Effects on the Vector Spectral Functionfrom Vector-Axialvector mixing

based on the Hidden Local Symmetrycombined with AdS/QCD

Masayasu Harada (Nagoya Univ.)@ 「素核宇宙融合」 × 「新ハドロン」 クロスオーバー研究会 (Kobe, June 23, 2011)based on

M.H. and C.Sasaki, Phys. Rev. C 80, 054912 (2009)] M.H., C.Sasaki and W.Weise, Phys. Rev. D 78, 114003 (2008)see also M.H. and C.Sasaki, PRD74, 114006 (2006) M.H., S.Matsuzaki and K.Yamawaki, PRD82, 076010 (2010) M.H. and M.Rho, arXiv:1102.5489 (to appear in PRD)

有限密度での対称性の回復とハドロンの性質

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

◎ Chiral symmetry restoration

Tcritical ～ 170 – 200 MeV

rcritical ～ a few times of normal nuclear matter density

Change of Hadron masses ?

Masses of mesons become light 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 vector meson mass ◎ 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 consistent with NO dropping vector meson mass

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

All PT

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

◎ NA60 ◎ CLASR. Nasseripour et al. PRL99, 262302 (2007).M.H.Wood et al. PRC78, 015201 (2008)

◎ Signal of chiral symmetry restoration other than dropping r ? axial-vector current (A1couples) ＝ vector current (ρ couples)

These must agree with each other

e-

e+vector mesons(ρ etc.)

e

νaxial-vector mesons

Impossible experimentally

But, in medium, this might be seen through the vector – axial-vector mixing !

How these mixing effects are seen in the vector spectral function ?ρ etc etc

e+

e-

, w, …

Outline

1. Introduction

2. Effect of Vector-Axialvector mixing

in hot matter

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

4. Summary

2. Effect of Vector-Axialvector mixing in hot matter

MH, C.Sasaki and W.Weise, Phys. Rev. D 78, 114003 (2008)

◎ Vector spectral function at T/Tc = 0.8

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 originated from r-A1-p interaction

◎ V-A mixing → small near Tc

◎ T-dependence of the mixing effect

☆ Vanishing V-A mixing (ga1rp = 0) at Tc ?

In quark level

A1

r

pLeft chirality

L

L

R

We need to flip chirality once in a1-r-p coupling

ga1rp < q∝ bar q > → 0 for T → Tc

Vector – axial-vector mixing vanishes at T = Tc !

3. Vector – Axial-vector mixingin dense baryonic matter

based on M.H. and C.Sasaki, Phys. Rev. C 80, 054912 (2009)see also M.H., S.Matsuzaki and K.Yamawaki, PRD82, 076010 (2010) M.H. and M.Rho, arXiv:1102.5489 (to appear in PRD)

☆ 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)

◎ 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)

Can infinite tower of w mesons contribute ?

This is related to a long-standing problem of QCD not clearly understood: The r/w meson dominance seems to work well.Here I would like to show some examples of the violation of r/w dominance

r meson dominance ⇒ ;

Example 1: p EM form factor• In an effective field theory for p and r based on the Hidden Local Symmetry p EM form factor is parameterized as

•In Sakai-Sugimoto model (AdS/QCD model), infinite tower of r mesons do contribute

k=1 : r mesonk=2 : r’ mesonk=3 : r” meson…

T.Sakai, S.Sugimoto, PTP113, PTP114

= 1.31 + (-0.35) + (0.05) + (-0.01) + …r’r r’’ r’’’

Example 1: p EM form factor

rmeson dominancec2/dof = 226/53=4.3

;

SS model : c2/dof = 147/53=2.8best fit in the HLS : c2/dof=81/51=1.6

Exp data :NA7], NPB277, 168 (1996)J-lab F(pi), PRL86, 1713(2001)J-lab F(pi), PRC75, 055205 (2007)J-lab F(pi)-2, PRL97, 192001 (2006)

Infinite tower works well as the r meson dominance !

MH, S.Matsuzaki, K.Yamawaki, PRD82, 076010 (2010)cf : MH, K.Yamawaki, Phys.Rept 381, 1 (2003)

Example 2: Proton EM form factor M.H. and M.Rho, arXiv:1102.5489

rmeson dominance : c2/dof=187

• best fit in the HLS : c2/dof=1.5

a = 4.55 ; z = 0.55

Violation of r/w meson dominance may indicate existence of the contributions from the higher resonances.Contribution from heavier vector mesons actually exists in several physical processes even in the low-energy region

• Hong-Rho-Yi-Yee (Hashimoto-Sakai-Sugimoto) model: c2/dof=20.2

a = 3.01 ; z = -0.042

◎ 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 model

In the following, I take C = 0.1 - 1 GeV.Note that e.g. C = 0.5 GeV corresponds to

C = 0.1 × (nB/n0) at nB = 5 n0

C = 0.5 × (nB/n0) at nB = n0

・・・

This may be too big, but we can expect some contributions from heavier w’, w’’, …

☆ 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

☆ Vector spectral function for C = 1 GeV

note : Gr = 0 for √s < 2 mp ◎ low 3-momentum (pbar = 0.3 GeV)

・ 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 3-momentum (pbar = 0.6 GeV) ・ 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

◎ Effect of vector - axial-vector mixing (V-A mixing) in hot matter ・ Effect of the dropping A1 to the vector spectral function might be relevant

through the V-A mixing.

Note : The mixing becomes small associate with the chiral restoration.

ga1rp ～ Fp2 → 0 at T = Tc

→ Observation of dropping A1 may be difficult

4. Summary

◎ Effect of V-A mixing (violating charge conjugation) in dense baryonic matter

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

→ ・ substantial modification of rho meson dispersion relation ・ broadening of vector spectral function ・・・ might be observed at J-PARC and GSI/FAIR

◎ 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 fixing C.

Note : Cw = 0.3 GeV at nB = 3 n0 . → This V-A mixing becomes relevant for nB > 3 n0

◎ Including dropping mass (especially dropping r) ?

・ This mixing will not vanish at the restoration. (cf: V-A mixing in hot matter becomes small near Tc.)

☆ Future work

・ Dropping r may cause a vector meson condensation at high density.

ex: mr*/mr = ( 1 – 0.1 nB/n0 ) suggested by KEK-E325 exp. C = 0.3 (nB/n0 ) [GeV] just as an example

Vector meson condensation !

vacuum r longitudinal r

transverse r

p0

p

nB/n0 = 2 nB/n0 = 3 nB/n0 = 3.1