy coefficients (v11, v, v2, 2, vv33, , vv44))

in A+Ain A+A

x

z

Anisotropy coefficientsAnisotropy coefficients

Non central Non central Au+Au Au+Au collisions :collisions : iinteraction between constituents nteraction between constituents leads to a leads to a pressure pressure gradientgradient => spatial asymmetry => spatial asymmetry is is converted converted toto an an asymmetry in momentum spaceasymmetry in momentum space => => collective flowcollective flow

vv2 2 > 0 > 0 indicates indicates in-planein-plane emission of particles emission of particles

vv2 2 < 0 < 0 corresponds to a corresponds to a squeeze-out squeeze-out perpendicular perpendicular

to the reaction plane (to the reaction plane (out-of-planeout-of-plane emission) emission)

vv2 2 > 0> 0

from S. A. Voloshin, arXiv:1111.7241from S. A. Voloshin, arXiv:1111.7241

3232

Directed flow signals of the Quark–Gluon PlasmaDirected flow signals of the Quark–Gluon Plasma

H. Stöcker, Nucl. Phys. A 750, 121 (2005)H. Stöcker, Nucl. Phys. A 750, 121 (2005)

Early hydro calculation predicted the Early hydro calculation predicted the “softest point” at E“softest point” at E

lablab= 8 AGeV= 8 AGeV

A linear extrapolation of the data (A linear extrapolation of the data (arrowarrow) ) suggests a suggests a collapse of flow at Ecollapse of flow at E

lablab= 30 AGeV= 30 AGeV

3333

Color scaleColor scale: : baryon number densitybaryon number densityBlack levelsBlack levels: QGP: QGP- parton density 0.6 and 0.01 fm- parton density 0.6 and 0.01 fm-3-3

Red arrowsRed arrows: : local velocity of baryon matterlocal velocity of baryon matter

t = 3 fm/ct = 3 fm/c t = 6 fm/ct = 6 fm/c

PHSD: snapshot of the reaction planePHSD: snapshot of the reaction plane

V. Konchakovski, W. Cassing, Yu. Ivanov, V. Toneev, V. Konchakovski, W. Cassing, Yu. Ivanov, V. Toneev,

PRC(2014), PRC(2014), arXiv:1404.2765arXiv:1404.2765

Directed flow vDirected flow v11 is is formed at an early formed at an early

stagestage of the nuclear interactionof the nuclear interaction

BaryonsBaryons are reachingare reaching positivepositive and and mesons – negativemesons – negative value of vvalue of v

11

3434

STAR Collaboration, arXiv:1401.3043 STAR Collaboration, arXiv:1401.3043 PHSD/HSD and 3D-fluid hydro:PHSD/HSD and 3D-fluid hydro: V. Konchakovski, W. Cassing, Yu. Ivanov, V. Toneev, PRC(2014), arXiv:1404.2765 V. Konchakovski, W. Cassing, Yu. Ivanov, V. Toneev, PRC(2014), arXiv:1404.2765 Hybrid/UrQMD/Hydro:Hybrid/UrQMD/Hydro: J. Steinheimer, J. Auvinen, H. Petersen, M. Bleicher, H. Stöcker, J. Steinheimer, J. Auvinen, H. Petersen, M. Bleicher, H. Stöcker, PRC 89 (2014) 054913PRC 89 (2014) 054913

Excitation function of vExcitation function of v11 slopes slopes

0=y1 |

dy

d=F

The slope of vThe slope of v11(y) (y)

at midrapidity:at midrapidity:

Models:Models:

HSD,HSD, PHSDPHSD

3D-Fluid Dynamic 3D-Fluid Dynamic approach (3FD)approach (3FD)

UrQMD UrQMD

Hybrid-UrQMDHybrid-UrQMD

1FD-hydro with chiral 1FD-hydro with chiral cross-over and Bag Model cross-over and Bag Model (BM) EoS(BM) EoS

smooth crossover?!crossover?!

