Overview of Transport Codes Evaluation Project (for Medium-Energy Heavy-Ion Collisions)

1. OverviewofTransport Codes Evaluation Project (for Medium-Energy Heavy-Ion Collisions) Hermann Wolter, University ofMunich Workshop „Challengesto Transport Theoryfor Heavy-Ion Collisions, ECT*, Trento, Italy, May 20-24, 2019

2. Motivation andaimsofthis talk: • Ideaforthisworkshopcamefromthe Transport Code Comparison (TCC) project • The TCC isconcernedabouttherobustnessofthedescriptionof heavy-ioncollisions • (HIC) bytransportcodes (and not in theinterpretationofdata) • TCC comparestransportcodesunderasmuchaspossibleidentical (i.e. controlled) • conditions in different scenarios • 1. full HIC atenergiesbetween 400 and 1500 AMeV • 2. infinite nuclear matter (approx. byperiodic box) with • onlyelasticcollisions (Cascade) • onlymeanfield (mf) propagation (Vlasov) • inelasticcascadeanddecayforpandD • Fromthe TCC welearn not onlyaboutdifferencesofcodes, but also aboutthe • innerworkingsoftransportsimulations • - fluctuations • - correlationsbetweencollisions • - pitfalls in thesimulationofinelasticprocessesanddecay • These andotherquestions (quantumeffects) will bediscussed in thisworkshop contentsofthis talk On behalf ofthe Transport Code Comparison Project - ofthe order of 30 participants - coregroup: Maria Colonna (Catania), Akira Ono (Sendai), Yingxun Zhang (CIAE, Beijing), Jun Xu (SINAP, Shanghai), Betty Tsang (MSU), Pawel Danielewicz (MSU), Jongjia Wang (Houzhou), HHW (Munich)

3. The Phase DiagramofStronglyInteractingMatter HIC: trajectories in phasediagram SIS 18, NSCL, RIKEN Asymmetryaxis --> searchforsymmetry energy Exoticnuclei Core collapse SN Note: HIC trajectoriesare non-equilibriumprocesses transporttheoryisnecessary but hasto check itsrobustness Extensive effortsby: - Microscopictheory - Neutron starobservations - HI experiments in thehadronicregime, onlywaytoinvestigatedenseneutron-rich matter in the lab

4. DL r Instabiitypoints Theoreticalfoundationoftransporttheory: based on a chainofapproximationsfrom real-time Green functions via Kadanoff-Baymeqs. to Boltzmann-Vlasoveq. (semi-classical , quasi-particleapprox.) Molecular-Dynamics-like (QMD/AMD) In practice: twofamiliesoftransportapproaches Boltzmann-Vlasov-like(BUU/BL/SMF) TD-Hartree(-Fock) (orclassicalmoleculardynamicswithextendedparticles, Hamiltonianeq. ofmotion) plus stochastic NN collisions Dynamics ofthe 1-body phasespacedistributionfunctionfwith 2-body dissipation (collisionterm, gainandloss) Solution withtestparticles, exactfor NTP∞ includefluctuationsarounddiss. solution Noquantumfluctuations, but classical N-bodyfluctuations, dampedbythesmoothing. Boltzmann- Langevineq.  amountcontrolledbywidthofsingleparticle packet DL f-space Will see, thatthe different amountoffluctuations accountsformuchofthe different behaviourof BUU and QMD

5. Status ofSymmetryEnergy Research successes Inconsistencies: example double ratioof n/p pre-equilibriumemiss. D.D.S.Coupland, et al., PRC94, 011601(R) (2016) ρ0 2ρ0 • H.J.Kong, et al., PRC91,047601 (2015) GW170817 Abbott et al. (2018) L=63±11 MeV SkM* L=46 MeV,mn*>mp* SLy4 L=46 MeV, mn*<mp* Reasonsfordifferencesoften not clear, sincecalculationsslightly different in thephysicalparameters. A needformoreconsistency in HI simulations.  thereforecomparisonofcalculationswithsame physicalinputand in simplifiedcases, i.e. undercontrolledconditions

