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

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### 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)

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

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

Experiment

•p-Au, Pb-Au [email protected]

KEK-PS E325

excess

excess

nucl-ex/0504016

Phys. Lett. 405(1998)

Yoshimasa Hidaka

NA60 and our calculation

NA60

ρspetrumin the HLS model with OPT

Chiral limit

Y.H. Ph.D Thesis(2005)

By E. Scomparin’s [email protected]

Yoshimasa Hidaka

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

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

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

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

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

Renormalization Group Equations

One-loop diagrams

RGEs are given by calculating these diagrams.

Yoshimasa Hidaka

Pion form factor and VMD

VMD

Standard fixed point

VM fixed point

Intermediate fixed point

Yoshimasa Hidaka

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

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

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