Masayasu Harada (Nagoya Univ.)

@KEK 理論センター研究会 「原子核・ハドロン物理」 (August 11, 2009)

based on M.H. and C.Sasaki, arXiv:0902.3608 M.H., C.Sasaki and W.Weise, Phys. Rev. D 78, 114003 (2008)

see also M.H. and C.Sasaki, PRD74, 114006 (2006)

Effects of vector – axial-vector mixing to dilepton spectrum

in hot and/or dense matter

Origin of Mass ?of Hadrons

of Us

One of the Interesting problems of QCD=

Origin of Mass = quark condensate

Spontaneous Chiral Symmetry Breaking

☆ QCD under extreme conditions・ Hot and/or Dense QCD・ large flavor QCD

◎ Chiral symmetry restoration

Tcritical ～ 170 – 200 MeV

rcritical ～ a few times of normal nuclear matter density

Nfcritical ～ 5 – 12 (still asymptotically free)

Change of Hadron masses ?

Masses of mesons become lighter due to chiral restoration

☆ Dropping mass of hadrons

◎ Brown-Rho scaling G.E.Brown and M.Rho, PRL 66, 2720 (1991)

for T → Tcritical and/or ρ → ρcritical

◎ NJL model T.Hatsuda and T.Kunihiro, PLB185, 304 (1987)

◎ QCD sum rule :T.Hatsuda and S.H.Lee, PRC46, R34 (1992)

T.Hatsuda, Quark Matter 91 [NPA544, 27 (1992)]

◎ Vector Manifestation M.H. and K.Yamawaki, PRL86, 757 (2001)M.H. and C.Sasaki, PLB537, 280 (2002)M.H., Y.Kim and M.Rho, PRD66, 016003 (2002)

☆ Di-lepton data consistent with dropping massAnalysis : R.Rapp and J.Wambach, ANP 25,1 (2000)Exp: G.Agakishiev et al. [CERES], PRL75, 1272 (1995) ◎ KEK-PS/E325 experiment

mr = m0 (1 - /0) for = 0.09

mf = m0 (1 - /0) for = 0.03

K.Ozawa et al., PRL86, 5019 (2001)M.Naruki et al., PRL96, 092301 (2006)R.Muto et al., PRL98, 042501 (2007)F.Sakuma et al., PRL98, 152302 (2007)

☆ Di-lepton data (NA60) consistent with NO dropping massH.v.Hees and R.Rapp, NPA806, 339 (2008)

All PT

J.Ruppert, C.Gale, T.Renk, P.Lichard and J.I.Kapusta, PRL100, 162301 (2008)

Outline

1. Introduction

2. Effect of Vector-Axialvector mixing

in hot matter

3. Effect of V-A mixing in dense baryonic matter

4. Summary

☆ A model including π, ρ, A1 based on the generalized hidden local symmetry

・ Generalized HLS M.Bando, T.Kugo and K.Yamawaki, NPB 259, 493 (1985) M.Bando, T.Fujiwara and K.Yamawaki, PTP 79, 1140 (1988)・ Loop effect in the G-HLS MH, C.Sasaki, PRD 73, 036001 (2006)

◎ Dropping A1 without dropping ρ

A1(1260) becomes light, while ρ does not

Effect of dropping A1 to di-lepton spectrum

(Standard Scenario for Chiral Restoration)

◎ Dropping A1 with dropping ρ

Both A1(1260) and ρ become light.

(Hybrid Scenario for Chiral Restoration)

2. Effect of Vector-Axialvector mixing in hot matterMH, C.Sasaki and W.Weise, Phys. Rev. D 78, 114003 (2008)

☆ T – dependence of ρ and A1 meson massesHadronic many body effects (p and A1 loop corrections) included

Note : mp = 0 (chiral limit)

◎ Dropping A1 without dropping ρ

A1 meson

A1 meson effects ・ Im Gv around the ρ pole is suppressed (collisional broadening) ・ Im Gv is enhanced around the A1-π threshold

e-

e+A1

π +ρ

e-

e+A1

π

ρ

◎ Effect of pion mass

e-

e+A1

π +ρ

e-

e+A1

π

ρ

Effects of pion mass ・ Enhancement around s1/2 = ma – mπ ・ Cusp structure around s1/2 = ma + mπ

◎ V-A mixing → small near Tc

☆ Dropping A1 with dropping ρ (mπ = 0)

T/Tc = 0.8

Effect of A1 meson

s1/2 = 2 mρ

Effect of dropping A1

・ Spectrum around the ρ pole is suppressed ・ Enhancement around A1-π threshold ・ Cusp structure around s1/2= 2mρ

All PT

J.Ruppert, C.Gale, T.Renk, P.Lichard and J.I.Kapusta, PRL100, 162301 (2008)

H.v.Hees and R.Rapp, NPA806, 339 (2008)

☆ Dropping A1 was seen ?

may need detailed analysis ?