6. Evolution of Code Comparison Project Steps • 2. Calculationsofnuclear matter (box withperiodicboundaryconditions) • testseparatelyingredients in a transportapproach: • a) collisiontermwithoutandwithblocking (Cascade) (MSU 2017) • Y.X. Zhang, et al., Phys. Rev. C 97, 034625 (2018) • b) p, Dproduction in Cascade (Busan 2018) • A. Ono, et al., PRC submitted, arXiv 1904.02888 • c) p,Dproduction in a full HIC : Sn+Sn, 270 AMeV • d) meanfieldpropagation (Vlasov) • e) instabilities , fragmentation ….. 1. Full heavy ioncollisions (Au+Au) a) highenergy ~1 AGeV: attentiontop,Kproduction (Trento 2004) E. Kolomeitsev, et al., J. Phys. G 31 (2005) S741 b) intermediate energy , 100, 400 AMeV, attentiontoflowand NN collisionrates (Trento 2009 and Shanghai 2014) J. Xu et al., Phys. Rev. C 93, 064609 (2016) -> considerablediscrepancies, but difficulttodisentangle done done in progress planned  19 codesofBUU- and QMD-type  non-rel. andrelativisticcodes  antisymmetrized QMD code: AMD, (CoMD)  BUU codeswith explicit fluctuations: SMF, BLOB  manynew Chinese codes: (I)QMD-XXX: muchnewactivity in China, originallycloselyrelated

7. Au+Auatb=7fm (midcentral) 400 AMeV, selectedcontourplots; different evolutionapparent quantifyspreadofsimulationsbyvalueofflowparameter =slopeoftransverseflowatmidrapidity BUU and QMD approx. consistent uncertainity 100 AMeV: ~30% 400 AMeV: ~13% Code ComparisonProject (1st stage): Differencesbetweencodesseen in - initialization, - densityevolution - collisionratesandblockingofcollisions -observables: flow Difficulttodisentangleoriginofdiscrepancies, sinceeffectsinteract

8. 2. Box calculationcomparison simulationofthestaticsystemof infinite nuclear matter,  solvetransportequation in a periodic box Usefulformanyreasons: - check thermodynamicalconsistencyofcalculation - check consistencyofsimulation: collisionnumbers, blocking, dissipationrelation,.. (oftenexactlimitsfromkinetictheory) - check different aspectsofsimulationseparately Cascade: onlycollisions without/withblocking Vlasov: onlymeanfieldpropagation - check strategiesforparticleproduction, e.g. pions Weconsider box calculations not asunrealisticphysicalsituation,butas an importanttool to understand transportsimulations Theyshouldleadto an improvementanddevelopmentoftransportapproaches: Thisisthethemeofthisworkshop

9. Collisionterm in box calculations no blocking collisionprobability Collisionrates in a cascade box calculation (w/o meanfield, T=0 and 5 MeV) withoutblocking Comparisontoexactlimit (vrelandaveragedepend on treatment ofrelativity) goodagreementwithcorrespondingexactresult collisionprobabilitygenerally ok -> but smalldeviations. Can one understand?

10. Collisionprobabilitiesand correlations N1 N2 Collisionprobability: - geometricalcriterion (Bertsch-Das Gupta, 1988) someissuesaboutreferenceframeandrelativisticeffectsforcalculationofand see Box-Cascadepaper, Phys. Rev. C97, 034625 (2018) - statisticalcriterionin a cell (pBUU) ormeanfreepathcriterion (SMF) (workslightlybetter) X N1 Correlationsbetweencollisions 1) particlesshould not collidetwice (crosssectionrepresents T-Matrix) N2 2) collisionofonepartnerwithanotherparticle X --> higher order correlation - enhancesinteractionwithgeometricalcriterion - not contained in classical Boltzmann result. Thusdifferences in comparisonwith „exact“ resultsplausible. - small in thiscase, but depends on time stepDt, increaseswithsmallerDt - physicaleffect ? (tobediscussed in workshop) - will bemoreimportantwhenparticleproductionconsidered (--> pions)

11. withblocking Sampling ofoccupation prob. in comp. toprescribed FD distribution (red) Simulation T=5 MeV 1st step time averaged kinetictheory (exact) widthandaveragesofcalculatedoccupationnumbers in different codes prescribedoccupation averagecalculatedoccupation averageof f<1 occupation (usedfortheblocking) - fluctuation in BUU controlledby TP number, canbe madearbritrarilysmall - fluctuation in QMD givenbywidthofwave packet Collisionrates - almost all codeshavetoolittleblocking, i.e. allowtoomanycollisions, - QMD codesmore, becauseof larger fluctuations Fluctuationsinfluencedynamicsoftransportcalculations. Howeverthe proper treatmentoffluctuations in transportisunderdebate.

