Enhancement of hadronic resonances in RHI collisions

1. Enhancement of hadronic resonances in RHI collisions Inga Kuznetsova and Johann Rafelski • We explain the relatively high yield of charged Σ±(1385) reported by STAR • We show if we have initial hadrons multiplicity above equilibrium the fractional yield of resonances A*/A (A*→Aπ) can be considerably higher than expected in SHM model of QGP hadronization. • We study how non-equilibrium initial conditions after QGP hadronization influence the yield of resonances. Department of Physics, University of Arizona Work supported by a grant from: the U.S. Department of Energy DE-FG02-04ER4131

2. Time evolution equation for NΔ, NΣ Δ(1232) ↔ Nπ, width Γ≈120 MeV (from PDG); Σ(1385)↔Λπ ,width Γ ≈ 35 MeV (from PDG). Reactions are relatively fast. We assume that others reactions don’t have influence on Δ (Σ) multiplicity. and are Lorentz invariant rates

3. Phases of RHI collision • QGP phase; • Chemical freeze-out (QGP hadronization); • We consider hadronic gas phase between chemical freeze-out (QGP hadronization) and kinetic freeze-out; the hadrons yields can be changed because of their interactions; M. Bleicher and J.Aichelin, Phys. Lett. B, 530 (2002) 81 M. Bleicher and H.Stoecker,J.Phys.G, 30, S111 (2004) • Kinetic freeze-out: reactions between hadrons stop; • Hadrons expand freely (without interactions).

4. Motivations • How resonance yield depends on the difference between chemical freeze-out temperature (QGP hadronization temperature) and kinetic freeze-out temperature? • How this yield depends on degree of initial non-equilibrium? • Explain yields ratios observed in experiment .

5. Distribution functions for in the rest frame of heat bath Multiplicity of resonance: where xi=mi /T; K2(x) is Bessel function; giis particle i degeneracy; Υiis particle fugacity, i = N, Δ, Σ, Λ;

6. Equations for Lorentz invariant rates

7. Bose enhancement factor: Fermi blocking factor: using energy conservation and time reversal symmetry: we obtained:

8. We obtained: I. Kuznetsova, T. Kodama and J. Rafelski, ``Chemical Equilibration Involving Decaying Particles at Finite Temperature '' in preparation. • Equilibrium condition: • is global chemical equilibrium. • If in initial state then Δ production is dominant. • If in initial state then Δ decay is dominant.

9. We don’t know decay rate, we know decay width or decay time in vacuum τΔvac =1/Γ. We can write time evolution equation as where is decay time in medium For Boltzmann distributions: We assume that no medium effects, τΔ≈τΔvac

10. Model assumptions • Δ(1232) ↔ N π is fast. Other reactions do not influence Δ yield or • The same for Σ(1385)↔Λπ • Large multiplicity of pions does not change in reactions • Most entropy is in pions and entropy is conserved during expansion of hadrons as

11. Equation for ΥΔ(Σ) τis time in fluid element comoving frame.

12. Expansion of hadronic phase • Growth of transverse dimension: • Taking we obtain: is expansion velocity At hadronization time τh:

13. Solution for ΥΔ Using particles number conservation: Δ + N = N0tot we obtain equation : where The solution of equation is:

14. Non-equilibrium QGP hadronization • γq is light quark fugacity after hadronization • Entropy conservation fixes γq (≠1). • Strangeness conservation fixes γs (≠1). • γq is between 1.6 for T=140 MeV and 1 for T=180 MeV; • Initially and Δ (Σ) production is dominant

15. Temperature as a function of time τ

16. The ratios NΔ/NΔ0, NN/NN0 as a function of T • NΔincreases during expansion after hadronization when γq>1 (ΥΔ< ΥNΥπ) until it reaches equilibrium. After that it decreases (delta decays) because of expansion. Opposite situation is with NN. If γq =1, there is no Δ enhancement, Δ only decays with expansion.

17. NΔ/Ntot ratio as a function of T. • Ntot (observable) is total multiplicity of resonances which decay to N. • Dot-dashed line is if we have only QGP freeze-out. • Doted line (SHARE) is similar to dot-dashed line with more precise decays consideration. • There is strong dependence of resulting ratio on hadronization temperature.

18. NΣ/Λtot ratio as a function of T Observable: Effect is smaller than for Δ because of smaller decay width Experiment: J.Adams et al. Phys.Rev. Lett. 97, 132301 (2006) S.Salur, J.Phys.G, 32, S469 (2006)

19. Future study • Γ≈ 150 MeV; Γ≈50 MeV Γ≈170 MeV

20. Conclusions • If we have initial hadrons multiplicity above equilibrium the fractional yield of resonances A*/A can be considerably higher than expected in SHM model of QGP hadronization. • Because of relatively strong temperature dependence, Δ/Ntot can be used as a tool to distinguish the different hadronization conditions as chemical non-equilibrium vs chemical equilibrium; • We have shown that the relatively high yield of charged Σ±(1385) reported by STAR is well explained by our considerations and hadronization at T=140 MeV is favored.