Hadron Resonance Gas Model

Hadron Resonance Gas Model Valentina Mantovani Sarti QGP lectures-torino 2016 6 April 2016 V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 1 / 6

References Particle production in heavy ion collisions, P. Braun-Munzinger, K. Redlich, J. Stachel (nucl-th/0304013v1) Properties of hot and dense matter from relativistic heavy ion collisions, P.Braun Munzinger, V. Koch et al. (nucl-th1510.00442) An Introduction to the statistical hadronization model, F. Becattini (arxiv:0901.3643) Hadron Production and Phase Changes in Relativistic Heavy Ion Collisions J.Letessier, J.Rafelski (nucl-th0504028) Production of light nuclei, hypernuclei and their antiparticles in relativistic nuclear collisions A. Andronic et al. (arxiv:1010.2995) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 2 / 6

Introduction the HRG model is somehow the upgraded version of the Hagedorn model main input provided by experimentally measured states from a continuous (ρ(m)) to a discrete spectrum factorization of the partition function Z into single particle contributions remarkable agreement with LQCD calculations in the low T regime WB Collaboration HotQCD Collaboration V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 3 / 6

Introduction the HRG model is somehow the upgraded version of the Hagedorn model main input provided by experimentally measured states from a continuous (ρ(m)) to a discrete spectrum factorization of the total partition function Z into single particle contributions remarkable agreement with experimenatal observables as particle yields/particle ratios (chemical freeze-out) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 3 / 6

Thermodynamics of HRG based on the assumption of thermal equilibrium of a system composed by FREE HADRONS AND RESONANCES resonances are indeed the essential d.o.f near deconfinement formation and decay of resonances as an approximation, at the thermodynamical level, of strong interactions properties and quantum numbers from measured excited states (PDG) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 4 / 6

Thermodynamics of HRG The thermodynamical quantities ln Z(T, µ, V ) = R Z R (T, µ, V ) = B Vg B (2π) 3 d 3 p ln[1 + λ B exp( ɛ B /T )] + M Vg M (2π) 3 spin-degeneracy g R, ɛ R = p 2 + mr 2 and fugacity λ R = exp(µ R /T ) = exp[(b R µ B + Q R µ Q + S R µ S )/T ] d 3 p ln[1 λ M exp( ɛ M /T )] V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 4 / 6

Thermodynamics of HRG P = T ln Z V n R = 1 V = g RT (2π 3 ) ln Z µ R T = g R (2π 3 ) d 3 p ln[1 + ( 1) B R +1 exp[(ɛ R µ R )/T ]] d 3 1 p exp[(ɛ R µ R )/T ] + ( 1) B R +1 The free parameters of the model temperature T and chemical potentials (µ B, µ Q, µ S ) strong interactions conservation of BQS charges constraints on µ Q and µ S provided by the experimental initial conditions of colliding nuclei ρ Q (T, µ B, µ Q, µ S ) = Z A ρ B(T, µ B, µ Q, µ S ) ρ S (T, µ B, µ Q, µ S ) = 0 only two model parameter (T, µ B ), BUT THE DEPENDENCE OF (µ S, µ Q ) ON THESE PARAMETERS STRONGLY DEPENDS ON THE RESONANCE SPECTRUM V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 4 / 6

Thermodynamics of HRG only two model parameter (T, µ B ), BUT THE DEPENDENCE OF (µ S, µ Q ) ON THESE PARAMETERS STRONGLY DEPENDS ON THE RESONANCE SPECTRUM Karsch (arxiv:1404.6511 [hep-lat]) Ratti QM2015 in general the hadron mass spectrum contains contributions up to 2 GeV inclusion of higher resonances, especially at high temperatures, is not negligible (poorly known) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 4 / 6

Comparison to experimental data: Partial Chemical Equilibrium description of the low temperature regime not accessible by lattice chemical freeze-out stage fully determined by (T, µ B ) good agreement between particle yields/ratios data and HRG system in thermal equilibrium in a very broad energy range ( s NN few GeV TeV ) stable hadrons lifetime longer than 10 fm/c (which survive and are measured at the detectors) physical properties and quantum numbers of measured resonances are crucial V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 5 / 6

Comparison to experimental data: Partial Chemical Equilibrium the main goal is to compare results from HRG to experimental data only a window of phase space is available cuts in rapidity y/pseudorapidity η, cuts in p t See VMS, Alba, Ratti et al. Phys.Lett.B738(2014)305 310 Some misunderstanding about HRG: does not contain info about the hadronization mechanism does not provide dynamical observables nor a time evolution of the chemical equilibrium (static approach) does not refer to a possible pre- hadronic phase V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 5 / 6

Comparison to experimental data: Partial Chemical Equilibrium Modifications 1 Suppression factor γ S for non-equilibrium of strange hadrons(becattini, Manninen et al. arxiv:hep-ph/0310049) slightly below unity and no statistically significant at mid-rapidity fits: exp( µ q R ) exp( µ q R )γ n S S 2 other non-equilibrium parameters (γ Q 1 for light quarks) do not lead to significant improvements (Letessier, Rafelski arxiv:nucl-th/0504028) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 5 / 6

Comparison to experimental data: Partial Chemical Equilibrium Modifications 1 Suppression factor γ S for non-equilibrium of strange hadrons(becattini, Manninen et al. arxiv:hep-ph/0310049) slightly below unity and no statistically significant at mid-rapidity fits: exp( µ q R ) exp( µ q R )γ n S S 2 other non-equilibrium parameters (γ Q 1 for light quarks) do not lead to significant improvements (Letessier, Rafelski arxiv:nucl-th/0504028) 3 repulsive interactions between hadrons Excluded Volume, namely each meson and baryon excludes a spherical volume with radius R M or R B (Rischke, Gorenstein et al. Z.Phys.C 51, 485 489, 1991) P excl. (T, µ) = P id. (T, µ V 0 P excl (T, µ)),, V 0 = 4 3 πr3 at LHC: R M = R B = 0.3 fm. V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 5 / 6

Applications of HRG model 1 to provide information on the underlying thermodynamic quantities characterizing the hadronic medium at freeze-out Chemical Freeze-Out Parameters (T, µ B ) INPUT: hadron spectrum, experimental data on yields/ratios OUTPUT: values of (T, µ B ) FO as a function of s NN (codes: THERMUS, SHARE) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 6 / 6

Applications of HRG model 1 to provide information on the underlying thermodynamic quantities characterizing the hadronic medium at freeze-out Chemical Freeze-Out Parameters (T, µ B ) INPUT: hadron spectrum, experimental data on yields/ratios OUTPUT: values of (T, µ B ) FO as a function of s NN (codes: THERMUS, SHARE) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 6 / 6

Applications of HRG model 1 to provide information on the underlying thermodynamic quantities characterizing the hadronic medium at freeze-out Chemical Freeze-Out Parameters (T, µ B ) INPUT: hadron spectrum, experimental data on yields/ratios OUTPUT: values of (T, µ B ) FO as a function of s NN (codes: THERMUS, SHARE) TENSION BETWEEN LIGHT AND STRANGE HADRONS V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 6 / 6

Applications of HRG model in recent years the study of fluctuations of conserved charges has become a complementary tool in the freeze-out analysis: V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 6 / 6

Applications of HRG model analysis based on net-proton and net-charge fluctuations with STAR data: proton puzzle at LHC behaviour of light and strange hadrons (flavour hierarchy??) V.Mantovani Sarti Hadron Resonance Gas Model 6 April 2016 6 / 6