Restoration of chiral symmetry and vector meson in the generalized hidden local symmetry

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. Outline • Introduction • Vector meson in the medium • Restoration pattern of chiral symmetry • Chiral restoration: π, ρ and A1 system • Generalized Hidden Local Symmetry(GHLS) • Restoration patterns • Summary Yoshimasa Hidaka

3. Introduction QCD phase diagram Restorationof chiral symmetry medium Lepton pair Yoshimasa Hidaka

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

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

6. NA60 and our calculation NA60 ρspetrumin the HLS model with OPT Chiral limit Y.H. Ph.D Thesis(2005) By E. Scomparin’s talk@QM2005 Yoshimasa Hidaka

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

8. Necessity of A1 Vector Manifestation with Hidden Local Symmetry model(π, ρ) Large-Nf(Harada and Yamawaki) Finite-T(Harada and Sasaki) Finite-μ(Harada, Kim and Rho) chiral partner ρ pairs with A1 in the standard scenario. chiral partner mixing (F. J. Gilman and H. Harari (1968), S. Weinberg(1969)) mixing angle The STAR Ratio A1 plays important role. (Brown, Lee and Rho nurcl-th/0507073) It is necessary to incorporate A1. Yoshimasa Hidaka

9. Generalized Hidden Local Symmetry(Bando, Kugo, Yamawaki (1985)) The GHLS model is an effective model based on the non-linear sigma model including π, ρand A1. Chiral symmetry π：NG bosons associated with global chiral symm. breaking. ρ, A1 : Gauge bosons σ, p：NG bosons associated with local chiral symm. breaking. 　　　　　　　⇒ σ and p are absorbed by the ρ and A1. Yoshimasa Hidaka

10. Generalized Hidden Local Symmetry The Lagrangian at lowest order parameters Decay constants masses ρππ coupling π-A1 mixing γ: mixing parameter betweenπ and A1 Yoshimasa Hidaka

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

12. Renormalization Group Equations One-loop diagrams RGEs are given by calculating these diagrams. Yoshimasa Hidaka

13. Renormalization Group Equations Renormalization Group Equations Yoshimasa Hidaka

14. Restoration Pattern Restoration condition and renormalization invariance Mixing angle Yoshimasa Hidaka

15. Pion form factor and VMD VMD Standard fixed point VM fixed point Intermediate fixed point Yoshimasa Hidaka

16. Decay width The rho-pi-pi coupling becomes weak due to . ρbecomes 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. Yoshimasa Hidaka

17. Summary • We have studied the restoration patterns of the chiral symmetry in GHLS model including A1 in addition to π and ρ. • By including A1 we have found three possibilities of the restoration patterns, • the Standard • VM • Intermediate • Both ρ and A1 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-Nf. Yoshimasa Hidaka