Kinetics of hadron resonances during hadronic freezeout Inga

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Kinetics of hadron resonances during hadronic freeze-out Inga Kuznetsova Department of Physics, University of

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 I. Kuznetsova and J. Rafelski, Phys. Lett. B, 668 105 (2008) [ar. Xiv: 0804. 3352]. I. Kuznetsova and J. Rafelski, Phys. Rev. C , 79, 014903 (2009) [ar. Xiv: 0811. 1409] I. Kuznetsova and J. Rafelski Phys. Rev. C, 82, 035203 (2010) [ar. Xiv: 1002. 0375 ]. Work supported by a grant from: the U. S. Department of Energy DE-FG 02 -04 ER 4131 Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition

Phases of RHI collision n QGP (deconfinement) phase; n Chemical freeze-out (QGP hadronization), hadrons

Phases of RHI collision n QGP (deconfinement) phase; n Chemical freeze-out (QGP hadronization), hadrons are formed; (140 <T 0 <180 Me. V) n Hadronic gas (kinetic) phase, hadrons interact; n Kinetic freeze-out : reactions between hadrons stop; n 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 2

Motivation We explain high ratio Σ(1385)/Λ 0 reported at RHIC (S. Salur, J. Phys.

Motivation We explain high ratio Σ(1385)/Λ 0 reported at RHIC (S. Salur, J. Phys. G 32, S 469 (2006)) and Λ(1520)/Λ 0 suppression reported in both RHIC and SPS experiments. (J. Adams et al. , Phys. Rev. Lett. 97, 132301 (2006)[ar. Xiv: 0604019]; C. Markert [STAR Collaboration], J. Phys. G 28, 1753 (2002) [ar. Xiv: nucl-ex/0308028]. ). 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? Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 3

Kinetic phase We assume that hadrons are in thermal equilibrium (except probably very high

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 Me. V) Resonance yields can be produced in kinetic scattering phase. 2 3 1 M. Bleicher and J. Aichelin, Phys. Lett. B, 530 (2002) 81 M. Bleicher and H. Stoecker, J. Phys. G, 30, S 111 (2004) Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 4

Observed yield, invariant mass method. Chemical freeze-out rescater Kinetic freeze-out Resonance yield can be

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. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 5

Dominant reactions n Σ(1385)↔Λπ , width Γ∑(1385) ≈ 35 Me. V (from PDG); n

Dominant reactions n Σ(1385)↔Λπ , width Γ∑(1385) ≈ 35 Me. V (from PDG); n Σ* ↔ Λ(1520) π, Γ∑* ≈ 20 -30 Me. V > ΓΛ(1520) = 15. 5 Me. V (from PDG); Σ* = Σ(1670), Σ(1750), Σ(1775), Σ(1940)) n Δ(1232) ↔ Nπ, width Γ≈120 Me. V (from PDG); n φ↔KK (83%), φ↔ ρπ (15%), Г = 4. 26 Me. V, Eth = mφ-2 m. K=30 Me. V is relatively small. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 6

Influence of backward reaction also depends on Eth. The smaller Eth is, the slower

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. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 7

Reactions for Σ(1385) and Λ(1520). Width of decay channel Inga Kuznetsova Workshop on Excited

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

A second scenario n Normally all reactions go in both directions. For the late

A second scenario n 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. n Dead channels scenario: For dead channels resonances decay only. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 9

Fugacity definition for in the rest frame of heat bath We assume chemical potential

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 K 2(x) is Bessel function; gi is particle i degeneracy; Υi is particle fugacity, i =1, 2, 3; Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 10

Time evolution equations Similar to 2 -to-2 particles reactions: P. Koch, B. Muller and

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. Mc. Lerran, Phys. Rev. D, 34, 783 (1986) Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 11

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

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

Detailed balance condition n Bose enhancement factor: n Fermi blocking factor: n using energy

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

Fugacity (Υ) computation Relaxation time: τ is time in fluid element co-moving frame. the

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

QGP Hadronization n We work in framework of fast hadronization to final state. n

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

Initial and Equilibrium Conditions γq > 1, for T 0 < 180 Me. V;

Initial and Equilibrium Conditions γq > 1, for T 0 < 180 Me. V; 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 Υ 3 increases faster than Υ 1Υ 2 and reaction would go towards resonance 3 decay: Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 16

Expansion of hadronic phase n Growth of transverse dimension: is expansion velocity n Taking

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

Competition of two processes: n Non-equilibrium results towards heavier resonances production in backward reaction.