12. Box simulations: test of m.f. dynamics (in progress) Maria Colonna • - Symmetric matter-- • Onlymean-fieldpotential • No surfaceterms • Compressibility K=240 and 500 MeV 1. Density oscillations in the stable regime, timeevolutionofρ(z); 2. Fourier transform in space, mode oscillation λ = 2π/k ρk (t) = ʃ dz sin(kz) ρ(z,t) k=k1 r(z,t=t0)= ρ0 + aρ sin(kiz) damping ki = ni 2π/L, aρ = 0.2 ρ frequency time evolution: strong damping 3. Fourier transform in time: extractresponsefunct., compare tolinearresponse ρk (t) ρk (ω) = ʃ dt cos(ωt) ρk(t) frequency example: SMF results damping ρk (ω) ω

13. Evolution ofdensityoscillation in different codes: --> differences in frequencyandamplitude detailat t=40 fm/c Seemstodepend on fluctuations, i.e. representationofphasespace. Test twospecificcodes: SMF changetestparticlenumber NTP ImQMDchangewidthofwave packet Dx

14. Timeevolutionof Fourier transformρk ρk (t) = ʃ dz sin(kz) ρ(z,t) Generally: strong damping - SMF (BUU-like, dashedcurves) smallernoof TP: moredamping, larger frequency - ImQMD (solid curves) decreasingwidthDxofwave packet: larger fluctuationsstrongerdamping larger effectiveforces larger frequencies SMF 40 TP SMF 1 TP ImQMD (Dx)2=.25 fm2 2 fm2 9 fm2 rk(t) [fm-2] Gradient along z-axis SMF: - Convergestoanalyticalresultwithincreasing TP number, - Dependence on TP number becauseof non-linearityofinteraction (r² term) ImQMD: - gradienttoolowforusualchoiceDx=2fm² - larger averagingthan in BUU - explainslowerfrequency Increasing NTP, smallerfluctuations ImQMDDx=0.25 fm2 Dx=2 fm2 Dx=9fm2 analytical SMF NTP=1 NTP=2 NTP=10 NTP=40 analytical IncreasingwidthDx smallerfluctuations, but moreaveraging

15. Timeevolutionof Fourier transformρk ρk (t) = ʃ dz sin(kz) ρ(z,t) Generally: strong damping - SMF (BUU-like, dashedcurves) smallernoof TP: moredamping, larger frequency - ImQMD (solid curves) decreasingwidthDxofwave packet: larger fluctuationsstrongerdamping larger effectiveforces larger frequencies SMF 40 TP SMF 1 TP ImQMD (Dx)2=.25 fm2 2 fm2 9 fm2 rk(t) [fm-2] Gradientsforcaseof K=500 MeVfor different codes: morestable, but systematicdiff, between BUU and QMD Increasing NTP, smallerfluctuations ImQMDDx=0.25 fm2 Dx=2 fm2 Dx=9fm2 analytical SMF NTP=1 NTP=2 NTP=10 NTP=40 analytical IncreasingwidthDx smallerfluctuations, but moreaveraging

16. Response fct. ρk (t) = ʃ dz sin(kz) ρ(z,t) ρk (ω) = ʃ dt cos(ωt) ρk(t) Fourier transformwithrespecttospace and time Fourier transformwithrespecttospace K=240 MeV SMF simulations without transient initialbehaviour n = 1 rk(w) [fm-1] n = 2 rk(t) [fm] n = 1, E ~ 18 MeV responsefunctioncomparison SMF-ImQMD (K=500 MeV) ImQMD rk(w) [arb. units] SMF Landau damping Fluctuationsstronglyinfluence propagationofcollectivemodes numerical damping

17. p,Dproduction in box cascadecalculation(arXiv1904.02888) Motivation: p+/p- ratioexpectedtobegood probe ofthehigh-densitysymmetryenergy expected but variouscalculations givevery different conclusions New feature: inelasticcollisions, pDdynamics dynamicsofparticleswith finite width Simplifysituationto understand differences: Box calculation, r=r0, T=60 MeV, asymmetryd=0., 0.2 Cascadecalculation: nom.f., no Pauli-blocking, standard x-sectionsandwidths NN ND NLK Np Exact: equilibrated ideal Boltzmann gas mixture orrate eq. (thermal but not chemicalequil.

