Masayasu Harada (Nagoya Univ.)

at 熱場の量子論とその応用(YITP, September 5, 2007)

based onM.H. and C.Sasaki, Phys.Rev.D74:114006,2006

see alsoM.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003)M.H. and C.Sasaki, Phys. Lett. B 537, 280 (2002) M.H., Y. Kim and M. Rho, Phys. Rev. D 66, 016003 (2002).M.H. and C.Sasaki, Nucl. Phys. A 736, 300 (2004)

1. Introduction

☆ ＱＣＤ in hot and dense matter

Hadron phase

Color-Superconducting phase

T Quark-Gluon-Plasma phase

μB

☆ Melting of quark – anti-quark condensate

〈 q q 〉

Is there a signal ?

☆ Brown-Rho scalingdropping ρ mass ⇔ chiral symmetry restoration

G.E.Brown and M.Rho, Phys. Rev. Lett. 66 2720 (1991)

Theoretical description of dropping ρ mass.M.H. and C.Sasaki, Phys. Lett. B 537, 280 (2002)M.H., Y. Kim and M. Rho, Phys. Rev. D 66, 016003 (2002).

☆ Vector Manifestation

longitudinal ρ = Chiral partner of π

near chiral restoration point

M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001)

Dropping ρ mass ・・・ signal of the chiral restoration based on the VM.

☆ Recent experiments exclude dropping ρ ?NA60 Nucl.Phys.A774:715-718,2006. CERES : Talk given by P. Braun-Munzinger at KIAS-APCTP Workshop

"Relativistic Heavy-Ion Collison : Present and Future"2006-09 Heavy Ion Meeting (HIM 2006-09).

dropping ρ??

☆ These analyses seem to assume the vector dominance (VD).

G. E. Brown and M. Rho, arXiv:nucl-th/0509001; arXiv:nucl-th/0509002.

☆ Strong violation of the VD ・・・ Prediction of the VMgives a substancial suppression !

Effect from the violation of the VD to the rate ?

Outline

1. Introduction2. Hidden Local Symmetry

and the Vector Dominance3. Thermal Dilepton Spectra

in the Vector Manifestation4. Summary

2. Hidden Local Symmetry and the Vector Dominance ◎ Hidden Local Symmetry ・・・ EFT for ρ and π based on chiral symmetry of QCD

M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, PRL 54 1215 (1985)M. Bando, T. Kugo and K. Yamawaki, Phys. Rept. 164, 217 (1988)

ρ = gauge boson of the HLS massive through the Higgs mechanism

◎ Systematic low-energy expansion including dynamical ρH.Georgi, PRL 63, 1917 (1989); NPB 331, 311 (1990):M.H. and K.Yamawaki, PLB297, 151 (1992); M.Tanabashi, PLB 316, 534 (1993): M.H. and K.Yamawaki, Physics Reports 381, 1 (2003)

loop expansion ⇔ derivative expansion◎ 3 parameters at the leading order

Fπ ・・・ pion decay constantg ・・・ gauge coupling of the HLSa ・・・ dimensionless parameter

⇔ validity of the vector dominance

m = ag Fπρ2 2 2

e+

e-

☆ Vector dominance (ρ dominance) at T = 0

a = 2 ⇒ vector dominance1 – a/2

long standing problem not clearly explained in QCD !

a/2

◎ HLS analysis [M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003)]

・ a = 4/3 in the large Nc limit

cf: AdS/QCD anlysis by Sakai-Sugimoto, PTP143,843 (2005)

・ a = 2 including 1/Nc corrections

see also AdS/QCD analysis by M.H., M.Matsuzaki and K.Yamawaki, PRD74, 076004 (2006).

ρ dominance is accidental only for Nc = 3 (and T = 0)

☆ ρ dominance at T > 0 ?e+

e-

a/21 – a/2◎ a = 2 kept fixed in several analyses (No T-dependence on a)

However

◎ Parameters of hadronic Lagrangians depend on T.・・・ Intrinsic temperature dependence

signature of internal structure of hadrons(Hadrons are constructed from quarks and gluons.)

・ VM predicts a(T) → 1 when mρ(T) → 0 for T→ Tc

Strong violation of ρ dominance in the VM

M.H. and C.Sasaki, Phys.Rev.D74:114006,2006

☆ Effect of violation of the vector dominance

VM (for T→ Tc)a(T) → 1when mρ(T) → 0

VM with VDa(T) = 2 kept fixedwhen mρ(T) → 0

v.s.

T = 0.4 Tc

No much difference !

Violation of VD is very important◎ Near Tc

VM

VM with VDvacuum ρ

T = 0.75 Tc

VM < vacuum ρ< VM with VD !!

T = 0.8 Tc

vacuum ρ< VM < VM with VD

T = 0.85 Tc

vacuum ρ≪ VM ≪ VM with VD !!

Signal of the VM

◎ Hidden Local Symmetry Theory ・・・ EFT for ρ and πSystematic chiral perturbation including dynamical ρ

◎ Explanation of the vector dominance in the HLS

・ a = 4/3 in the large Nc limit

・ a = 2 including 1/Nc corrections

◎ Vector Manifestation in hot matter ・・・ mρ → 0 for T→ Tc

⇒mρ → 0 ・・・ signal of the chiral symmetry restoration !

・ strong violation of the VD・・・ important for the dilepton rate

◎ future direction ・ Effects of collisional broadening including A1, N, Δ, …・・・ work in progress (M.H. and C.Sasaki)