スライド 1

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1 @ ( based on M.H., C.Sasaki and W.Weise, arxiv: , arxiv: see also G.E.Brown, M.H., J.W.Holts, M.Rho and C.Sasaki, arxiv: M.H. and C.Sasaki, Phys. Rev. D74, (2006) M.H. and C.Sasaki, Phys. Rev. D 73, (2006) M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003)

2

3 of Hadrons Origin of Mass? of Us = One of the Interesting problems of QCD

4 Origin of Mass = quark condensate Spontaneous Chiral Symmetry Breaking

5 QCD under extreme conditions Hot and/or Dense QCD large flavor QCD Chiral symmetry restoration T critical MeV ρ critical a few times of normal nuclear matter density Nf critical 5 12 (still asymptotically free)

6 - C. Bernard et al. PRD71, (2005)

7 Dropping mass of hadrons NJL model T.Hatsuda and T.Kunihiro, PLB185, 304 (1987) Brown-Rho scaling G.E.Brown and M.Rho, PRL 66, 2720 (1991) QCD sum rule : T.Hatsuda, Quark Matter 91 [NPA544, 27 (1992)] T.Hatsuda and S.H.Lee, PRC46, R34 (1992) for T T critical and/or critical Vector Manifestation M.H. and K.Yamawaki, PRL86, 757 (2001) M.H. and C.Sasaki, PLB537, 280 (2002) M.H., Y.Kim and M.Rho, PRD66, (2002) axial-vector meson M.H., C.Sasaki and W.Weise, arxiv: , arxiv:

8 Outline 1. Introduction 2. Dropping ρ and Di-lepton spectrum 3. Di-lepton spectrum from the dropping axial-vector meson 5. Summary

9 2. Dropping And Dilepton Spectra

10 for T Tc ; c (dropping in the vector manifestation) (Standard scenario) (Hybrid scenario)

11 QCD T B

12 Little Bang

13 temperature T [MeV] early universe LHC RHIC SPS thermal freeze-out KEK-PS ELSA hadron gas chemical freeze-out AGS SIS atomic nuclei quark-gluon plasma deconfinement chiral restoration neutron stars baryonic chemical potential µ B [GeV] SIS (GSI; Germany) AGS (Brookhaven; USA) SPS (CERN;Swintzerland) RHIC (Brookhaven; USA) KEK-PS (KEK; ) ELSA (Bonn; Germany) LHC (CERN) J-PARC ( + KEK) FAIR (GSI)

14 e - e +

15 CERN/SPS (1995, 1996)

16 G.Q.Li, C.M.Ko and G.E.Brown NPA 606, 568 (1996)

17 BR scaling m ρ 0 (d 2 N ee /dηdm)/(dn ch /dη) [100MeV/c 2 ] CERES/NA45 Pb(158AGeV)+Au p t >0.2GeV 2.1<η<2.65 Θ ee >35mrad <N ch >= data 95 data M ee [GeV] Rapp-Wambach, 2000

18 Dilepton production rate ; dilepton invariant mass photon self-energy e - 2 ~ Im e +

19 Im Π R R = (e + e - ) (e + e ) e - e + e + ~ q e - q q Nc = 3

20 e + e ( s < 1 GeV dominant) Im Im EM form factor

21 Dilepton Production from + - e + e - Im

22 A 1 e + e - ; N* N e + e - ; A 1, N*,, N, e - e + H.v.Hees and R.Rapp, NPA806, 339 (2008)

23 H.v.Hees and R.Rapp, NPA806, 339 (2008) dn/dm (per 20 MeV/c 2 ) 1000 J.Ruppert, C.Gale, T.Renk, P.Lichard and J.I.Kapusta, PRL100, (2008) GeV < P T < 2GeV NA60 diff. eta subtraction NA60 Data 4 π In-medium ρ & ω Vacuum ρ QGP D, Dbar Sum dn/dm (per 20 MeV/c 2 ) All P T M [GeV/c 2 ]

24 (H.v.Hees and R.Rapp, hep-ph/ )

25 intrinsic broadening (QCD sum rule) J.Ruppert and T.Renk, EPJ C49, 219 (2007) T

26 temperature T [MeV] early universe LHC RHIC SPS thermal freeze-out KEK-PS ELSA hadron gas chemical freeze-out AGS SIS atomic nuclei quark-gluon plasma deconfinement chiral restoration neutron stars baryonic chemical potential µ B [GeV] SIS (GSI; Germany) AGS (Brookhaven; USA) SPS (CERN;Swintzerland) RHIC (Brookhaven; USA) KEK-PS (KEK; ) ELSA (Bonn; Germany) LHC (CERN) J-PARC ( + KEK) FAIR (GSI)

27 Dilepton Spectrum

28 SPS/NA60 RHIC SPS RHIC RHIC???

29 temperature T [MeV] early universe LHC RHIC SPS thermal freeze-out KEK-PS ELSA hadron gas chemical freeze-out AGS SIS atomic nuclei quark-gluon plasma deconfinement chiral restoration neutron stars baryonic chemical potential µ B [GeV] SIS (GSI; Germany) AGS (Brookhaven; USA) SPS (CERN;Swintzerland) RHIC (Brookhaven; USA) KEK-PS (KEK; ) ELSA (Bonn; Germany) LHC (CERN) J-PARC ( + KEK) FAIR (GSI)

