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 <T 0 <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.

Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 3 We explain high ratio Σ(1385)/Λ 0 reported at RHIC (S.Salur, J.Phys. G 32, S469 (2006 ) ) and Λ(1520)/Λ 0 suppression reported in both RHIC and SPS experiments. (J. Adams et al., Phys. Rev. Lett. 97, (2006)[arXiv: ]; C. Markert [STAR Collaboration], J. Phys. G 28, 1753 (2002) [arXiv:nucl-ex/ ]. ). We predict ∆(1232)/N ratio. We study φ meson production during kinetic phase in KK→ φ. By suppression (enhancement) here we mean the suppression (enhancement) compared to scaled pp (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? Motivation

Inga Kuznetsova 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) ≈ 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) 1 2 3

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

Inga Kuznetsova 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 ∑ * ≈ MeV > Γ Λ(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, E th = m φ -2m K =30 MeV is relatively small.

Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 7 Influence of backward reaction also depends on E th. The smaller E th is, the slower excited state decays back with cooling due expansion, larger higher mass resonance enhancement. The larger E th 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.

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

Inga Kuznetsova 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.

Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 10 Fugacity definition forin the rest frame of heat bath where K 2 (x) is Bessel function; g i is particle i degeneracy; Υ i is particle fugacity, i =1, 2, 3; Multiplicity of resonance (when ‘1’ in f i is negligible): We assume chemical potential μ=0, particle-antiparticle symmetry

Inga Kuznetsova 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)

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

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

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

Inga Kuznetsova 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. γ q and γ s are strange and light quarks fugacities: Strangeness conservation: fixes γ s. Entropy conservation: fixes γ q >1 at T < 180 MeV. In QGP γ 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: γ q > 1, for T 0 < 180 MeV; for strange baryons: For one reaction equilibrium condition is: If γ q = 1 at hadronization, we have equilibrium. However with expansion Υ 3 increases faster than Υ 1 Υ 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 Δ /N Δ 0, N N /N N 0 as a function of T Υ π = const N Δ increases during expansion after hadronization when γ q >1 (Υ Δ < Υ N Υ π ) until it reaches equilibrium. After that it decreases (delta decays) because of expansion. Opposite situation is with N N. If γ q =1, there is no Δ enhancement, Δ only decays with expansion. Δ(1232) ↔ Nπ

Inga Kuznetsova 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

Inga Kuznetsova 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.

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 Λ(1520) by reaction Λ(1520)π→ ∑* increases. ∑*∑* Λ(1520) π Λ, N, ∑ π, N, K

Inga Kuznetsova 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. T k ≈100 MeV; T h ≈ 140 MeV

Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 24 Observable ratio ∑(1385)/Λ as a function of T ∑(1385)/Λ is enhanced when reaction Λπ →Σ(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 Λ(1520) and Σ(1385). Γ Λ(1520) = 15.6 MeV; E th for Λ(1520) production > E th for Σ * s excitation Γ Σ(1385) ≈ 36 MeV; E th for Σ(1385) production < E th for Σ * s excitation m Σ(1385) n Λ(1520) A lesser fraction of the lighter mass particle is needed to equilibrate the higher mass particle. Λ(1520) + π → Σ * is dominant over → Λ(1520) Λ 0 + π → Σ(1385) is dominant over Σ(1385) + π → Σ*

Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 26 φ evolution (φ↔KK ) 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 After non-equilibrium hadronization production of φ must be dominant over relatively long period of time (small E th ) T, MeV γ

Inga Kuznetsova 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 Λ 0 + π → Σ(1385) and N + 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%

Inga Kuznetsova 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.

Inga Kuznetsova 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). E th 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).

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 τ

Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 33 In medium effects for resonances If particle 2 is pion (m 2 = m π ) in medium effects may have influence. For heavy particle m 3, m 1 >> m π :

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, Υ 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 φ meson Г = 4.26 MeV φ↔KK (83%), φ ↔ ρπ (15%) E th = m φ -2m K =30 MeV After non-equilibrium hadronization production of φ must be dominant over relatively long period of time