Spectral Properties of Light Meson Resonances in Hot and Dense Matter: Understanding the QGP through Spectral Functions

1. Angel Gómez Nicola Universidad Complutense Madrid IN MEDIUM LIGHT MESON RESONANCES AND CHIRAL SYMMETRY RESTORATION Understanding the QGP through Spectral Functions and Euclidean Correlators BNL April 2008

2. r→ dilepton spectrum (CERES,NA60) and nuclear matter Broadening vs Mass shift (scaling?) f0 (600)/s→ vacuum quantum numbers, chiral symmetry restoration Observed in nuclear matter experiments (CHAOS, …) through threshold enhancement? Any chance for Heavy Ions (finite T)? What can medium effects tell about the nature of these states? Spectral properties of light meson resonances in hot and dense matter: Motivation

3. Rapp-WambachBrown/Rho meson cocktail 2000 data DILEPTONS NA60 (m+m-) NA45/CERES (e+e-) Compatible with both broadening and dropping-mass scenarios Broadening favored, dropping mass almost excluded

4. normal nuclear matter density r→ e+e- IN NUCLEAR MATTER Signals free of T≠0 complications Linear decrease of vector meson masses from scaling&QCD sum rules: Brown, Rho ‘91 Hatsuda, Lee ‘92 Other many-body approaches give negligible mass shift Chanfray,Schuck ‘98 Urban, Buballa, Rapp,Wambach ‘98 Cabrera,Oset,Vicente-Vacas ‘02 Experiments not fully compatible: KEK-E325 (C,Fe-Ti): a = 0.0920.002 Jlab-CLAS (C,Cu): a = 0.020.02

5. Crystal Ball CHAOS MAMI-B ppproduction in Nuclear Matter: threshold enhancement in the s(I=J=0) channel pA→ ppA’ gA→ p0p0A’

6. Ms <s> decreases, so that when Ms 2mp , phase space is squeezed Gs 0 and the s pole reaches the real axis Hatsuda, Kunihiro ‘85 Narrow resonance argument ! O(N) modelsat finite Tshow that the s remains broad when Ms 2mp Further in-medium strength causes 2nd-sheet pole to move into 1st sheet  pp bound state. Patkos et al ‘02 Hidaka et al ‘04 Finite density analysis compatible with threshold enhancement of pp cross section Davesne, Zhang, Chanfray ‘00 Roca et al ‘02 Threshold enhancement as a signal of chiral symmetry restoration:

7. Inverse Amplitude Method “Thermal” poles Dynamically generated (no explicit resonance fields) OUR APPROACH: UNITARIZED CHIRAL PERTURBATION THEORY AGN, F.J.Llanes-Estrada, J.R.Peláez PLB550, 55 (2002), PLB606:351-360,2005 A.Dobado, AGN, F.J.Llanes-Estrada, J.R.Peláez, PRC66, 055201 (2002) D.Fernández-Fraile,AGN, E.Tomás-Herruzo, PRD76:085020,2007 + CHIRAL SYMMETRY UNITARITY pp scattering amplitude and ppg form factors in T > 0 SU(2) one-loop ChPT

8. Chiral Perturbation Theory: Relevant for low and moderate temperatures below Chiral SSB Most general derivative and mass expansion of NGB mesons compatible with the SSB pattern of QCDmodel-independentlow-energy predictions. NLSM Weinberg’s chiral power counting:

9. Two-pion thermal phase space enhancement Enhancement Absorption Unitarization: The Inverse Amplitude Method ChPT does not reproduce resonances due to the lack of exact unitarity (resonances saturate unitarity bounds). In the two-pion c.om. frame: (static resonaces): Perturbative Unitarity

10. * + Exact unitarity ChPT matching at low energies Thermal s and r poles (2nd Riemann sheet) Very sucessful at T=0 for scattering data up to 1 GeV and low-lying resonance multiplets, also for SU(3) Dobado, Peláez, Oset, Oller, AGN. * At T>0, valid for dilute gas (only two-pion states).

