Hagedorn States in Relativistic Heavy Ion Collisions

Transcription

1 Hagedorn States in Relativistic Heavy Ion Collisions Jacquelyn Noronha-Hostler Frankfurt Institute for Advanced Studies, Frankfurt am Main Excited Hadrons : February 25 th, 211 : Jefferson Lab Newport News, VA USA

2 Outline 1 Introduction:Hagedorn States 2 Transport Coefficients 3 Chem. Eq. Time 4 Thermal Fits 5 Conclusions

3 Hagedorn s Original Idea Hagedorn States "fireballs consist of fireballs, which consist of fireballs..." Proposed an exponentially increasing mass to explain spectra in p p and π p scattering Original model included hadronic states up to (1232) Broniowski,Florkowski,Glozman,PRD7,11753(24) Exponential mass spectrum Constant : energy of system, new particles, NOT Lead to Statistical Bootstrap Model: M ρ(m) = M A [ m 2 +(m ) 2] 5 4 e m dm

4 Comparison to Lattice Results = 196 MeV, M = 15 GeV, M = 2 GeV, A =.5 GeV 3 2, B = 25 GeV 4, and m = 5 MeV ΘT 4 Bielefeld-BNL-Columbia Collaboration (BBC) Lattice HS st Lattice HS TMeV BNL et al,prd77(28)14511; PRD8(29) TMeV

5 Comparison to Lattice Results Budapest-Marseille-Wuppertal Collaboration (BMW) 15GeV ρ(m) = 2GeV εt 4 st GeV 3 2 m [ m 2 + (.5GeV) 2] 5 e 176MeV dm 4 Lattice HS TMeV 14 Lattice 12 1 HS TMeV et 4 Fodor et al, JHEP 61, 89 (26); JNH et al, PLB 643, 46 (26) Lattice HS HS TMeV 2 2.5GeV.715 ρ(m) = 1.7GeV 252MeV em/252mev dm -no volume corrections Majumder and Muller,PRL15(21) Lattice HS st pt HS TGeV Lattice HS HS TMeV JNH, Jorge Noronha, Carsten Greiner

6 Volume Corrections p xv = ε xv = p pt (T ) 1 p pt(t ) 4B ε pt (T ) 1+ ε pt(t ) 4B T = s xv = n xv = T 1 p pt(t ) 4B s pt (T ) 1+ ε pt(t ) 4B n pt (T ) 1+ ε pt(t ) 4B

7 η/s in a Hadronic gas near T c JNH, Jorge Noronha, and Carsten Greiner, PRL13(29)17232 η/s can be rewritten: ( η = s) η HG +η HS tot s HG + s HS [ s (η ) = HG s HG + s HS s From kinetic theory arguments: η NR = 1 3 p i = m i v i = 3T m i λ i = τ i v i v i = 3T m i τ i = 1 Γ i most conservative estimate! ( η s) HS = HG + η ] HS s HG i n i p i λ i i T n iτ i s HS. (1)

8 Result: η/s Ηs BBC Η s BMW HRG HS 176 MeV HS M&M KSS TGeV JNH, Jorge Noronha, and Carsten Greiner, PRL13(29) TMeV JNH, Jorge Noronha, Carsten Greiner Because HS allow for η/s to drop to the KSS limit, it provides a smooth transition for hydro Sufficiently near T c, η/s can be close to the viscosity bound already in the hadronic phase!!!!

9 Theory: c 2 s c 2 s = dp/dε.3 BBC.4.3 BMW HS 176 MeV HS M&M cs 2.2 c s Ε 14 GeVfm 3 14 Note that c 2 s does not go to zero Ε 14 GeVfm 3 14

10 Strangeness Enhancement SPS SPS observed enhancement of anti-hyperons, multi-strange baryons, and kaons compared to pp-data Used binary collisions Binary strangeness production reactions π + p K + Λ (2) Binary strangeness exchange reactions K + p π + Λ (3) Gave small cross-sections QGP! Because strange quarks produced more efficiently by gluon fusion. P. Koch, B. Muller, and J. Rafelski Strangeness enhancement was considered a signal for QGP!

