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Kinetics of hadron resonances during hadronic freeze-out

Kinetics of hadron resonances during hadronic freeze-out. Inga Kuznetsova Department of Physics, University of Arizona Workshop on Excited Hadronic States and the Deconfinement Transition February 23-25, 2011 Thomas Jefferson National Accelerator Facility Newport News, VA.

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Kinetics of hadron resonances during hadronic freeze-out

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  1. Kinetics of hadron resonances during hadronic freeze-out Inga Kuznetsova Department of Physics, University of Arizona Workshop on Excited Hadronic States and the Deconfinement TransitionFebruary 23-25, 2011Thomas Jefferson National Accelerator FacilityNewport News, VA I. Kuznetsova and J. Rafelski, Phys. Lett. B, 668 105 (2008) [arXiv:0804.3352]. I. Kuznetsova and J. Rafelski, Phys. Rev. C ,79, 014903 (2009) [arXiv:0811.1409] I. Kuznetsova and J. Rafelski Phys. Rev. C, 82, 035203 (2010) [arXiv:1002.0375 ]. Work supported by a grant from: the U.S. Department of Energy DE-FG02-04ER4131

  2. Phases of RHI collision • QGP (deconfinement) phase; • Chemical freeze-out (QGP hadronization), hadrons are formed; (140 <T0 <180 MeV) • Hadronic gas (kinetic) phase, hadrons interact; • Kinetic freeze-out: reactions between hadrons stop; • Hadrons expand freely (without interactions, decaying only). We study how strange and light resonance yields change during the kinetic phase. Final yields of ground state p, n, π, K, Λ do not change compared to statistical hadronization model. Workshop on Excited Hadronic States and Deconfinement transition

  3. Motivation We explain high ratio Σ(1385)/Λ0 reportedat RHIC (S.Salur, J.Phys. G 32, S469 (2006)) and Λ(1520)/Λ0 suppression reported in both RHIC and SPS experiments. (J. Adams et al., Phys. Rev. Lett. 97, 132301 (2006)[arXiv:0604019]; C. Markert [STAR Collaboration], J. Phys. G 28, 1753 (2002) [arXiv:nucl-ex/0308028].). We predict ∆(1232)/N ratio. Westudy φ meson production during kinetic phase in KK→ φ. By suppression (enhancement) here we mean the suppression (enhancement) compared to scaledpp (or low number of participants) collisions, and to the chemical SHM (statistical hadronization model) without kinetic hadronic gas phase. We study how non-equilibrium initial conditions after QGP hadronization influence the yield of resonances. How does resonance yield depend on the difference between chemical freeze-out temperature (QGP hadronization temperature) and kinetic freeze-out temperature? Workshop on Excited Hadronic States and Deconfinement transition

  4. Kinetic phase We assume that hadrons are in thermal equilibrium (except probably very high energy pions, which may escape). Resonances have short lifespan (width Γ(1/τ) ≈ 10- 200 MeV) Resonance yields can be produced in kinetic scattering phase. M. Bleicher and J.Aichelin, Phys. Lett. B, 530 (2002) 81 M. Bleicher and H.Stoecker,J.Phys.G, 30, S111 (2004) 2 3 1 Workshop on Excited Hadronic States and Deconfinement transition

  5. Observed yield, invariant mass method. Chemical freeze-out rescater Kinetic freeze-out Resonance yield can be reconstructed by invariant mass method only after kinetic freeze-out, when decay products do not rescatter. The yields of ground state almost does not change. Everything decays back to ground states. Workshop on Excited Hadronic States and Deconfinement transition

  6. Dominant reactions • Σ(1385)↔Λπ ,width Γ∑(1385) ≈ 35 MeV (from PDG); • Σ* ↔ Λ(1520) π, Γ∑* ≈ 20-30 MeV > ΓΛ(1520) = 15.5 MeV (from PDG); Σ*= Σ(1670), Σ(1750), Σ(1775), Σ(1940)) • Δ(1232) ↔ Nπ, width Γ≈120 MeV (from PDG); • φ↔KK (83%), φ↔ ρπ (15%), Г = 4.26 MeV, Eth = mφ-2mK=30 MeV is relatively small. Workshop on Excited Hadronic States and Deconfinement transition

  7. Influence of backward reaction also depends on Eth. The smaller Eth is, the slower excited state decays back with cooling due expansion, larger higher mass resonance enhancement. The larger Eth is, the less population of exited state in equilibrium is, the less lower mass particles are needed to excite this state, the less lower mass resonance suppression is; Λ(1520) is more suppressed by lower mass Σ*excitation. Workshop on Excited Hadronic States and Deconfinement transition