Elliptic flow vElliptic flow v22 vs. collision energy for Au+Au vs. collision energy for Au+Au

vv2 2 in PHSD is larger than in HSD in PHSD is larger than in HSD due to due to

the repulsive scalar mean-field potential the repulsive scalar mean-field potential UUss(ρ) for partons(ρ) for partons

vv2 2 grows with bombarding energygrows with bombarding energy due to due to

the increase of the parton fractionthe increase of the parton fraction

V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, V. Voronyuk, Phys. Rev. C 85 (2012) 011902Phys. Rev. C 85 (2012) 011902

Flow coefficients versus centrality at RHICFlow coefficients versus centrality at RHIC

increase of increase of vv2 2 with impact with impact

parameter but flat parameter but flat vv3 3 and and vv4 4

V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, Phys. Rev. C 85 (2012) 044922 Phys. Rev. C 85 (2012) 044922

Fluctuations and correlationsFluctuations and correlations

Lattice QCD: Critical PointLattice QCD: Critical Point

Fluctuations of theFluctuations of the quark number densityquark number density ((susceptibilitysusceptibility) at ) at qq>0>0 [F. Karsch et al.]

fixedT

42q

2

2q

T

P

T/T

Lattice QCDLattice QCDpredictions:predictions:q (quark number density fluctuations) (quark number density fluctuations) will diverge at thewill diverge at the critical chiral point =>critical chiral point =>

Experimental observation Experimental observation – look for– look fornon-monotonic behaviornon-monotonic behavior of the of the observables near the critical pointobservables near the critical point : baryon number fluctuationsbaryon number fluctuations charge number fluctuationscharge number fluctuations multiplicity fluctuationsmultiplicity fluctuations particle ratio fluctuations (K/particle ratio fluctuations (K/,, K/p, K/p, )) mean pmean pTT fluctuations fluctuations 2 particle correlations2 particle correlations ......

Multiplicity fluctuations in p+pMultiplicity fluctuations in p+p

N

NN

N

Var(N)22

Scaled variance - multiplicity fluctuations in some acceptance (charge, strangeness, etc.):

The excitation functions of NThe excitation functions of Nchch and and charge multiplicity fluctuations charge multiplicity fluctuations chch from from HSDHSD are approximately in line with experimental data are approximately in line with experimental data

Multiplicity fluctuations for 1%MC Multiplicity fluctuations for 1%MC practically do not practically do not depend on atomic depend on atomic mass for mass for y>0y>0 and onlyand only slightly grow slightly grow with increasing collision energy.with increasing collision energy.

rapidityrapidity y>0y>0

HSD (and UrQMD) show a plateauHSD (and UrQMD) show a plateau on top of which the SHINE on top of which the SHINE Collaboration expects to find increasing multiplicity fluctuations as a Collaboration expects to find increasing multiplicity fluctuations as a "signal" for the critical point !"signal" for the critical point !

Multiplicity fluctuations in HSD: 1%MCMultiplicity fluctuations in HSD: 1%MC

4040

Konchakovski, Lungwitz, Gorenstein, Bratkovskaya, Phys. Rev. CKonchakovski, Lungwitz, Gorenstein, Bratkovskaya, Phys. Rev. C78 (2008) 02490678 (2008) 024906

Gazdzicki, PoS CPOD2006:016Gazdzicki, PoS CPOD2006:016

Charge fluctuationsCharge fluctuations

4141

TheThe decay of resonancesdecay of resonances strongly modifies the initial QGP fluctuations!strongly modifies the initial QGP fluctuations!