18. Numbers ofD‘sandp‘s(thinblacklines: rate eqs.) In rathergoodagreementwithexactresult. Now turn on pproduction large differencesbetweenmodelsandexactresultwhenincludingD decay. However, wearereallyinterested in ratiosofpions. Perhapsbetter?

19. Ratiosofparticlenumbers (dashed: rate eq.) Thisisthep-/p+ratioobserved after all theD‘sdecay Dependence on time stepDt: 0.2 fm/c and time stepusedbythecodeforlatetimes, (twocodesaretimestepfree (collisionsorderedaccordingto linear extrapolationofpath)), tendencytoconvergeto rate eq. resultforDt-->0 . earlytimes, 10<t<30 fm/c; non-equilibriumphase, lesscloseto rate eq.

20. Ratiosofparticlenumbers (dashed: rate eq.) Thisisthep-/p+ratioobserved after all theD‘sdecay Dependenceof time stepDt: 0.2 fm/c and time stepusedbythecodeforlatetimes, (twocodesaretimestepfree (collisionsorderedaccordingto linear extrapolationofpath)), tendencytoconvergeto rate eq. resultforDt-->0 . • The p-likeratiofor all codesiswithin 5%! Consistencyofcodes in this observable, especially in the • limitDt-->0 • But weneedto understand betterthereasonforthediscrepanciesofthecodesandtheagreement • in theratio. • Twofactors: • Collision-decaysequence: strategy, howtheelastic, inelasticanddecaysaretreated in thesimulation • Correlationsbetweencollisions

21. Collision-decaysequencestrategies: In a given time step k thevariousreactionsareprocessed in a givensequence: Ck: elasticandinelasticcollisions: NN->NN, NN-<ND, ND->NN, Np->D, thus ND , Np Dk: decaysD->Np , thus ND , Np Someexamplesofstrategies: Particlenumbersrecordedat end ofcomputationalstep Collisionprocessed in sequence ofeventtimes, „time stepfree“, but morecomplicatedwith mf propagation SequenceCk, Dk: NDlow, Nphigh SequenceDk, Ck: Nplow, NDhigh Random, fixedlistofCk, Dk But producedp‘sareinactive, Nphigh Collision-decaysequencecaninfluenceparticleratios, andevenleadtoapparentsymmetryviolation Effectshoulddisappearfor time stepDt-> 0 (seenpartly in Dtdependence), but practicaldifficulties , andincreasedcorrelations (seenext)

22. Higher order correlations Alreadydiscussedaboveforonlyelasticscattering, but thereeffectsmall. More significantwhenparticlescanchangetheiridentities: Examplesofhigher order correlationswithD,p‘s.: RecreatesthedecayedDj, Increases ND Enhancestheprobabilityof a secondNiNjcollisiontoproduce a D. Increases ND EnhancestheprobabilityoftheNi‘Dj‘ collisiontodestroy a D. Decreases ND X • Consequences: • These correlationschangesthepandDratios, andcanleadtoisospinviolation • IncreasewithsmallerDt, sincethepartnersare still close after the intermediate collisionwith X • (becauseofgeometricalcollisioncriterion) • The importanceofthesevarioushigher order correlationsdepends on thecollision-decaysequence N1 N2 • Conclusionsfromthepion box studies • togetherthetwoeffectscanmakemostofthedifferencesbetweenthecodes plausible • randomizethecollision-decaysequenceandremovesomehigher-order correlations • It was not known in thisdetailbefore, that different strategies (whichare not fixedbytheequations) • affect observables significantly • somecodesalreadyimproved, others will improveas a consequenceofthisstudy (but not easilydone) • in thisstudytheimportantp-likeratioisrather robust, within 5% in theequilibratedregime. • hastobeseenhowthistranslatesintoactual HIC (in progress)

