Masayasu Harada (Nagoya Univ.)

1. Effects of vector – axial-vector mixing to dilepton spectrum in hot and/or dense matter Masayasu Harada (Nagoya Univ.) @KEK理論センター研究会 「原子核・ハドロン物理」 (August 11, 2009) based on M.H. and C.Sasaki, arXiv:0902.3608 M.H., C.Sasaki and W.Weise, Phys. Rev. D 78, 114003 (2008) see also M.H. and C.Sasaki, PRD74, 114006 (2006)

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

3. ? Origin of Mass = quark condensate Spontaneous Chiral Symmetry Breaking

4. ☆ QCD under extreme conditions ・ Hot and/or Dense QCD ・ large flavor QCD ◎ Chiral symmetry restoration Tcritical～ 170 – 200 MeV rcritical～ a few times of normal nuclear matter density Nfcritical～ 5 – 12 (still asymptotically free) Change of Hadron masses ?

5. M.H. and K.Yamawaki, PRL86, 757 (2001) ◎Vector Manifestation M.H. and C.Sasaki, PLB537, 280 (2002) M.H., Y.Kim and M.Rho, PRD66, 016003 (2002) ☆ Dropping mass of hadrons Masses of mesons become lighter due to chiral restoration ◎ NJL model T.Hatsuda and T.Kunihiro, PLB185, 304 (1987) ◎ Brown-Rho scaling G.E.Brown and M.Rho, PRL 66, 2720 (1991) for T → Tcritical and/or ρ → ρcritical T.Hatsuda, Quark Matter 91 [NPA544, 27 (1992)] ◎ QCD sum rule : T.Hatsuda and S.H.Lee, PRC46, R34 (1992)

6. All PT ☆ Di-lepton data consistent with dropping mass K.Ozawa et al., PRL86, 5019 (2001) M.Naruki et al., PRL96, 092301 (2006) R.Muto et al., PRL98, 042501 (2007) F.Sakuma et al., PRL98, 152302 (2007) Analysis : R.Rapp and J.Wambach, ANP 25,1 (2000) Exp: G.Agakishiev et al. [CERES], PRL75, 1272 (1995) ◎KEK-PS/E325 experiment mf=m0 (1 -  /0) for  = 0.03 mr=m0 (1 -  /0) for  = 0.09 ☆ Di-lepton data (NA60) consistent with NO dropping mass H.v.Hees and R.Rapp, NPA806, 339 (2008) J.Ruppert, C.Gale, T.Renk, P.Lichard and J.I.Kapusta, PRL100, 162301 (2008)

7. Outline 1. Introduction 2. Effect of Vector-Axialvector mixing in hot matter 3. Effect of V-A mixing in dense baryonic matter 4. Summary

8. 2. Effect of Vector-Axialvector mixing in hot matter MH, C.Sasaki and W.Weise, Phys. Rev. D 78, 114003 (2008) ☆ A model including π, ρ, A1 based on the generalized hidden local symmetry ・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, 036001 (2006) ◎ Dropping A1 without dropping ρ A1(1260) becomes light, while ρ does not (Standard Scenario for Chiral Restoration) ◎ Dropping A1 with dropping ρ Both A1(1260) and ρ become light. (Hybrid Scenario for Chiral Restoration) Effect of dropping A1 to di-lepton spectrum

9. ◎ Dropping A1 without dropping ρ ☆ T – dependence of ρ and A1 meson masses Hadronic many body effects (p and A1 loop corrections) included Note : mp = 0 (chiral limit)

10. A1 meson + e- π ρ A1 e+ π e- ρ A1 e+ A1meson effects ・ImGv around the ρpole is suppressed (collisional broadening) ・ImGv is enhanced around the A1-π threshold

11. ◎ Effect of pion mass + e- π ρ A1 e+ π e- ρ A1 e+ Effects of pion mass ・Enhancement around s1/2 = ma – mπ ・ Cusp structure around s1/2 = ma + mπ

12. ◎ V-A mixing → small near Tc

13. ☆ Dropping A1 withdropping ρ (mπ = 0) T/Tc = 0.8 Effect of A1meson s1/2 = 2 mρ Effect of dropping A1 ・ Spectrum around the ρ pole is suppressed ・ Enhancement around A1-πthreshold ・ Cusp structure around s1/2= 2mρ

14. ☆ Dropping A1 was seen ? J.Ruppert, C.Gale, T.Renk, P.Lichard and J.I.Kapusta, PRL100, 162301 (2008) All PT H.v.Hees and R.Rapp, NPA806, 339 (2008) may need detailed analysis ?