HSD: Phys. Rev. CHSD: Phys. Rev. C74 (2006) 6491174 (2006) 64911NA49: Phys. Rev. CNA49: Phys. Rev. C70 (2004) 06490370 (2004) 064903

sensitive to the sensitive to the EoSEoS at the early stage of the collision and to its at the early stage of the collision and to its changes in the deconfinement phase transition regionchanges in the deconfinement phase transition region

net-charge fluctuations are net-charge fluctuations are smaller in QGP than in a hadron gassmaller in QGP than in a hadron gas

Jeon, Koch, PRL85 (2000) 2076Jeon, Koch, PRL85 (2000) 2076Asakawa, Heinz, Muller PRL85 (2000) 2072Asakawa, Heinz, Muller PRL85 (2000) 2072

K/K/-ratio fluctuations: Transport models vs Data-ratio fluctuations: Transport models vs Data

4242

• Exp. data show a plateau from top SPS up to RHIC energies and an increase towards lower SPS energies

evidence for a critical point at low SPS energies ?

• but the HSD (without QGP!) results shows the same behavior

• K/-ratio fluctuation is driven by hadronic sources No evidence for a critical point in the K/ratio ?

• K/ ratio fluctuation is sensitive to the acceptance!

HSD: Phys. Rev. C 79 (2009) 024907HSD: Phys. Rev. C 79 (2009) 024907UrQMD: UrQMD: J. Phys. G 30 (2004) S1381, PoS CFRNC2006,017J. Phys. G 30 (2004) S1381, PoS CFRNC2006,017NA49: 0808.1237NA49: 0808.1237STAR: 0901.1795STAR: 0901.1795

In GCE for ideal Boltzman gas:In GCE for ideal Boltzman gas:

4343

Outlook - PerspectivesOutlook - Perspectives

What is the stage of matter close to TWhat is the stage of matter close to Tc c

and large and large ::

1st order phase transition? 1st order phase transition?

‚‚Mixed‘ phase = interaction of partonic Mixed‘ phase = interaction of partonic and hadronic degrees of freedom?and hadronic degrees of freedom?

Open problems:Open problems:

• How to describe a How to describe a first-order phase first-order phase transition transition in transport models? in transport models?

• How to describe parton-hadron interactions inHow to describe parton-hadron interactions in a ‚mixed‘ phase a ‚mixed‘ phase??

Lattice EQS for m=0 Lattice EQS for m=0 ‚crossover‘ , T > T ‚crossover‘ , T > Tcc

4444

FIAS & Frankfurt UniversityFIAS & Frankfurt UniversityElena Bratkovskaya Elena Bratkovskaya

Rudy MartyRudy MartyHamza BerrehrahHamza BerrehrahDaniel Cabrera Daniel Cabrera Taesoo SongTaesoo SongAndrej IlnerAndrej Ilner

Giessen UniversityGiessen UniversityWolfgang CassingWolfgang Cassing

Olena LinnykOlena LinnykVolodya KonchakovskiVolodya Konchakovski

Thorsten SteinertThorsten SteinertAlessia PalmeseAlessia PalmeseEduard SeifertEduard Seifert

External CollaborationsExternal CollaborationsSUBATECH, Nantes University:SUBATECH, Nantes University:

Jörg Aichelin Jörg Aichelin Christoph HartnackChristoph Hartnack

Pol-Bernard GossiauxPol-Bernard GossiauxVitalii OzvenchukVitalii Ozvenchuk

Texas A&M University:Texas A&M University:Che-Ming KoChe-Ming Ko

JINR, Dubna:JINR, Dubna:Viacheslav ToneevViacheslav ToneevVadim VoronyukVadim Voronyuk

BITP, Kiev University:BITP, Kiev University:Mark GorensteinMark Gorenstein

Barcelona University:Barcelona University:Laura TolosLaura Tolos

Angel RamosAngel Ramos

PHSD groupPHSD group

4545

strongly interacting quasi-particles strongly interacting quasi-particles - massive quarks and gluons (g, q, q- massive quarks and gluons (g, q, qbarbar) )

with sizeable collisional widths in with sizeable collisional widths in self-generated self-generated mean-field potentialmean-field potential

PParton-arton-HHadron-adron-SString-tring-DDynamics (ynamics (PHSDPHSD))

