Spectrum of vector meson at finite temperature in hidden local symmetry model

1. Spectrum of vector meson at finite temperature in hidden local symmetry model M. Ohtani (KEK) withY. Hidaka (RIKEN-BNL), O. Morimatsu (KEK) • Introduction • di-lepton invariant mass in HI collisions • Hidden Local Symmetry • Spectrum of vector meson and complex pole • Summary July 7 @ Montpellier

2. Introduction Chiral restoration : as T,m Hot / dense matter is qualitatively different from vacuum.  dynamical quark mass Mq~g BR scaling: hadron masses scale to the order param. fp cf. NG bosons • Inspection by Lattice QCD, sum rule, effective models… • experimental signature in heavy ion collision invariant mass distribution of di-lepton or 2p … Brown Rho, PRL 66(’91)2720 • How are meson spectra modified in medium?

3. Indication of modification in HI collisions  CERES/NA45 (Agakishiev et al.), PLB422(’98)405 Invariant Mass Spectrum of e+e- in p-Au, Pb-Au @ CERES

4. excess excess mr* ~0.9 mr(vac) @ r0 the excess over the known hadronic sources on the low mass side ofwpeak has been observed. Dropping r mass according to density  Naruki, et.al, PRL96(2006)092301 Invariant Mass Spectrum of e+e- in p-A @KEK-PS E325

5. Width broadening models are favored than dropping mass scenario • NA60 Collab (Floris et al.), nucl-ex/0606023 Width broadening in medium Invariant Mass Spectrum of m+m- in A-A coll. @ CERN-SPS NA60 • Talk by Scomparin for NA60 Collab @ QM05

6. = a Ta: NG boson of [ SU(Nf )L SU(Nf )R] global symmetry breaking s =sa Ta : NG boson of [ SU(N f ) V] local symmetry breaking Hidden Local Symmetry M.Bando, T.Kugo, S.Uehara, K.Yamawaki and T.Yanagida, PRL 54, 1215 (1985)  Bando et al, Phys. Rep. 164 (’88) 297 [ SU (N f ) LSU (N f ) R] global[SU (N f ) V ]local  [SU (N f ) v ] global U=e2ip /Fp=xL†xR } h [ SU(N f ) V ] local g L, R[ SU(N f ) L, R]global xL,R = eis /Fs eip /Fp hxL,R gL,R rm=rma Ta: HLS gauge boson

7. Hidden Local Symmetry • Maurer-Cartan 1-forms • Lagrangian Fp ;g grpp ; Mr = g Fs

8. Optimized perturbation theory Chiku & Hatuda, Phys. Rev. D58 (’98) 076001 OPT : resummation technique in thermal field theory 1. Introduce optimal parameters, treated as perturbation 2. The optimal parameters are determined so that perturbative corrections become small.

9. Gradual broadening of spectral peak at low T, rapid modification near Tc. T dependence of spectrum • T dependence of decay constants and spectrum

10. T = 220 MeV Close to Tc As T increases T =180 MeV pole of propagator in comlex p0 plane T = 0 MeV Im p0 T = 204 MeV Re p0

11. 0 -1 -2 -3 Vector manifestation & s pole in the chiral limit • Vector Manifestation Weinberg, PR 166 (‘68) 1568 ; Harada, Sasaki, PLB.537(2002) 280 chiral partner of p : longitudinal mode of r  mr  0 as TTc w/ Wilsonian matching & RG • s pole in linear sigma model  Patkos, et.al, PRD66(2002)116004

12. Complex pole of propagator and spectrum Im p0 Re p0

13. Summary • vector mesons as gauge boson of hidden local symmetry • spectrum of vector meson with finite T  resummation via OPT gradualbroadening of width for low T & rapiddropping of r mass near Tc • T dependence of spectrum pole of propagator in complex plane • vector manifestation mr  0 as TTc • space-time evolution of medium is essential for analysis of • heavy ion collisions