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 Work supported by a grant from: the U.S. Department of Energy DE-FG02-04ER4131 I. Kuznetsova and J. Rafelski, Phys. Lett. B, (2008) [arXiv: ]. I. Kuznetsova and J. Rafelski, Phys. Rev. C,79, (2009) [arXiv: ] I. Kuznetsova and J. Rafelski Phys. Rev. C, 82, (2010) [arXiv: ]. Kinetics of hadron resonances during hadronic freeze-out Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 2 Phases of RHI collision QGP (deconfinement) phase; Chemical freeze-out (QGP hadronization), hadrons are formed; (140 1 at T < 180 MeV. In QGP q QGP = 1. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 16 Initial and Equilibrium Conditions reaction goes toward production of particle 3: q > 1, for T 0 < 180 MeV; for strange baryons: For one reaction equilibrium condition is: If q = 1 at hadronization, we have equilibrium. However with expansion 3 increases faster than 1 2 and reaction would go towards resonance 3 decay: Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 17 Expansion of hadronic phase Growth of transverse dimension: Taking we obtain: is expansion velocity Inga Kuznetsova 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. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 19 The ratios N /N 0, N N /N N 0 as a function of T = const N increases during expansion after hadronization when q >1 ( < N ) until it reaches equilibrium. After that it decreases (delta decays) because of expansion. Opposite situation is with N N. If q =1, there is no enhancement, only decays with expansion. (1232) N Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 20 (1232) enhancement (1232) N , width 120 MeV; is enhanced when N + (1232) reaction dominates Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 21 Resonances yields after kinetic phase: (1520) is suppressed due to * excitation during kinetic phase. (1385)/ is enhanced when reaction (1385) dominates. Inga Kuznetsova 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 (1520) by reaction (1520) * increases. ** (1520) , N, , N, K Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 23 Observable ratio (1520)/ as a function of T (1520) is suppressed due to * excitation during kinetic phase. There is additional suppression in observable ratio because *s are suppressed at the end of kinetic phase and less of them decay back to (1520) during free expansion. T k 100 MeV; T h 140 MeV Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 24 Observable ratio (1385)/ as a function of T (1385)/ is enhanced when reaction (1385) dominates. The influence of reactions with higher mass resonances is small. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 25 Difference between (1520) and (1385). (1520) = 15.6 MeV; E th for (1520) production > E th for * s excitation (1385) 36 MeV; E th for (1385) production < E th for * s excitation m (1385) n (1520) A lesser fraction of the lighter mass particle is needed to equilibrate the higher mass particle. (1520) + * is dominant over (1520) 0 + (1385) is dominant over (1385) + * Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 26 evolution (KK ) For comparison at equilibrium hadronization for decay only to KK, yield decreases by 7.5%; in inelastic scattering by 15%. Alvarez-Ruso and V.Koch, 2002 KK and non-equilibrium hadronization conditions can noticeably change the result After non-equilibrium hadronization production of must be dominant over relatively long period of time (small E th ) T, MeV Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 27 Summary (1520) yield is suppressed due to excitation of heavy *s in the scattering process during kinetic phase and *s preferable decay to ground states during kinetic phase. (1385) and are enhanced due to 0 + (1385) and N + (1232) reactions for non equilibrium initial conditions. We have shown that yields of (1385) and (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 yield can be enhanced by 6-7% by dominant KK. For equilibrium hadronization yield suppression is about 4% Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 28 Future research , = 150 MeV is much enhanced in pp collisions K * K, = 50.8 MeV K * and can participate in many other reactions. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 29 Difference between (1385) and (1520). Decay width for (1385) to ground state is larger than for (1520). Decay widths of * s to (1385) is smaller than those to (1520). E th for (1385) excitation by ground states is smaller than for * s excitation by (1385) and fusion. Opposite situation is for (1520). Inga Kuznetsova 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. Inga Kuznetsova 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. Particle 3 rest frame Observer (heat bath) frame v Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 32 Temperature as a function of time Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 33 In medium effects for resonances If particle 2 is pion (m 2 = m ) in medium effects may have influence. For heavy particle m 3, m 1 >> m : Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 34 (1385) decay\production relaxation time in pion gas. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 35 Fugacity as a function of T(t) If there are no reactions N i = const, i is proportional to exp(m i /T) for nonrelativistic Boltzmann distribution Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 36 * reaction rates evolution (no dead channels) Larger difference m 3 -(m 1 +m 2 ) sooner decay in this channel becomes dominant. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 37 Motivation B.I.Abelev et al., Phys. Rev. C 78, (2008) Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 38 meson = 4.26 MeV KK (83%), (15%) E th = m -2m K =30 MeV After non-equilibrium hadronization production of must be dominant over relatively long period of time