◎ V-A mixing from the current algebra analysis in the low density region B.Krippa, PLB427 (1998)

3. Effect of V-A mixing in dense baryonic matter

・ This is obtained at loop level in a field theoretic sense.・ Is there more direct V-A mixing at Lagrangian level ? such as ￡ ～ Vm Am ? ・・・ impossible in hot matter due to parity and charge conjugation invariance ・・・ possible in dense baryonic matter since charge conjugation is violated but be careful since parity is not violated

[M.H. and C.Sasaki, arXiv:0902.3608]

☆ A possible V-A mixing term violates charge conjugation but conserves parity

generates a mixing between transverse r and A1

ex : for pm = (p0, 0, 0, p) no mixing between V0,3 and A0,3 (longitudinal modes) mixing between V1 and A2, V2 and A1 (transverse modes)

S.K.Domokos, J.A.Harvey, PRL99 (2007)

◎ Dispersion relations for transverse r and A1

+ sign ・・・ transverse A1 [p0 = ma1 at rest (p = 0)] - sign ・・・ transverse r [p0 = mr at rest (p = 0)]

☆ Determination of mixing strength C ◎ An estimation from w dominance

・ r A1 w interaction term

an empirical value : (cf: N.Kaiser,U.G.Meissner, NPA519,671(1990))

・ wNN interaction provides the w condensation in dense baryonic matter

an empirical value :

・ Mixing term from w dominance

◎ An estimation in a holographic QCD (AdS/QCD) model

・ Infinite tower of vector mesons in AdS/QCD models

w, w’, w”, …

・ These infinite w mesons can generate V-A mixing

・ This summation was done in an AdS/QCD modelS.K.Domokos, J.A.Harvey, PRL99 (2007)

☆ Dispersion relations

r meson A1 meson

・ C = 0.5 GeV : small changes for r and A1 mesons・ C = 1 GeV : small change for A1 meson substantial change in r meson・ C ～ 1.1 GeV : p0

2 < 0 for r → vector meson condensation ? [S.K.Domokos, J.A.Harvey, PRL99 (2007)]

☆ Integrated vector spectrum for C = 1 GeV

2 mp note : Gr = 0 for √s < 2 mp

◎ low p region ・ longitudinal mode : ordinary r peak ・ transverse mode : an enhancement for √s < mr and no clear r peak a gentle peak corresponding to A1 meson ・ spin average (Im GL + 2 Im GT)/3 : 2 peaks corresponding to r and A1

◎ high p region ・ longitudinal mode : ordinary r peak ・ transverse mode : 2 small bumps and a gentle A1 peak ・ spin averaged : 2 peaks for r and A1 ; Broadening of r peak

☆ Di-lepton spectrum at T = 0.1 GeV with C = 1 GeV

2 mp

・ A large enhancement in low √s region → result in a strong spectral broadening ・・・ might be observed in with low-momentum binning at J-PARC, GSI/FAIR and RHIC low-energy running

note : Gr = 0 for √s < 2 mp

☆ Effects of V-A mixing for w and f mesons・ Assumption of nonet structure → common mixing strength C for r-A1, w-f1(1285) and f-f1(1420)

・ Vector current correlator

note : we used the following meson widths

◎ f meson spectral functionspin averaged, integrated over 0 < p < 1 GeV

・ C = 1 GeV : suppression of f peak (broadening)・ C = 0.3 GeV : suppression for √s > mf enhancement for √s < mf

☆ Integrated rate with r, w and f mesons for C = 0.3, 0.5, 1 GeV

・ An enhancement for √s < mr , mw (reduced for decreasing C)・ An enhancement for √s < mf from f-f1(1420) mixing → a broadening of f width

(at T = 0.1GeV)

4. Summary ◎ Effect of vector - axial-vector mixing in hot matter

・ Dropping A1 in the standard scenario

Through the V-A mixing, we may see the dropping A1.

(Note: might be difficult since V-A mixing becomes small at T=Tc ?)

・ Dropping A1 with dropping ρ,

effect of A1 suppress the di-lepton spectrum

◎ Effect of V-A mixing in dense baryonic matter

for r-A1, w-f1(1285) and f-f1(1420)

→ ・ modification of dispersion relations ・ change in vector spectral function (broadening)

○ Large C ? :

・ If C = 0.1GeV, then this mixing will be irrelevant.・ If C > 0.3GeV, then this mixing will be important.・ We need more analysis for estimation.