Masayasu Harada (Nagoya Univ.)

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

at Chiral 07 (Osaka, November 14, 2007)

see also M.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)

Hadron phase

Color-Superconducting phase

T Quark-Gluon-Plasma phase

☆ ＱＣＤ in hot and dense matter

μB

1. Introduction

☆ Melting of quark – anti-quark condensate

〈 q q 〉

Is there a signal ?

☆ Vector Manifestation

longitudinal = Chiral partner of

near chiral restoration point

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

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

☆ Brown-Rho scalingdropping mass ⇔ chiral symmetry restoration

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

Theoretical description of dropping 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).

☆ Dropping mass (Brown-Rho scaling) can explain

dropping massbased on Brown-Rho scaling

R.Rapp-J.Wambach, ANP 25,1 (2000)KEK-PS E325

CB/TAPS@ELSA

☆ 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 VM

gives a substancial suppression !

Effect from the violation of the VD to the rate ?

☆ 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??

Outline

1. Introduction

2. Hidden Local Symmetry

and the Vector Dominance

3. Thermal Dilepton Spectra

in the Vector Manifestation

4. Summary

2. Hidden Local Symmetry and the Vector Dominance

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)

H.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)

◎ Systematic low-energy expansion including dynamical

◎ Hidden Local Symmetry ・・・ EFT for and based on chiral symmetry of QCD

= gauge boson of the HLS massive through the Higgs mechanism

loop expansion ⇔ derivative expansion

☆ Hidden Local Symmetry

［SU(N ) × SU(N ) ］ ×［SU(N ) ］ → ［SU(N ) ］f f fL R Vglobal local Vf global

［SU(N ) × SU(N ) ］ ×［SU(N ) ］ → ［SU(N ) ］f f fL R Vglobal local Vf global

U = e = ξ ξ2iπ/ F πL†

R

ξ = e e → h ξ g±iπ / Fπiσ / FσL,R L,R L,R

†ξ = e e → h ξ g±iπ / Fπ±iπ / Fπiσ / Fσiσ / FσL,R L,R L,R

†

F , F ・・・ Decay constants of π and σπ σ

h ∈ ［ SU(N ) ］f V local

g ∈ ［ SU(N ) ］fL,R L,R global

・ Particles

ρμ = ρμa T a ・・・ HLS gauge boson

π=πaTa ・・・ NG boson of ［ SU(Nf)L×SU(Nf)R ］ global symmetry breaking

σ=σaTa ・・・ NG boson of ［ SU(Nf)V ］ local symmetry breaking

◎ 3 parameters at the leading order

F ・・・ pion decay constantg ・・・ gauge coupling of the HLS

a = (F/F)2 ⇔ validity of the vector dominance

m = ag Fπρ2 2 2

e+

e-

☆ Vector dominance ( dominance) at T = 0

a = 2 vector dominance⇒a/21 – a/2

long standing problem not clearly explained in QCD !

◎ 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).

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

☆ dominance at T > 0 ?

e+

e-

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

a/21 – a/2

◎ 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 m(T) → 0 for T → Tc

Strong violation of dominance in the VM

Strong suppression of contribution to the dilepton spectrum

0 → 1 1 → 1/2

☆ Intrinsic temperature dependence of parameters

・・・ obtained by integrating out heavier hadrons

・ Effects of heavy hadrons are negligible ?

・・・ Not True near the critical temperature

e.g., Hagedon temperature based on string model large Nc QCD each contribution from hadrons is suppressed by 1/Nc phase transition is driven by infinite number of hadrons

・ Infinite number of hadrons contribute near Tc

Integrating out infinite number of hadrons near Tc

→ a large T dependence of the parameters for effective models for light hadrons (e.g., π and ρ in the HLS)

in real-life QCD

・・・ Wigner realization of chiral symmetry

longitudinalρ ＝ chiral partner of π

c.f. conventional linear-sigma model manifestation

scalar meson = chiral partner of π

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

Quark Structure and Chiral representation

coupling to currents and densities

(S. Weinberg, 69’)longitudinal components

mρ → 0 is necessary ・・・ support BR scaling

Chiral Restoration

linear sigma modelvector manifestation

◎ Intrinsic T dependence ・・・ basic ingredient for the Vector Manifestation (VM)

◎ VM predicts

; dropping

; strong violation of the vector dominancea ☆ T-dependences of physical parameters

・・・ intrinsic T dependence + hadronic temperature effects from thermal π and ρ

intrinsic T dependence for T > Tf = 0.7 Tc

Tf/Tc

ρ mass mρ → 0

Tf/Tc

ρ width Γρ → 0

◎ Vector dominance ?

direct γππ coupling ： 1 – a/2

Tf/Tc

VD is good strong violation of the VD

・ Strong violation of the VD occurs near Tc

due to the intrinsic effect.

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

☆ Effect of violation of the vector dominance

VM (for T → Tc)

a(T) → 1

when m(T) → 0

VM with VD

a(T) = 2 kept fixed

when m(T) → 0

T = 0.4 Tc

No much difference !

v.s.

◎ 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

Violation of VD is very important

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

◎ 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

◎ Vector dominance in the HLS

・ a = 4/3 in the large Nc limit

・ a = 2 including 1/Nc corrections

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