30 γ CBELSA/TAPS TAPS, ω π 0 γ with γ+a ω π 0 γ mω = pπ + advantage: π 0 γ large branching ratio (8 %) no ρ-contribution (ρ π 0 γ : ) disadvantage: p γ γ ( p ) 2 γa ω+ X γ π 0 γ γγ D. Trnka et al., PRL 94 (2005) after background subtraction σ m = 3. % m 0 π 0 -rescattering m ω =m 0 (1 - αρ/ρ 0 ) for α = 0.13

31 temperature T [MeV] early universe LHC RHIC SPS thermal freeze-out KEK-PS ELSA hadron gas chemical freeze-out AGS SIS atomic nuclei quark-gluon plasma deconfinement chiral restoration neutron stars baryonic chemical potential µ B [GeV] SIS (GSI; Germany) AGS (Brookhaven; USA) SPS (CERN;Swintzerland) RHIC (Brookhaven; USA) KEK-PS (KEK; ) ELSA (Bonn; Germany) LHC (CERN) J-PARC ( + KEK) FAIR (GSI)

32 KEK-PS/E325 in-medium mass modification K.Ozawa et al., PRL86, 5019 (2001) M.Naruki et al., PRL96, (2006) R.Muto et al., PRL98, (2007) F.Sakuma et al., PRL98, (2007) events[/10 MeV/c 2 ] (b) Cu counts/[6.7mev/c 2 ] Data Fitting Result 50 [GeV/c 2 ] m ρ =m 0 (1 - αρ/ρ 0 ) for α = [GeV/c 2 ] m φ =m 0 (1 - αρ/ρ 0 ) for α = 0.03

33 for T Tc ; c (dropping in the vector manifestation) (Standard scenario) (Hybrid scenario)

34 3. Di-lepton spectrum from the dropping axial-vector meson M.H., C.Sasaki and W.Weise, arxiv: , arxiv:

35 V-A mixing e - e e + M.Dey, V.L.Eletsky and B.L.Ioffe, PLB252, 620 (1990) cf: H.v.Hees and R.Rapp [NPA806, 339 (2008)] multi-pion

36 A model including,, A1 based on the generalized hidden local symmetry A 1 Generalized HLS M.Bando, T.Kugo and K.Yamawaki, NPB 259, 493 (1985) M.Bando, T.Fujiwara and K.Yamawaki, PTP 79, 1140 (1988) Loop effect in the G-HLS MH, C.Sasaki, PRD 73, (2006) without A1(1260) (Standard Scenario for Chiral Restoration) A 1 with A1(1260) (Hybrid Scenario for Chiral Restoration) Di-lepton A1

37 Chiral Lagrangian Non-Linear Realization of Chiral Symmetry SU(N ) SU(N ) SU(N ) f f f L R V Basic Quantity U = e Lagrangian L = F 2 4 a 2i T a /F L g U g R tr U U ; g SU(N ) L,R U U i L U + i U R L, R ; gauge fields of SU(N ) f L,R f L,R

38 Hidden Local Symmetry SU(N ) SU(N ) SU(N ) SU(N ) f L f R global f V local f V global 2i / F L U = e = i / F i / F L,R L,R L,R = e e h g F, F Particles Decay constants of and R h SU(N ) f V local g SU(N f ) L,R L,R global = a T a HLS gauge boson = a Ta NG boson of SU(N f ) L SU(N f ) R global symmetry breaking = a Ta NG boson of SU(N f ) V local symmetry breaking 3 parameters at the leading order F π pion decay constant m 2 = g 2 F 2 g gauge coupling of the HLS a = (F σ /F π ) 2 validity of the vector dominance

39 Generalized Hidden Local Symmetry Bando-Kugo-Yamawaki, NPB 259, 493 (1985); PTP 73, 1541 (1985); Phys.Rept. 164, 217 (1988) Bando-Fujiwara-Yamawaki, PTP 79, 1140 (1988) covariant derivatives

40 1-forms Lagrangian

41 Current correlators and Weinberg s sum rules Weinberg s sum 1 st and 2 nd sum rules stable against quantum corrections M.H. and C.Sasaki, Phys. Rev. D 73, (2006) Weinberg s sum rules

42 A1 without A1 Intrinsic T dependence

43 A1 + e - A1 e + e - A 1 pole ImGv A 1 - threshold A1 e +

44 V-A mixing Tc

45 + e - A1 e + e - s 1/2 = m a -m s 1/2 = m a + m A1 e +

46 V-A mixing Tc

47 A1 with (m = 0) T/Tc = 0.8 A1 s 1/2 = 2 m A 1 pole A 1 - threshold s 1/2 = 2m

48 A1 J.Ruppert, C.Gale, T.Renk, P.Lichard and J.I.Kapusta, PRL100, (2008) dn/dm (per 20 MeV/c 2 ) All P T M [GeV/c 2 ] H.v.Hees and R.Rapp, NPA806, 339 (2008)

49 4. Summary, A1 CERN/NA60 Dilepton NA60 RHIC KEK-PS/E325 CBELSA/TAPS A1 V-A mixing dropping A1 V-A mixing T=Tc CERN/NA60 dropping A1 dropping A1 with dropping A1 di-lepton spectrum s 1/2 = 2m

50

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