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Strong and Electroweak Matter 2004. Helsinki, 16-19 June.

CHIRAL MESONS. IN HOT MATTER. Angel Gómez Nicola. Universidad Complutense Madrid. Strong and Electroweak Matter 2004. Helsinki, 16-19 June. Motivation. Motivation. T>0 ChPT pion electromagnetic form factors. Thermal  and s poles. L 2.

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Strong and Electroweak Matter 2004. Helsinki, 16-19 June.

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  1. CHIRAL MESONS IN HOT MATTER Angel Gómez Nicola Universidad Complutense Madrid Strong and Electroweak Matter 2004. Helsinki, 16-19 June.

  2. Motivation Motivation T>0 ChPT pionelectromagnetic form factors Thermal  and s poles

  3. L2 After QGP hadronization and SB, the description of the meson gas must rely onChiral Perturbation Theory (model independent, chiral power counting p,T << 1 GeV ) L22 L4 L6 Derivative and mass expansion S.Weinberg, ‘79 J.Gasser&H.Leutwyler ’84,’85 nonlinear -model Only NGB mesons (and photons) involved. L2loops are O(p2), divergences absorbed in L4 and so on.

  4. T T=0 T T=0 J.Gasser&H.Leutwyler ‘87 P.Gerber&H.Leutwyler ‘89 A.Bochkarev&J.Kapusta ‘96 A.Dobado, J.R.Peláez ’99 ’01. point towards Chiral Symmetry Restoration:

  5. J.L.Goity&H.Leutwyler, ‘89 A.Schenk, ‘93 R.Pisarski&M.Tytgat, ‘96 D.Toublan, ‘97 J.M.Martinez Resco&M.A.Valle, ‘98 Pion dispersion law: Nonequilibrium ChPT: f (t),  amplification via parametric resonance. AGN ‘01

  6. Needed to explain observed phenomena in RHIC. Enhancement consistent with a dropping Mrand a significant broadening Gr  in the hadron gas at freeze-out. K.Kajantie et al ’96 C.Gale, J.Kapusta ’87 ‘91 G.Q.Li,C.M.Ko,G.E.Brown ‘95 H.J.Schulze, D.Blaschke ‘96,’03 V.L.Eletsky et al ‘01 However, ChPT alone cannot reproduce the light resonances (,, ...)

  7. OUR APPROACH + UNITARITY pp scattering amplitudeand ppgform factors inT > 0 SU(2) ChPT Inverse Amplitude Method “Thermal” poles Dynamically generated (no explicit resonance fields) AGN, F.J.Llanes-Estrada, J.R.Peláez PLB550, 55 (2002), hep-ph/0405273 A.Dobado, AGN, F.J.Llanes-Estrada, J.R.Peláez, PRC66, 055201 (2002) CHIRAL SYMMETRY BREAKING

  8. T>0 ChPT pionelectromagnetic form factors Motivation T>0 ChPT pionelectromagnetic form factors Thermal  and s poles

  9. Pion form factors enter directly in the dilepton rate: In the central region the dominant channel is pion annihilation: e+ p+ p+ e+ g r g (thermal equilibrium) ~ + ... e- e- p- p-

  10. At T>0 a more general structure is allowed: k = p1- p2 S = p1+ p2 Related by gauge invariance to p dispersion law in hot matter ChPT to O(p4) (At T = 0, Ft (S2)= Fs(S2), Gs= 0)

  11. T>0 ChPT calculation to O(p4): L2 one loop L4 tree level (including renormalization) T0 limit (J.Gasser&H.Leutwyler 1984). Gauge invariance condition. Thermal perturbative unitarity in the c.o.m. frame (see later)

  12. Model independent ! Confirms Dominguez et al ’94 (QCD sum rules) (rough) deconfinement estimate: Kapusta The pion electromagnetic charge radius at T>0 Charge screening

  13. Consider c.om. frame ( , back to back dileptons) 1 to lowest order I=J=1 pp scattering partial wave 2pthermal phase space: (1+nB)2-nB2 H.A.Weldon ’92 Enhancement Absorption Likewise, for the thermal amplitude: Thermal perturbative unitarity:

  14. Thermal  and s poles Motivation T>0 ChPT pionelectromagnetic form factors Thermal  and s poles

  15. + Exact unitarity at T>0 ChPT matching at low energies ! Valid to O(nB) (only 2p thermal states, dilute gas). T.N.Truong, ‘88 A.Dobado, M.J.Herrero,T.N.Truong, ‘90 A.Dobado&J.R.Peláez, ’93,’97 J.A.Oller, E.Oset, J.R.Peláez, ’99 A.Dobado, M.J.Herrero, E.Ruiz Morales ‘00 AGN&J.R.Peláez ‘02 Excellent T=0 data description up to 1 GeV energies and resonance generation as s poles in the complex amplitude. Unitarization: The Inverse Amplitude Method

  16. Significant r broadening as required by dilepton data. Thermal s and r poles I=J=0 I=J=1 Small Mrchange at low T (VMD*). Further decrease consistent with phenomenological estimates and observed behaviour (STAR ppr) Consistent with Chiral Symmetry Restoration:: Ms  Ms  mp (mp (T) much softer) Gs  first by phase spacebut decreases as Ms  2mp suppresses s 2p decay. (similar results to T.Hatsuda, T.Kunihiro et al, ’98,’00) * * M.Dey, V.L.Eletsky&B.L.Ioffe, 1990  (770) 2nB (Mr/2)  0.3 SU(2) L4 constants from T=0 fit of phase shifts:

  17. The unitarized form factor Peak reduction and spreading around Mr compatible with dilepton spectrum (nB contributions alone overestimate data) and other calculations including explicitly resonances under VMD assumption (C.Song and V.Koch, ’96) mp = 139.6 MeV fp = 92.4 MeV (T=0 form factor fit)

  18. Chiral Perturbation Theory provides model-independent predictions for meson gas properties. In one-loop ChPT, we have calculated scattering amplitudes and the two independent form factors, checking gauge invariance and thermal unitarity. The electromagnetic pion radius grows for T>100 MeV, favouring a deconfinement temperature Tc~200 MeV. Imposing unitarity in SU(2) allows to describe the thermal r and s poles in the amplitudes and form factors. Our results show a clear increase of Gr(T) and a slow Mr(T) reduction consistently with theoretical and experimental analysis, including dilepton data. Gs(T) and Ms(T) behave according to Chiral Symmetry Restoration. Angular dependence, plasma expansion, K+K-  f  e+e-, baryon density, hadronic photon spectrum, ... CONCLUSIONS

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