Melting and freeze-out conditions of hadrons in a thermal medium. Juan M. Torres-Rincon

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1 Melting and freeze-out conditions of hadrons in a thermal medium Juan M. Torres-Rincon Frankfurt Institute for Advanced Studies Frankfurt am Main, Germany in collaboration with J. Aichelin, H. Petersen, J-B. Rose and J. Tindall Strangeness in Quark Matter 2017 conference July 14, 2017 Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 1/18

2 Hadron chemical freeze-out Chemical freeze-out No more inelastic collisions total yield per species (approx.) fixed T ch = 174 MeV, µ B,ch = 46 MeV Statistical Thermal Model Cleymans and Satz, Z.Phys.C57 (1993) 135 Braun-Munzinger et al. PLB518 (2001) 41 Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 2/18

3 Tensions in T ch particle ratio Pb-Pb s NN =2.76 TeV Preliminary Multistrange hadrons prefer larger T ch (also in STAR data ) Data: ALICE, 0-20% (preliminary) Model calc. with parameters: T=148 MeV, ( = 1 MeV fixed) b T=164 MeV, = 1 MeV b T ch (nonstrange) = 148 MeV T ch (multistrange) = 164 MeV K + / K / p/ p / / / / + - / Preghenella et al. [ALICE Coll.] Acta Phys. Pol.B (2012), Abelev et al. [ALICE Coll], PRL109, (2012) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 3/18

4 Tensions in T ch particle ratio Pb-Pb s NN =2.76 TeV Preliminary Multistrange hadrons prefer larger T ch (also in STAR data ) Data: ALICE, 0-20% (preliminary) Model calc. with parameters: T=148 MeV, ( = 1 MeV fixed) b T=164 MeV, = 1 MeV b T ch (nonstrange) = 148 MeV T ch (multistrange) = 164 MeV K + / K / p/ p / / / / + - / Preghenella et al. [ALICE Coll.] Acta Phys. Pol.B (2012), Abelev et al. [ALICE Coll], PRL109, (2012) 1 Missing hadronic resonances in thermal models (see S. Chatterjee talk) 2 Use of non-equilibrium distributions (see V. Begun talk) 3 Flavor-dependent freeze-out temperature (see S. Chatterjee and P. Alba talks) Chatterjee et al. PLB 727 (2013) 554 Alba et al. PLB 738 (2014) 305 Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 3/18

5 Deconfinement transition Similar difference in susceptibilities computed by lattice QCD χ uds ijk = ( µ u T i+j+k ) i ( µ d T ) j ( µ s T ) k ( P T 4 ) strange quark χ 4 /χ 2 light quark χ 4 /χ 2 HRG prediction for the strange quark for the light quarks T [MeV] χ 2 u cont. χ 2 s cont. Borsanyi et al. JHEP 1201 (2012) 138 also Bellwied et al. PRD 92, (2015) T [MeV] See talk by R. Bellwied Bellwied et al. PRL111 (2013) T light 145 MeV, T strange 160 MeV Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 4/18

6 Outline Question Additional indications for sequential deconfinement and freeze-out temperatures? Methodology Use simple systems where these quantities can be extracted unambiguously 1. Deconfinement temperature Melting (or Mott) temperature in the PNJL model of QCD 2. Freeze-out temperature Decoupling temperature in an expanding system using a transport model Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 5/18

7 Outline Question Additional indications for sequential deconfinement and freeze-out temperatures? Methodology Use simple systems where these quantities can be extracted unambiguously 1. Deconfinement temperature Melting (or Mott) temperature in the PNJL model of QCD 2. Freeze-out temperature Decoupling temperature in an expanding system using a transport model Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 6/18

8 Nambu-Jona-Lasinio model We use an effective model model of QCD: Nambu-Jona-Lasinio model Limited to low energies, but valid at finite T and µ B Effective Lagrangian L int = g [ q i γ µ T a δ ij q j ] [ q k γ µt a δ kl q l ] + six-point t Hooft interaction Flavor: i, j = 1...N f = 3 ; T a : Gell-Mann matrices a = 1...N 2 c 1 = 8 Reviews: Vogl, Weise (1991), Klevansky (1992), Ebert, Reinhardt, Volkov (1994), Hatsuda, Kunihiro (1994), Buballa (2004)... Gluonic contribution via the Polyakov loop effective potential: PNJL model Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 7/18