11. = 20 MeV THETHERMALrPOLE (2nd Riemann sheet) Thermal phase space enhancement + Increase of effective rpp vertex, small mass reduction up to Tc. (for a narrow Breit-Wigner resonance)

12. The unitarized EM pion form factor shows also broadening compatible with dilepton data and VMD analysis:

13. = 20 MeV T=100 MeV However, the pole remains wide even for M~2 mp (spectral function not peaked around the mass for broad resonances) THETHERMALf0(600)/sPOLE (2nd Riemann sheet) Strong pole mass reduction (chiral restoration) means phase space squeezing, which overcomes low-T thermal enhancement

14. Narrow vs Broad Resonances

15. NARROW: Phase space squeezing Threshold enhancement differential decay rate 2-particle differential phase space (R “particle” at rest) r(s) strongly peaked around r(s) broadly distributed BROAD: s pole away from the real axis ChPT approach valid at threshold  no enhancement Generalized decay rate: H.A.Weldon, Ann.Phys.228 (1993) 43 NO phase-squeezing for wide enough r(s) ! Narrow vs Broad Resonances

16. Narrow vs Broad Resonances:

17. No problem for I=J=1  REAL AXIS POLES AND ADLER ZEROS AGN,J.R.Peláez,G.Ríos PRD77, 056006 (2008) Require extra terms in the IAM to account properly for Adler zeros  t(sA)=0. Otherwise, spurious real poles below threshold in the 1st,2nd Riemann sheets. Preserving chiral symmetry+unitarity: No difference away from sA Alternatively derived with dispersion relations. No additional poles for T0 with the redefined amplitudes.

18. Does not behave as a (thermal) state, not even near the chiral limit Consistent with not- scalar nonet (tetraquark,glueball,meson-meson…) “molecule” picture M.Alford,R.L.Jaffe ‘00 J.R.Peláez ‘04 THE NATURE OF THERMAL RESONANCES: f0(600)/s

19. Brown&Rho ‘05 Harada&Sasaki ‘06 THE NATURE OF THERMAL RESONANCES: r No BR-like scaling with condensate. Mass dropping only very near “critical” (too high) T0 , as in BR-HLS models Nature of our thermal r dominated by non-restoring effects (broadening)

20. Justified by approximate validity of GOR (r0,T=0) Non chiral-restoring many-body effects not included (p-h, p-wave p self-energy, …) Cabrera,Oset,Vicente-Vacas ‘05 Chiral restoring expected to be important in the s-channel as densityapproachesthe transition . No broadening to compete with now ! NUCLEAR CHIRAL RESTORING EFFECTS Chiral restoring effects at T=0 and finite nuclear density approx. encoded in fp Thorsson,Wirzba ‘95 Meissner,Oller,Wirzba ‘02

21. ppbound state (“molecule” behaviour) r = r 1 . 9 0 s

22. “non-molecular” ( ) r Compatible with BR-like scaling Brown,Rho ‘04 No threshold enhancement for reasonably high densities. Mass linear fits: Compatible with some theoretical estimates and KEK experiment. However, additional medium effects (important in this channel!) might lead to negligible mass shift

23. In-medium light meson resonances studied through scattering poles in Unitarized ChPT provide chiral symmetry predictions for their spectral properties and nature. The f0(600)/sshows chiral symmetry restoration features but remains as a T0wide not- state  no threshold enhancement at finite T. The r finite-T behaviour is dominated by thermal broadening in qualitative agreement with dilepton data. Mass dropping does not scale with the condensate. Nuclear density chiral-restoring effects encoded in fp (r) drive the poles to the real axis giving threshold enhancement in the s-channel and BR-like scaling in the r-channel. pp bound states of different nature formed near the transition. CONCLUSIONS Full finite-density analysis, SU(3) extension (f-,K*,a0,…)