15. 3. Effect of V-A mixing in dense baryonic matter [M.H. and C.Sasaki, arXiv:0902.3608] ◎ V-A mixing from the current algebra analysis in the low density region B.Krippa, PLB427 (1998) ・ This is obtained at loop level in a field theoretic sense. ・ Is there more direct V-A mixing at Lagrangian level ? such as ￡ ～ Vm Am ? ・・・ impossible in hot matter due to parity and charge conjugation invariance ・・・ possible in dense baryonic matter since charge conjugation is violated but be careful since parity is not violated

16. ☆ A possible V-A mixing term violates charge conjugation but conserves parity S.K.Domokos, J.A.Harvey, PRL99 (2007) generates a mixing between transverser and A1 ex : for pm = (p0, 0, 0, p) no mixing between V0,3 and A0,3 (longitudinal modes) mixing between V1 and A2, V2 and A1 (transverse modes) ◎ Dispersion relations for transverse r and A1 + sign ・・・ transverse A1 [p0 = ma1 at rest (p = 0)] - sign ・・・ transverse r[p0 = mr at rest (p = 0)]

17. ☆ Determination of mixing strength C ◎ An estimation from w dominance ・ r A1winteraction term (cf: N.Kaiser,U.G.Meissner, NPA519,671(1990)) ・ wNN interaction provides the w condensation in dense baryonic matter an empirical value : an empirical value : ・ Mixing term from w dominance

18. ◎ An estimation in a holographic QCD (AdS/QCD) model ・ Infinite tower of vector mesons in AdS/QCD models w, w’, w”, … ・ These infinite w mesons can generate V-A mixing ・ This summation was done in an AdS/QCD model S.K.Domokos, J.A.Harvey, PRL99 (2007)

19. ☆ Dispersion relations r meson A1 meson ・ C = 0.5 GeV : small changes for r and A1 mesons ・ C = 1 GeV: small change for A1 meson substantial change in r meson ・ C ～ 1.1 GeV : p02 < 0 for r→ vector meson condensation ? [S.K.Domokos, J.A.Harvey, PRL99 (2007)]

20. ☆ Integrated vector spectrum for C = 1 GeV 2 mp note : Gr = 0 for √s < 2 mp ◎ low p region ・ longitudinal mode : ordinary r peak ・ transverse mode : an enhancement for √s < mr and no clear r peak a gentle peak corresponding to A1 meson ・ spin average (Im GL + 2 Im GT)/3 :2 peaks corresponding to r and A1 ◎ high p region ・ longitudinal mode : ordinary r peak ・ transverse mode : 2 small bumps and a gentle A1 peak ・ spin averaged : 2 peaks for r and A1 ; Broadening of r peak

21. ☆ Di-lepton spectrum at T = 0.1 GeV with C = 1 GeV 2 mp note : Gr = 0 for √s < 2 mp ・ A large enhancement in low √s region → result in a strong spectral broadening ・・・ might be observed in with low-momentum binning at J-PARC, GSI/FAIR and RHIC low-energy running

22. ☆ Effects of V-A mixing for w and f mesons ・Assumption of nonet structure → common mixing strength C for r-A1, w-f1(1285) and f-f1(1420) ・ Vector current correlator note : we used the following meson widths

23. ◎ f meson spectral function spin averaged, integrated over 0 < p < 1 GeV ・C = 1 GeV : suppression of f peak (broadening) ・C = 0.3 GeV: suppression for √s > mf enhancement for √s < mf

24. ☆ Integrated rate with r, w and f mesons for C = 0.3, 0.5, 1 GeV (at T = 0.1GeV) ・ An enhancement for √s < mr , mw (reduced for decreasing C) ・ An enhancement for √s < mf from f-f1(1420) mixing → a broadening of f width

25. 4. Summary ◎ Effect of vector - axial-vector mixing in hot matter ・ Dropping A1 in the standard scenario Through the V-A mixing, we may see the dropping A1. (Note: might be difficult since V-A mixing becomes small at T=Tc ?) ・ Dropping A1 with dropping ρ, effect of A1 suppress the di-lepton spectrum ◎ Effect of V-A mixing in dense baryonic matter for r-A1, w-f1(1285) and f-f1(1420) → ・ modification of dispersion relations ・ change in vector spectral function (broadening) ○Large C ? : ・ If C = 0.1GeV, then this mixing will be irrelevant. ・ If C > 0.3GeV, then this mixing will be important. ・ We need more analysis for estimation.

26. The End