  8. Reactions for Σ(1385) and Λ(1520). Width of decay channel Workshop on Excited Hadronic States and Deconfinement transition

  9. A second scenario • Normally all reactions go in both directions. For the late stage of the expansion, at relatively low density this assumption may not be fully satisfied, in particular pions of high momentum could be escaping from the fireball. • Dead channels scenario: For dead channels resonances decay only. Workshop on Excited Hadronic States and Deconfinement transition

  10. Fugacity definition for in the rest frame of heat bath We assume chemical potential μ=0, particle-antiparticle symmetry Multiplicity of resonance (when ‘1’ in fi is negligible): where K2(x) is Bessel function; giis particle i degeneracy; Υiis particle fugacity, i =1, 2, 3; Workshop on Excited Hadronic States and Deconfinement transition

  11. Time evolution equations Similar to 2-to-2 particles reactions: P.Koch, B.Muller and J.Rafelski Phys.Rept.142, 167 (1986); T.Matsui, B.Svetitsky and L.D. McLerran, Phys.Rev.D, 34, 783 (1986) Workshop on Excited Hadronic States and Deconfinement transition

  12. Lorentz invariant rates Workshop on Excited Hadronic States and Deconfinement transition

  13. Bose enhancement factor: Fermi blocking factor: using energy conservation and time reversal symmetry: we obtained detailed balance condition: Detailed balance condition Workshop on Excited Hadronic States and Deconfinement transition

  14. Fugacity (Υ) computation Relaxation time: τis time in fluid element co-moving frame. the entropy is conserved We solve system of equations numerically, using classical forth order Runge-Kutta method Workshop on Excited Hadronic States and Deconfinement transition

  15. QGP Hadronization • We work in framework of fast hadronization to final state. • Physical conditions (system volume, temperature) do not change. • γq and γs are strange and light quarks fugacities: • Strangeness conservation: fixesγs . Entropy conservation: fixes γq>1 at T < 180 MeV. In QGPγqQGP = 1 . Workshop on Excited Hadronic States and Deconfinement transition

  16. Initial and Equilibrium Conditions γq > 1, for T0 < 180 MeV; for strange baryons: reaction goes toward production of particle 3: For one reaction equilibrium condition is: If γq = 1 at hadronization, we have equilibrium. However with expansion Υ3 increases faster than Υ1Υ2 and reaction would go towards resonance 3 decay: Workshop on Excited Hadronic States and Deconfinement transition

  17. Expansion of hadronic phase • Growth of transverse dimension: • Taking we obtain: is expansion velocity Workshop on Excited Hadronic States and Deconfinement transition

  18. Competition of two processes: • Non-equilibrium results towards heavier resonances production in backward reaction. • Cooling during expansion influence towards heavier states decay. Workshop on Excited Hadronic States and Deconfinement transition

  19. The ratios NΔ/NΔ0, NN/NN0 as a function of T Δ(1232) ↔ Nπ • Υπ= const • 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. Workshop on Excited Hadronic States and Deconfinement transition

  20. ∆(1232) enhancement Δ(1232) ↔ N π, width Γ≈120 MeV; Δ is enhanced when N + π→ Δ(1232) reaction dominates Workshop on Excited Hadronic States and Deconfinement transition

  21. Resonances yields after kinetic phase: Λ (1520) is suppressed due to Σ* excitation during kinetic phase. ∑(1385)/Λ is enhanced when reaction Λπ →Σ(1385) dominates. Workshop on Excited Hadronic States and Deconfinement transition

  22. Dead channels In presence of dead channels the effect is amplified. ∑* decays to ‘dead channels’ fast, the suppression of Λ(1520)byreaction Λ(1520)π→ ∑* increases. Λ, N, ∑ Λ(1520) ∑* π π, N, K Workshop on Excited Hadronic States and Deconfinement transition

  23. Observable ratio Λ (1520)/Λ as a function of T Λ (1520) is suppressed due to Σ* excitation during kinetic phase. There is additional suppression in observable ratio because Σ*s are suppressed at the end of kinetic phase and less of them decay back to Λ(1520) during free expansion. Tk≈100 MeV; Th≈ 140 MeV Workshop on Excited Hadronic States and Deconfinement transition