11 Strangeness Enhancement SPS Used multi-mesonic reactions For anti-protons p + N nπ (4) R. Rapp and E. Shuryak For anti-hyperons Σ, Λ+N nπ + K Ξ+N nπ + 2K Ω+N nπ + 3K Ȳ + N nπ + n K Ȳ (5) Giving the time scale τȳ := 1 1 = ΓȲ σ N Ȳ nπ+nȳ K vȳ N ρ B (6) assuming σ ρ Ȳ σ ρ p 5 mb, ρ B fm, and 3 v.5.6 c (typical for SPS) Time Scale τȳ 1 3 fm c (7) Fits within typical lifetime of fireball of 5-1 fm c! C. Greiner and S. Leupold.

12 Strangeness Enhancement RHIC At T = 17 MeV ρ eq B = ρeq B σv 3 mb c Time Scale.4 fm 3 τ B 1 fm c. (8) Too large!!! In fireball τ 4 fm c. Suggestions Born in Equilibrium? Near T c, extra large particle density overpopulated with pions and kaons? Overpopulation of (anti-)baryons, which cannot be killed off Hagedorn resonances?

13 Contribution of HS to Chemical Equilibrium Values Effective X = p, K, or Λ Ñ X = N X + i Effective π s Ñ π = N π + i N i X i N i n i X i and n i are calculated within a microcanonical model Liu, et.al. PRC68(23)2495, JPG3(24)S589, PRC69(24)542 N eq N Π eq N HS N eq Π, N eq Π,p p N eq Π,K K a N TMeV eq N p p eq N K K eq N a TMeV.5 shsstot T c 176 MeV T c 196 MeV eq N Π eq N HS N eq Π, N eq Π,p p N eq Π,K K b TMeV eq N p p TMeV eq N K K eq N b TMeV

14 Rate Equations for the Chem. Eq. Time of Hadrons nπ HS n π + X X dλ i dt dλ π dt dλ X X dt ( ( = Γ i,π B i,n λ n π λ i )+Γ i,x X n = ( ) N eq i Γ i,π N eq λ i n i B i,n nλ n π i π n + Γ i,x X n i,x Neq ( i N eq λ i λ n i,x π λ 2 X i π X = N eq ( ) i Γ i,x X N eq λ i λ n i,x π λ 2 X X i X X λ n i,x π ), λ 2 X X λ i ), λ = N N eq, N is the total number of each particle, its equilibrium value is N eq.

15 Time Scale Estimates Naively, we would assume N π N eq π and N i N eq i, then dλ X X dt = i Γ i,x X N eq ( i N eq X X = N eq i Γ i,x X N eq i X X ( ) ( φ+1 exp 2t φ 1 λ X X = ( φ+1 φ 1 where φ := λ X X() and τ X X := ) exp λ i λ n i,x π ( ) 1 λ 2 X X τ ( X X 2t τ X X ) + 1 ) 1 N eq X i X Γ < 1 fm i,x X Neq c i λ 2 X X Only true when the pions and the resonances are held in equilibrium! ) Time Scalefmc Time Scalefmc a Τ p p Τ K K Τ Τ TMeV 1 8 b Τ p p Τ K K Τ Τ TMeV

16 Fireball Expansion Use an isentropic expansion... Find T(t) for the 5% most central collisions S π N π dnπ dy = s(t)v(t) = const. dy Volume V eff (t t ) = π ct (r + v (t t )+.5a (t t ) 2) 2 Time [fm/c] v =.3, a =.35 v =.5, a =.25 v =.7, a = Temperature [MeV] 12

17 Particle Ratios = 176 MeV p Π K Π a eq IC 2.4 IC IC IC TMeV a eq IC 2 IC.5 IC 3 1 IC Π Π a eq IC 2 IC IC 3 1 IC TMeV eq IC 2 IC 4 a.12 IC 1 IC

18 Particle Ratios = 196 MeV p Π K Π b eq IC 2 IC IC 3 1 IC TMeV b.2 eq IC 2 IC IC 3 1 IC Π Π b eq IC 2 IC IC 3 1 IC TMeV b eq IC 2 IC IC 3 1 IC