9 Generation of mesons MESONS via Bethe-Salpeter equation for qq JMTR, B. Sintes and J. Aichelin, PRC91 (2015), G meson(p 0, p) = K 1 KΠ(p 0, p) 1 KΠ(M meson iγ meson/2, 0) = 0 pole R Stable meson T < T Mott pole C Unstable meson T > T Mott Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 8/18

10 Generation of baryons DIQUARKS via Bethe-Salpeter equation for qq C C C C C C C C C C C Baryon = Diquark + Quark G baryon (p 0, p) = G 0 + G 0ZG baryon (p 0, p) C C = + Baryon masses G baryon (p 0, p) = G 0 1 G 0Z 1 G 0Z(p 0 = M baryon, p = 0) = 0 JMTR, B. Sintes and J. Aichelin, PRC91 (2015), Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 9/18

11 Hadron melting temperatures in the PNJL model JMTR, B. Sintes and J. Aichelin, PRC91 (2015), mass (MeV) Ξ Σ Λ p temperature (MeV) mass (MeV) f rep. 10 f rep. 200 Ω * Ξ * Σ temperature (MeV) Meson π K η η ρ K ω φ T Mott (MeV) Baryon p Λ Σ Ξ Σ Ξ Ω T Mott (MeV) T Mott (Ξ) T Mott (Ω) > T Mott (p) (as suggested by thermal fits) T Mott (φ) abnormally large. Small T Mott (Σ) due to threshold proximity Multistrange states have larger T Mott (except Ξ ) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 10/18

12 Outline Question Additional indications for sequential deconfinement and freeze-out temperatures? Methodology Use simple systems where these quantities can be extracted unambiguously 1. Deconfinement temperature Melting (or Mott) temperature in the PNJL model of QCD 2. Freeze-out temperature Decoupling temperature in an expanding system using a transport model Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 11/18

13 Freeze-out temperatures Realization of freeze-out process in a simple system Inspiration comes from Cosmology: thermal history of the universe Dynamical extraction of decoupling condition Scattering rate: Γ = nσ v n: density σ: cross section v : relative velocity Hubble rate: H = 1 da(t) a(t) dt a(t): scale factor t: time time Friedmann-Robertson-Walker metric: ds 2 = dt 2 a 2 (t)(dx 2 + dy 2 + dz 2 ) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 12/18

14 Simulating Many Accelerated Strongly-interacting Hadrons SMASH is a new transport approach to simulate low-energy HICs (J. Weil et al. Phys.Rev. C94 (2016) no.5, ) Applied to strangeness, dileptons+photons, collectivity signatures, transport coefficients... HERE: Expanding box on a FRW spacetime Perfect agreement with known exact solutions of Boltzmann equation J. Tindall, JMTR, J.B. Rose and H. Petersen, PLB770 (2017) 532 D. Bazow, G.S. Denicol, U. Heinz, M. Martinez and J. Noronha, PRL 116 (2016) time Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 13/18

15 Application: Decoupling of particles Single species interacting via binary collisions (constant σ) Equilibrium reached and maintained if Γ H Freeze-out (Γ = H) takes place between t = 5 fm and t = 20 fm t = 0.1 fm t = 5 fm t = 20 fm J. Tindall et al. PLB770 (2017) 532 f equilibrium (t, k) = g k 2 +m 2 µ(t) (2π) 3 e T (t) Not in equilibrium! Γ < H 2 parameters fixed by conservation of particle number and entropy per particle Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 14/18

16 Freeze-out time Fit at t = 20 fm to frozen distribution for t > t D ( ) 2 ( f freeze out (t, k) = f equilibrium t D, k a(t) ) k a(t) exp a D a D + m 2 T D momentum redshift a D a(t D ) ; T D T (t D ) t D = 5.3 ± 0.6 fm t = 20 fm Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 15/18