PHSD PHSD is a is a non-equilibrium transport modelnon-equilibrium transport model with with explicit explicit phase transitionphase transition from hadronic to partonic degrees of freedom from hadronic to partonic degrees of freedom lQCD EoSlQCD EoS for the partonic phase for the partonic phase explicit explicit parton-parton interactionsparton-parton interactions - between quarks and gluons - between quarks and gluons dynamical dynamical hadronizationhadronization

QGP phase is QGP phase is described by thedescribed by the DDynamical ynamical QQuasiuasiPParticle article MModel odel (DQPMDQPM)

Transport theoryTransport theory: : generalized off-shell transport equationsgeneralized off-shell transport equations based on based on

the 1st order gradient expansion of Kadanoff-Baym equations (the 1st order gradient expansion of Kadanoff-Baym equations (applicable applicable for strongly interacting systemfor strongly interacting system!)!)

A. Peshier, W. Cassing, PRL 94 (2005) 172301;A. Peshier, W. Cassing, PRL 94 (2005) 172301; W. Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, NPA 791 (2007) 365: NPA 793 (2007)

W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; W. Cassing, W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; W. Cassing, EEPJ ST PJ ST 168168 (2009) (2009) 33

Spectral functions:Spectral functions:

(T)ω4(T)Mpω

(T)ω4)T,(ρ

2i

222i

22

ii

)g,q,qi(

4646

DileptonsDileptons

4747

Dilepton sourcesDilepton sources

from the QGP from the QGP via partonic (q,qbar, g) interactions:via partonic (q,qbar, g) interactions:

from hadronic sources:from hadronic sources:

•direct decay direct decay of vector of vector mesonsmesons ( (JJ‘)‘)

•Dalitz decay Dalitz decay of mesons of mesons and baryonsand baryons ( (00,,, , ,…),…)

•correlated D+Dbar pairscorrelated D+Dbar pairs

•radiation fromradiation from multi-meson reactions multi-meson reactions ((++, , ++, , ++, , ++, , +a+a11) -) - ‚4‚4‘‘

• hadronic bremsstrahlunghadronic bremsstrahlung

**

gg **

**

qq l+

l--

**

qq

qq

qq

qq

qqqq

gggg

qq

c c

0DK

0D

K

c c

0DK

0D

K +qq+qq

Plot from A. DreesPlot from A. Drees

‚‚thermal QGP‘thermal QGP‘

4848

Lessons from SPS: NA60Lessons from SPS: NA60

PHSD:PHSD: Linnyk et al, PRC 84 (2011) Linnyk et al, PRC 84 (2011) 054917054917

Dilepton invariant mass spectra:Dilepton invariant mass spectra:

Fireball model – Renk/Ruppert Fireball model – Renk/Ruppert Fireball model – Rapp/vanHees Fireball model – Rapp/vanHees Ideal hydro model – Dusling/ZahedIdeal hydro model – Dusling/Zahed

Hybrid-UrQMD:Hybrid-UrQMD: Santini et al., Santini et al., PRC84 (2011) 014901 PRC84 (2011) 014901

Message from SPS: (based on NA60 and CERES data)Message from SPS: (based on NA60 and CERES data)

1) 1) Low mass spectraLow mass spectra - evidence for the - evidence for the in-medium broadening of in-medium broadening of -mesons-mesons 2) 2) Intermediate mass Intermediate mass spectra above 1 GeVspectra above 1 GeV - dominated by - dominated by partonic partonic radiationradiation3) 3) The rise and fall of The rise and fall of TTeffeff – evidence for the thermal – evidence for the thermal QGP radiationQGP radiation4) 4) Isotropic angular distributionIsotropic angular distribution – indication for a – indication for a thermal origin of dimuonsthermal origin of dimuons

Inverse slope parameter TInverse slope parameter Teffeff: : spectrum from QGP is softer than from hadronic phase since the QGP spectrum from QGP is softer than from hadronic phase since the QGP emission occurs dominantly before the collective radial flow has emission occurs dominantly before the collective radial flow has developed developed

