Testing freezeout by resonances E.Shuryak, Stony Brook

1. Testing freezeout by resonancesE.Shuryak, StonyBrook • Time when`visible resonances’ are produced • Absorbtion and optical depth • Universal expansion • Resonance mass and width modification, yields • Resonances above Tc (L=0 vs L=1, baryons vs mesons): but I don’t see a special role of strangeness

2. ``Resonances as clocks” needed to test if we really understand freezeout(old idea, far from really implemented…) The four players involved are: • Expansion • Decays • (Re)-production • Product absorption To understand them properly we will discuss them one-by-one

3. A time picture Optical depth = probablity for all Decay product to escape without rescattering this time, t(visible) Is the maximum of the production of resonances visible to the detector It is maximal when absobtion of products and their production in the decay have the same rate! Before t(chem) the decay and production processes are in chemical equilibrium, After it the production does not keep up with decays

4. Popular (but very naïve) myths • All hadrons including resonances are produced at the same chemical freezeout time, at “T=Tc” • after it one can ignore reproduction but include decays only. Also there is no rescattering. • But, T=Tc is not a time moment but actually a rather long period of time – the mixed phase, about 4 fm/c - in which densities change by a large factor • At t(chem) both rates are in fact equal, while • at very late time reproduction must dominate since it decays as a power of time, not exponent . • There are no thousends of Maxwell demons which would prevent collisions: trust your (n sigma v) formula!

5. Universal expansion for RHIC(but different for SPS) From P.Kolb, nucl-th/0304036 • Transition from 1d to 3d expansion happensin the mixed phase • T remains constant till the onset of hadronic phase • but density changes all the time • little dependence on r – position of the fluid cell • But scales with R – the size of the system (centrality) • – because hydro is scale independent

6. Let me propose very simple parameterization of the volume(t) • 1+2(tau/tau_fs) till free streaming • 3 after that

7. Rate eqn Decay width Reproduction term is proportional to the product of product densities, thus the power is the number of all products N(prod) Usually N(prod)=2 e.g. for pi,pi<=>rho But can be much larger e.g. Nbar N <=> 6pi Or for hyperons Ybar Y < = > KK few pi (Rapp, ES), so production must be switched off very quickly after chem.freezeout (PBM, Stachel, Wetterich) For baryons and hyperons the production term may change by many orders of magnitude in the mixed phase => Thus Tch=Tc Generically, two terms cancel each other till the chemical freezout time t(ch) At later times the second term is smaller, but it decays as a power of time only and cannot be ignored for short-lived resonances

8. The easiest to predict should be those which are produced very late, thus in dulite gas of hadrons • This should be d=(pn) bound state, it has really huge absorption cross section on pions and optical depth allows it to be produced only at t(visible)>20 fm/c. (Ideal test for coalescence model and v2: Certainly not without absorption as people do it now…) To my knowledge, no good data yet

9. If one is interested in absoptionand t(visible), compare similar resonances with similar production in QGP but different products • Example: rho,K*,phi • Expectation: phi is produced at Tc, K* a bit later while rho much later (its lifetime is only about 1 fm) => Different dependence of their yield on centrality • Unfortunately rho was only measured at periph.bin so far…

10. Old theory of effective potentialsfor resonances: from other resonances M is forward scattering amplitude, e.g. M changes sign when sqrt(s)>m(sigma)!

11. Rho,K* mass shifts observed G.Brown+ES introduced sigma-induced attraction to all hadrons except pions, contributed about -30 MeV to the observed rho mass shift and nothing to the width It is comparable to downward shift from rho-pi, rho-N forward amplitude • Explains the difference of rho mass in pp and AuAu (periph), unfortunately in conditions more like SPS (central) • Visible rhos come from T about 120 MeV • The width is not changed inspite of 10% lower mass while phase space and p-wave would require 30% reduction in width… => compensated by rescattering width • Tested at SPS (CERES and recently at NA60) by dileptons from higher T • shift is seen but not very large. The width is larger but not so large

12. STAR rho (P.Fachini) No rho in central AuAu so far In pp/dAu there should be only a ``heat bath” effect, delta M=-Gamma^2/8T (Brown_ES) But STAR data show larger effect also for K* (next slide): I have no idea what is it. Can it be a detector thing? It is safer to consider AuAu/pp difference anyway.

13. STAR K* (C.Markert)

14. For those who are not interestedin rescattering/absoption • Select resonances with similar width and decay products, but different internal structure • PiPi resonaces rho, f0(980) and f2(1200): they all produced at about the same time. Are their ratio thermal (with T at that time)? • At T=Tc or in QGP s-wave ones (rho,K*) are expected to survive while p-wave (f0,f2) melt down. Does it matter for yields? (if reproduction is very robust, it should not be…)

15. Two more extreme pipi resonances • f0(500) or old sigma meson. Expected to get shifted toward zero mass at Tc and gets very narrow (suppressed 2pi decays). • It is the lowest resonance ever, good for cool late stages • There were STAR indications for it, never published (to my knowledge…) • Another is f0(1700) the glueball candidate: • Would there be anything special for its production from glue-rich QGP?

16. Pi-N and K-N resonances: few successes • Delta was predicted to go up in mass by old theory, and it does, The width grows. • Lambda(1520) shows a bit of decrease of its ratio to Lambda as as function of centrality, while K*/K does not; product absorption or melting of p-wave resonances? • But overall too many open question and no consistent picture yet: more data are needed

17. What happens with resonances in QGP/mixed phase? • S-wave hadrons seem to survive, Including mesons (rho,K*,phi) and baryons (N,Delta,Y…) up to 1.6Tc or so, getting heavier (!) • P-wave ones do not (e.g. f_0(980),f_2, Lambda(1520) or N*(1440)) • The formers show yield larger than expectation (from chem fr.at Tc), the latter ones more suppressed

18. J.Liao,ES: quantum mechanical calculation 0f the bining, in the interacting quasi- Particle model with lattice-based V and M hep-ph

19. Baryons go from light to heavy! J.Liao, ES hep-ph/ Unlike colored objects, Such as q, qg, qq etc, Baryons (N…) should Evolve through the QCD phase transition Continuously Their mass grows Into the sQGP side because Quasiparticle quarks are heavy This will generate T and mu Derivatives! Delta N Mq(T)

20. Lattice baryonic susceptibilities Baryons: Fading or Gaining weight? C. R. Allton et al., Phys. Rev. D 71, 054508 (2005) [arXiv:hep-lat/0501030] High n sensitive to baryons

21. How the contribution of N,Delta Baryons(plus all others) look like:The peak in d4 and a wiggle in d6 are reproducedThe wiggle due to baryon mass dependence with a inflection pointM” changes sign

22. Baryons dominate d4 and d6 • Derivatives work like this: • For quarks d_In/d_n=1 • For N and Delta+, Delta0=1/9 • For Delta ++ and Delta -=1 • For 4 N and 16 Delta = .466 N+D

23. conclusions • No ``standard model” yet as a benchmark, which may be much much simpler than R(Ur)QMD… • Some small mass shifts and widths modifications (rho,Delta) were understood • Not enough data on yields, mass shifts, widths, radial and elliptic flows for all resonances to develop comparisons • is there any trace of what is expected to happen in QGP (survival of s-state meson and baryons, growing masses) in the data? What about melting of all p-wave states ? Glueballs? Massless and narrow sigma meson?