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

The ratios NΔ/NΔ 0, NN/NN 0 as a function of T Δ(1232) ↔ Nπ

The ratios NΔ/NΔ 0, NN/NN 0 as a function of T Δ(1232) ↔ Nπ n Υπ = const n NΔ increases 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. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 19

∆(1232) enhancement Δ(1232) ↔ N π, width Γ≈120 Me. V; Δ is enhanced when

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

Resonances yields after kinetic phase: Λ (1520) is suppressed due. Workshop to Σ* ∑(1385)/Λ

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

Dead channels In presence of dead channels the effect is amplified. ∑* decays to

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, N, ∑ Λ(1520) ∑* π Inga Kuznetsova π, N, K Workshop on Excited Hadronic States and Deconfinement transition 22

Observable ratio Λ (1520)/Λ as a function of T Λ (1520) is suppressed due

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 Me. V; Th ≈ 140 Me. V Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 23

Observable ratio ∑(1385)/Λ as a function of T ∑(1385)/Λ is enhanced when reaction Λπ

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 24

Difference between Λ(1520) and Σ(1385). n ΓΛ(1520) = 15. 6 Me. V; Eth for

Difference between Λ(1520) and Σ(1385). n ΓΛ(1520) = 15. 6 Me. V; Eth for Λ(1520) production > Eth for Σ*s excitation Λ(1520) + π → Σ* is dominant over 1 + 2 → Λ(1520) n ΓΣ(1385) ≈ 36 Me. V; Eth for Σ(1385) production < Eth for Σ*s excitation Λ 0 + π → Σ(1385) is dominant over Σ(1385) + π → Σ* n mΣ(1385) < mΛ(1520) → nΣ(1385) > nΛ(1520) n A lesser fraction of the lighter mass particle is needed to equilibrate the higher mass particle. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 25

φ evolution (φ↔KK ) T, Me. V γ After non-equilibrium hadronization production of φ

φ evolution (φ↔KK ) T, Me. V γ 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 Inga Kuznetsova KK→φ and non-equilibrium hadronization conditions can noticeably change the result 26 Workshop on Excited Hadronic States and Deconfinement transition

Summary n Λ(1520) yield is suppressed due to excitation of heavy Σ*s in the

Summary n 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. n Σ(1385) and Δ are enhanced due to Λ 0 + π → Σ(1385) and N + π → Δ(1232) reactions for non equilibrium initial conditions. n 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 Me. V is favored. Kinetic freeze-out is at T ≈ 100 Me. V n 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 27

Future research n ρ↔ππ, Г = 150 Me. V ρ is much enhanced in

Future research n ρ↔ππ, Г = 150 Me. V ρ is much enhanced in pp collisions n K* ↔ Kπ, Г = 50. 8 Me. V K* and ρ can participate in many other reactions. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 28

Difference between Σ(1385) and Λ(1520). n Decay width for Σ(1385) to ground state is

Difference between Σ(1385) and Λ(1520). n Decay width for Σ(1385) to ground state is larger than for Λ(1520). n Decay widths of Σ*s to Σ(1385) is smaller than those to Λ(1520). n 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). Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 29

∑* evolution ∑(1775) is suppressed by decay to channels with lightest product, especially in

∑* 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 30

Calculation of particle 3 decay / production rate Particle 3 decay / production rate

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 31

Temperature as a function of time τ Inga Kuznetsova Workshop on Excited Hadronic States

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

In medium effects for resonances n If particle 2 is pion (m 2 =

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

∑(1385) decayproduction relaxation time in pion gas. Inga Kuznetsova Workshop on Excited Hadronic States

∑(1385) decayproduction relaxation time in pion gas. Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 34

Fugacity as a function of T(t) If there are no reactions Ni = const,

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 Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 35

∑* reaction rates evolution (no dead channels) Larger difference m 3 -(m 1+m 2)

∑* reaction rates evolution (no dead channels) Larger difference m 3 -(m 1+m 2) sooner decay in this channel becomes Workshop on Excited Hadronic States and 36 Inga Kuznetsova dominant. Deconfinement transition

Motivation B. I. Abelev et al. , Phys. Rev. C 78, 044906 (2008) Inga

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

φ meson n Г = 4. 26 Me. V n φ↔KK (83%), φ↔ ρπ

φ meson n Г = 4. 26 Me. V n φ↔KK (83%), φ↔ ρπ (15%) n Eth = mφ-2 m. K=30 Me. V After non-equilibrium hadronization production of φ must be dominant over relatively long period of time Inga Kuznetsova Workshop on Excited Hadronic States and Deconfinement transition 38