  24. Observable ratio ∑(1385)/Λ as a function of T ∑(1385)/Λis enhanced when reaction Λπ→Σ(1385) dominates. The influence of reactions with higher mass resonances is small. Workshop on Excited Hadronic States and Deconfinement transition

  25. Difference between Λ(1520) and Σ(1385). • ΓΛ(1520) = 15.6 MeV; Eth forΛ(1520) production > Ethfor Σ*s excitation • ΓΣ(1385) ≈ 36 MeV; Eth forΣ(1385) production < Ethfor Σ*s excitation • mΣ(1385) < mΛ(1520) → nΣ(1385) > nΛ(1520) • A lesser fraction of the lighter mass particle is needed to equilibrate the higher mass particle. Λ(1520) + π → Σ* is dominant over 1 + 2 → Λ(1520) Λ0 + π → Σ(1385) is dominant over Σ(1385) + π → Σ* Workshop on Excited Hadronic States and Deconfinement transition

  26. φ evolution (φ↔KK ) γ T, MeV After non-equilibrium hadronization production of φ must be dominant over relatively long period of time (small Eth) For comparison at equilibrium hadronization for φ decay only to KK, φ yield decreases by 7.5%; in inelastic scattering by 15%. Alvarez-Ruso and V.Koch, 2002 KK→φ and non-equilibrium hadronization conditions can noticeably change the result Workshop on Excited Hadronic States and Deconfinement transition

  27. Summary • Λ(1520) yield is suppressed due to excitation of heavy Σ*s in the scattering process during kinetic phase and Σ*s preferable decay to ground states during kinetic phase. • Σ(1385) and Δ are enhanced due to Λ0+ π→Σ(1385)andN + π→ Δ(1232) reactions for non equilibrium initial conditions. • We have shown that yields of Σ(1385) and Λ(1520) reported in RHIC and SPS experiments are well explained by our considerations and hadronization at T=140 MeV is favored. Kinetic freeze-out is at T ≈ 100 MeV • For non-equilibrium hadronization φ yield can be enhanced by 6-7% by dominant KK→φ. For equilibrium hadronization φ yield suppression is about 4% Workshop on Excited Hadronic States and Deconfinement transition

  28. Future research • ρ↔ππ, Г = 150 MeV ρ is much enhanced in pp collisions • K* ↔ Kπ, Г = 50.8 MeV K* and ρ can participate in many other reactions. Workshop on Excited Hadronic States and Deconfinement transition

  29. Difference between Σ(1385) and Λ(1520). • Decay width for Σ(1385) to ground state is larger than for Λ(1520). • Decay widths of Σ*s to Σ(1385) is smaller than those to Λ(1520). • Eth for Σ(1385) excitation by ground states is smaller than for Σ*s excitation by Σ(1385) and π fusion. Opposite situation is for Λ(1520). Workshop on Excited Hadronic States and Deconfinement transition

  30. ∑* evolution ∑(1775) is suppressed by decay to channels with lightest product, especially in the case with ‘dead’ channels. Workshop on Excited Hadronic States and Deconfinement transition

  31. Calculation of particle 3 decay / production rate Particle 3 decay / production rate in a medium can be calculated, using particle 3 decay time in the this particle rest frame. Observer (heat bath) frame Particle 3 rest frame v Workshop on Excited Hadronic States and Deconfinement transition

  32. Temperature as a function of time τ Workshop on Excited Hadronic States and Deconfinement transition

  33. In medium effects for resonances • If particle 2 is pion (m2 = mπ) in medium effects may have influence. For heavy particle m3, m1 >> mπ: Workshop on Excited Hadronic States and Deconfinement transition

  34. ∑(1385) decay\production relaxation time in pion gas. Workshop on Excited Hadronic States and Deconfinement transition

  35. Fugacity as a function of T(t) If there are no reactions Ni = const, Υi is proportional to exp(mi/T) for nonrelativistic Boltzmann distribution Workshop on Excited Hadronic States and Deconfinement transition

  36. ∑*reaction rates evolution (no dead channels) Larger difference m3-(m1+m2) sooner decay in this channel becomes dominant. Workshop on Excited Hadronic States and Deconfinement transition

  37. Motivation B.I.Abelev et al., Phys. Rev. C 78, 044906 (2008) Workshop on Excited Hadronic States and Deconfinement transition

  38. φ meson • Г = 4.26 MeV • φ↔KK (83%), φ↔ ρπ (15%) • Eth = mφ-2mK=30 MeV After non-equilibrium hadronization production of φmust be dominantover relatively long period of time Workshop on Excited Hadronic States and Deconfinement transition

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