23. Summary -Transport approaches indispensable toextractphysicsinformationfrom heavy ioncollisions. Questions in theapplicationoftransporttheories: - physics(degreesoffreedom, fieldsand in-medium cross-sections, fluctuations, correlations, shortrange) - implementation: simulation, ratherthansolutionofthetransportequations - involvesstrategies , such as representationofthephasespace (fluctuations), criteriaforcollisions (e.g. geometrical) correlations, Pauli blocking - mayaffectthededuction on physicsfromcollisionsandleadto a kindofsystematicaltheoretical error - hereattemptto understand, quantifyandhopefullyreducetheseuncertainities in a Transport Code ComparisonunderControlledConditions Results: - Comparisonoffull HIC makes evident thediscrepancies, but difficulttodisentangle - Box calculationstostudythe different ingredientsoftransportseparately (collisionprobability, blocking, mf evolution, particleproduction) - Importantinfluenceoffluctuations on blockingand mf propagation - Higher order correlations, generatedbygeometricalstrategyaffectsparticleproduction - Fluctuationsandcorrelationsgobeyondtheone-bodydescription. Implementionsdiffer in BUU (explicit fluctuationterm) and QMD (classicalcorrelations + smoothingbywave packet) - quantumeffects(atlowenergy), off-shellofparticleswithspectralfct Extensionsof 1-body semi-classicaltransportapproachnecessary. Subjectofthisworkshop. Thankyoufortheattention

25. Momentumandmodedistributions Fluctuationsactas a disspativeforve (Reinhard, Ayik) SMF rk(n) (t) [fm-3] n Initial n=1, distributionatvarioustimes Dampingofinitialmode, diffusionintoothermodes

26. ρk (ω) = ʃ dt cos(ωt) ρk(t) ρk (t) = ʃ dz sin(kz) ρ(z,t) Fourier transformwithrespecttospace and time Fourier transformwithrespecttospace K=240 MeV SMF simulations without transient initialbehaviour n = 1 rk(w) [fm-1] n = 2 rk(t) [fm] ω / (k vF ) ~ 1 n = 1, E ~ 18 MeV - QMD-likemodels: appearstructureless, largedamping - BUU-likemodels: differences in frequency and damping verypreliminary ! rk(w) [fm-1] Fluctuationsstronglyinfluence propagationofcollectivemodes

27. p,Dproduction in box cascadecalculation (arXiv1904.02888) Motivation: p+/p- ratioexpectedtobegood probe ofthehigh-densitysymmetryenergy expected but variouscalculations givevery different conclusions New feature: inelasticcollisions, pDdynamics dynamicsofparticleswith finite width Simplifysituationto understand differences: Box calculation, r=r0, T=60 MeV, asymmetryd=0., 0.2 Cascadecalculation: nom.f., no Pauli-blocking, standard x-sectionsandwidths NN ND NLK Np Exact: equilibrated ideal Boltzmann gas mixture or rate eq. (thermal but not chemicalequil.

28. ratio of pion yields, Au+Au,0.4-1.2 GeV/A Esym r/r0 variousmodels blue: stiffersymmenergy red: softer symmenergy  noconsensus, evenon ordering Why Code Comparison? Failures B.A.Li, PRL 88, 192701 (2002) data FOPI Reasonsfordifferencesoften not clear, sincecalculationsslightly different in thephysicalparameters. A needformoreconsistency in HI simulations: examples  thereforecomparisonofcalculationswith same physicalinput, i.e. undercontrolledconditions

29. 1 + 1/F0 = s/2 ln[(s+1)/(s-1)] LinearizedVlasovequation stationarysolutions (oscillations)  extract the oscillationfrequency s = ω / (k vF ) Landau parameter F0 = K / (6 εF ) - 1 K = 240 MeV F0 = 0.1 analytical relation betweenoscillation frequencyand compressibilityK s stable regime Landau damping unstable regime Fluctuations are amplified  fragmentformation, interestingfor box comparison in the future s ~ 1 n = 1, E ~ 18 MeV --> Second roundofcalculationswith K=500 MeV

30. BUU BUU BUU withblocking QMD Sampling ofoccupation prob. in comp. toprescribed FD distribution (red) - fluctuation in BUU controlledby TP number, canbemadearbritrarilysmall - fluctuation in QMD givenbywidthof wave packet widthandaveragesofcalculatedoccupationnumbers in different codes prescribedoccupation averagecalculatedoccupation averageof f<1 occupation (usedfortheblocking)

31. Collisionrateswithblocking - almost all codeshavetoolittleblocking, i.e. allowtoomanycollisions, - QMD codesmore, becauseof larger fluctuations Simulation T=5 MeV 1st step time averaged kinetictheory (exact) Evolution ofmomentumdistributions - themomentumdistributionmoves awayfromthestable Fermi-Dirac distributiontowardstheclassical Maxwell-Boltzmann distribution (dottedline), - depending on collisionrates Fluctuationsinfluencedynamicsoftransportcalculations. Howeverthe proper treatmentoffluctuations in transportisunderdebate. time