19 Summary Graph: Dynamic Chem. Eq. with HS Dividing Γ i by IC 1 =176 MeV IC 2 =176 MeV IC 3 =176 MeV IC 4 =176 MeV IC 1 =196 MeV IC 2 =196 MeV IC 3 =196 MeV IC 4 =196 MeV IC 1 =176 MeV IC 2 =176 MeV IC 3 =176 MeV IC 4 =176 MeV IC 1 =196 MeV IC 2 =196 MeV IC 3 =196 MeV IC 4 =196 MeV.1 Dividing Γ i by 4 p/π K/π Λ/π Ω/π.1 p/π K/π Λ/π Ω/π IC 1 =176 MeV IC 2 =176 MeV IC 3 =176 MeV IC 4 =176 MeV IC 1 =196 MeV IC 2 =196 MeV IC 3 =196 MeV IC 4 =196 MeV.1.1 p/π K/π Λ/π Ω/π

20 Comparison of Thermal Fit with Hagedorn States JNH, et al.,prc82(21)24913 No Hagedorn States Hagedorn States RHIC 2 GeV Au+Au RHIC 2 GeV Au+Au with HS T=16.4 MeV µ=22.9 MeV χ 2 =21.2 STAR PHENIX 1-2 T=165.9 MeV µ=25.3 MeV χ 2 =2.9 (T c =196 MeV) T=172.6 MeV µ=39.7 MeV χ 2 =17.8 (T c =176 MeV) 1-3 π - /π + p/p Κ /Κ + Κ + /π + p/π + (Λ+Λ)/π 1-3 π - /π + p/p Κ /Κ + Κ + /π + p/π + (Λ+Λ)/π χ 2 = 21.6 Fit without Hagedorn States Matches other thermal fit models well: T ch = MeV and µ b = 2 3 MeV (PLB518,41(21);PRC65,6495(22); arxiv:nucl-th/4568; Nucl.Phys.A757,12(25); Nucl. Phys. A 772, 167 (26) PRC78,5491(28)) χ 2 = 17.8 Fit with = 176 MeV χ 2 = 2.9 Fit with = 196 MeV

21 Quest for Branching Ratios BSQ-Canonical Model: M. Beitel, JNH, C. Greiner Up until now we have been limited by the branching ratios of the Hagedorn states Using a canonical model that conserves baryon number (B), strangeness (S), and charge (Q), we are able to calculate the average number of X that a large resonance can decay into. Mesonic, non-strange cluster at T=16 MeV B=2, S=, Q=2 cluster at T=16 MeV <N> Λ Σ + Ξ - Ω M HS [GeV] <N> Λ Σ + Ξ - Ω M HS [GeV]

22 Conclusions Conclusions We showed that the exponentially increasing Hagedorn spectrum (a property of QCD) may already account for the near perfect fluid behavior of hadronic matter close to T c Hagedorn states are catalysts for quick dynamical reactions that can explain short chemical equilibrium times at RHIC, consistent with thermal fits. Thus, the hadrons do not need to be "born in equilibrium." As of yet they have shown little effects on the thermal fits.

23 Outlook Outlook Include Hagedorn States in transport models (such as UrQMD) Consider effects of Hagedorn states at larger baryonic chemical potential (QCD critical point???) Consider strange and/or baryonic Hagedorn states (either for chemical equilibrium times or at large µ b ) Is strangeness enhancement really a signature of QGP or can it be described entirely by dynamical reactions within the hadronic phase?

24 Decay Width Linear fit (PDG) Γ i =.15m i 58 = 25 1 MeV multiplicity 4 2 HS π E (GeV) 1 HS K MeV exp fit lo high MMeV X X (microcanonical) HS p HS n HS Λ Notation.6 ε=.75gev/fm 3.4 ε=.5gev/fm 3.2 ε=.25gev/fm Γ i,x X = X Γ i Γ i,π = Γ i Γ i,x X C. Greiner et al., J.Phys.G31:S725-S732,25. B.6 to.4 K.4 to.5 Λ.1 to.2

25 Branching Ratios Branching ratios for nπ HS are described by a Gaussian distribution B i,n 1 e (n n i ) 2 2σ i 2 σ i 2π Average pion number (Liu, Werner, Aichelin, Phys. Rev. C 68, 2495 (23).) Standard deviation n i = m i m p σ 2 i = (.5 m i m p ) 2 After cutoff n 2, n i 3 to 9 and σ 2 i.8 to 11 For HS n π + X X, n i,x = 2 4