1. Restoration of chiral symmetry and vector meson in the generalized hidden local symmetry Munehisa Ohtani (RIKEN) Osamu Morimatsu （ KEK ） Yoshimasa Hidaka(TITech) Based on Phys. Rev. D73,036004(2006)

2. 2005/11/14Yoshimasa Hidaka2 Outline Introduction –Vector meson in the medium –Restoration pattern of chiral symmetry Chiral restoration: π, ρ and A 1 system –Generalized Hidden Local Symmetry(GHLS) –Restoration patterns Summary

3. 2005/11/14Yoshimasa Hidaka3 Introduction QCD phase diagram Restoration of chiral symmetry medium Lepton pair

4. 2005/11/14Yoshimasa Hidaka4 becomes larger by interaction with medium particle Restoration of chiral symmetry Rapp-Wambach, Asakawa-Ko,..... Spectral function Mass Spectral function Mass Spectral function Mass Dropping Masses Melting Resonances QSR, B-R scaling…. Hatsuda-Lee, Brown-Rho….

5. 2005/11/14Yoshimasa Hidaka5 Experiment p-Au, Pb-Au collisions@CERES Phys. Lett. 405(1998)nucl-ex/0504016 KEK-PS E325 excess

6. 2005/11/14Yoshimasa Hidaka6 NA60 and our calculation Y.H. Ph.D Thesis(2005) Chiral limit NA60 By E. Scomparin’s talk @QM2005 ρspetrum in the HLS model with OPT

7. 2005/11/14Yoshimasa Hidaka7 Restoration Scenario of Chiral symmetry Which representation does the pion belong at restoration point ? Chiral partner of π Scalar mesonσ Chiral partner of π Vector meson(longitudinal)ρ Experiment: (F. J. Gilman and H. Harari (1968), S. Weinberg(1969)) Standard scenario Vector Manifestation scenario Helicity zero state (Harada, Yamawaki(2001))

8. 2005/11/14Yoshimasa Hidaka8 Necessity of A 1 It is necessary to incorporate A 1. ρ pairs with A 1 in the standard scenario. mixing chiral partner (F. J. Gilman and H. Harari (1968), S. Weinberg(1969)) mixing angle Vector Manifestation with Hidden Local Symmetry model(π, ρ) The STAR Ratio (Brown, Lee and Rho nurcl-th/0507073) A 1 plays important role. Large-N f (Harada and Yamawaki) Finite-T(Harada and Sasaki) Finite-μ(Harada, Kim and Rho)

9. 2005/11/14Yoshimasa Hidaka9 Generalized Hidden Local Symmetry (Bando, Kugo, Yamawaki (1985)) The GHLS model is an effective model based on the non-linear sigma model including π, ρ and A 1. π ： NG bosons associated with global chiral symm. breaking. ρ, A 1 : Gauge bosons σ, p ： NG bosons associated with local chiral symm. breaking. ⇒ σ and p are absorbed by the ρ and A 1. Chiral symmetry

10. 2005/11/14Yoshimasa Hidaka10 Generalized Hidden Local Symmetry The Lagrangian at lowest order masses Decay constants γ: mixing parameter between π and A 1 parameters π-A 1 mixing ρππ coupling

11. 2005/11/14Yoshimasa Hidaka11 Restoration Pattern in the GHLS model The vector and axial vector current correlators Restoration condition Renormalization group invariance at restoration point. This condition should be satisfied for all energy scale.

12. 2005/11/14Yoshimasa Hidaka12 Renormalization Group Equations One-loop diagrams RGEs are given by calculating these diagrams.

13. 2005/11/14Yoshimasa Hidaka13 Renormalization Group Equations

14. 2005/11/14Yoshimasa Hidaka14 Restoration condition and renormalization invariance Restoration Pattern Mixing angle Fixed point (μ→0) (I)VM1000 (II)VM Standard Intermediate 1 ∞ 3/2 0 ∞ 1/2 0 1 1/3 0

15. 2005/11/14Yoshimasa Hidaka15 Pion form factor and VMD VMD VM fixed point Intermediate fixed point Standard fixed point

16. 2005/11/14Yoshimasa Hidaka16 Decay width The rho-pi-pi coupling becomes weak due to. ρ becomes stable. Dileption emission A narrow ρ peak but weak magnitude in the pion background will be observed. The difference of restoration patterns will appear as a quantity of pion background and how the rho meson becomes narrow.

17. 2005/11/14Yoshimasa Hidaka17 Summary We have studied the restoration patterns of the chiral symmetry in GHLS model including A 1 in addition to π and ρ. By including A 1 we have found three possibilities of the restoration patterns, –the Standard –VM –Intermediate Both ρ and A 1 masses drop in all scenarios These three scenarios are different in the violation of the vector meson dominance. Further analysis –finite temperature and/or density, –Large-N f.