17 Toy model for freeze-out Indications for a sequential freeze-out in our toy model: t D (fm) 6 4 t D (fm) m (GeV) σ (mbarn) J. Tindall, JMTR, J.B. Rose and H. Petersen, PLB770 (2017) 532 Earlier freeze-out (higher temperature) for more massive particles Later freeze-out (lower temperature) for states with larger cross section To improve for HICs: 1 Hadronic mixture + physical interactions 2 Realistic model for a(t) e.g. Blast-wave model Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 16/18

18 Conclusions Using the PNJL model we have computed the mass of mesons and baryons as functions of the temperature Multistrangeness particles (φ, Ξ, Ω) have a higher Mott temperatures than nonstrange hadrons Melting temperature depends on flavor content but does not follow a clear pattern A toy model for decoupling is implemented in SMASH transport code, where freeze-out can be determined with precision Clear dependence of the freeze-out time (temperature) on mass and cross section We obtain indications for a sequential freeze-out, but more refined investigations are needed to decide how important is the effect in HICs Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 17/18

19 Melting and freeze-out conditions of hadrons in a thermal medium Juan M. Torres-Rincon Frankfurt Institute for Advanced Studies Frankfurt am Main, Germany in collaboration with J. Aichelin, H. Petersen, J-B. Rose and J. Tindall Strangeness in Quark Matter 2017 conference July 14, 2017 Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 18/18

20 Tension in multistrangeness multiplicities at STAR 1 0,1 Ratios 0,01 0, GeV STAR data T=146 MeV, µ B =24.3 MeV T=166 MeV, µ B =24.3 MeV 0,0001 π /π + K - /K + p /p Λ /Λ Ξ + /Ξ K + /π + K - /π p/π Λ/π Ξ /π Ω/π Figure taken from Alba et al. PLB 738 (2014) 305 Feed-down corrected ratios taken from Andronic et al. NPA (2013) 535c Blue param: Cleymans et al. PRC73 (2006) Go back ) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 1/6

21 Tension in multistrangeness multiplicities at ALICE Figure taken from Bellwied, JoP:CS 736 (2016) LHC Data from Floris: NPA931, 103 (2014) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 2/6

22 NJL for mesons Exchange Lagrangian: accounts for mesons Pseudoscalar mesons L ex = G ( q i τ a ij I ciγ 5 q j ) ( q k τ a kl I ciγ 5 q l ) ; G = (N 2 c 1)/N 2 c g I c: color singlet interaction τ a : flavor generators a = (N f = 3). (Other terms not shown, e.g. the one accounting for scalar mesons iγ 5 I) The effective Lagrangian should share the global symmetries of (massless) QCD: Symmetries of massless NJL model SU V (3) SU A (3) U V (1) U A (1) In our scheme, chiral symmetry is explicitly broken to SU V (3) by the bare quark masses. We keep an isospin SU V (2) symmetry. The U A (1) is broken by quantum effects. Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 3/6

23 Polyakov-NJL Model Gluon (static) properties are implemented in the model through an effective potential for the Polyakov loop U(T, Φ, Φ) = b2(t ) T 4 2 ΦΦ b3 6 ( Φ 3 + Φ 3) + b4 4 ( ΦΦ) 3 b 2(T ) = a 0 + a 1 T 0 T + a2 ( T0 T ) 2 ( ) 3 T0 + a 3 T a 0 = 6.75, a 1 = 1.95, a 2 = 2.625, a 3 = 7.44, b 3 = 0.75, b 4 = 7.5 from fit to lattice-qcd results of gluodynamics and T 0 = 190 MeV. 1.0 Φ is the order parameter of the deconfinement transition ( Φ = 1 N c Tr c P exp β ) dτa0(x, τ) 0 Φ temperature (MeV) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 4/6

24 Mesons at finite temperature masses (MeV) m q +m s 2 m q η' η K π Pseudoscalar mesons in the NJL model at µ = T (MeV) Pion mass (blue line) and decay width (grey band) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 5/6

25 Chiral symmetry restoration Restoration of chiral symmetry at large temperatures mass (MeV) a 1 ρ f 0 =σ π T (MeV) Juan M. Torres-Rincon Melting and freeze-out conditions of hadrons in a thermal medium 6/6