NA60:NA60: Eur. Phys. J. C 59 (2009) 607 Eur. Phys. J. C 59 (2009) 607

QGPQGP

PRL 102 (2009) 222301PRL 102 (2009) 222301

4949

cococcktailktail

HSDHSDIdeal hydro Ideal hydro

Dusling/ZahedDusling/Zahed

Fireball model Fireball model Rapp/vanHees Rapp/vanHees cococcktailktail

HSDHSDIdeal hydro Ideal hydro

Dusling/ZahedDusling/Zahed

Fireball model Fireball model Rapp/vanHees Rapp/vanHees

Dileptons at RHIC: PHENIXDileptons at RHIC: PHENIX

Message:Message:

• ModelsModels provide a provide a good description of pp data good description of pp data andand peripheral peripheral Au+AuAu+Au data, however, data, however, fail in describing the excess for central fail in describing the excess for central collisionscollisions even with even with in-medium scenariosin-medium scenarios for the vector meson for the vector meson spectral functionspectral function•The The ‘missing source’(?)‘missing source’(?) is located at is located at low plow pTT

• Intermediate mass spectra – dominant QGP contributionIntermediate mass spectra – dominant QGP contribution

PHENIX: PHENIX: PRC81PRC81 (2010) (2010) 034911034911

Linnyk et al., PRC 85 (2012) 024910Linnyk et al., PRC 85 (2012) 024910

5050

Dileptons at RHIC: STAR data vs model predictionsDileptons at RHIC: STAR data vs model predictions

Centrality dependence of dilepton yieldCentrality dependence of dilepton yield(STAR: (STAR: arXiv:1407.6788arXiv:1407.6788 ) )

Message: Message: STAR dataSTAR data are described by models within a are described by models within a collisional broadeningcollisional broadening scenario scenario for the vector meson spectral function + for the vector meson spectral function + QGPQGP

Excess in low mass region, min. biasExcess in low mass region, min. bias

Models (predictions):Models (predictions): Fireball modelFireball model – R. Rapp – R. Rapp PHSDPHSDLow masses:Low masses: collisional broadening of collisional broadening of Intermediate masses: Intermediate masses: QGP dominant QGP dominant

5151

Dileptons from RHIC BES: STARDileptons from RHIC BES: STAR

Message:Message:

• BES-STARBES-STAR data data show ashow a constant low mass constant low mass excess excess (scaled with N((scaled with N()) within the measured )) within the measured energy range energy range

• PHSD model: PHSD model: excess increasing with excess increasing with decreasing energydecreasing energy due to a longer due to a longer -propagation -propagation in the high baryon density phasein the high baryon density phase

Good perspectives for future experiments – Good perspectives for future experiments – CBM(FAIR) / MPD(NICA)CBM(FAIR) / MPD(NICA)

(Talk by Nu Xu at QM‘2(Talk by Nu Xu at QM‘2014014))(Talk by Nu Xi at 23d CBM Meeting‘(Talk by Nu Xi at 23d CBM Meeting‘1414))

5252

Dileptons at LHCDileptons at LHC

Message:Message:

low masses -low masses - hadronic sources: hadronic sources: in-medium effects for in-medium effects for mesons are small mesons are small

intermediate masses:intermediate masses: QGP + D/Dbar QGP + D/Dbar

charm ‘background’ is smaller than thermal QGP yieldcharm ‘background’ is smaller than thermal QGP yield

QGP(qbar-q)QGP(qbar-q) dominates at M>1.2 GeV dominates at M>1.2 GeV clean signal of QGP at LHC!clean signal of QGP at LHC!

O. Linnyk, W. Cassing, J. Manninen, E.B., P.B. O. Linnyk, W. Cassing, J. Manninen, E.B., P.B. Gossiaux, J. Aichelin, T. Song, C.-M. Ko, Gossiaux, J. Aichelin, T. Song, C.-M. Ko, Phys.Rev. C87 (2013) 014905Phys.Rev. C87 (2013) 014905; arXiv:1208.1279; arXiv:1208.1279

QGPQGP