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Effects on the Vector Spectral Function from Vector- Axialvector mixing

有限密度での対称性の回復と ハドロンの性質. Effects on the Vector Spectral Function from Vector- Axialvector mixing based on the Hidden Local Symmetry combined 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

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Effects on the Vector Spectral Function from Vector- Axialvector mixing

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  1. 有限密度での対称性の回復と ハドロンの性質 Effects on the Vector Spectral Function from Vector-Axialvector mixing based on the Hidden Local Symmetry combined 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)

  2. of Hadrons of Us ? Origin of Mass = One of the Interesting problems of QCD

  3. ? Origin of Mass = quark condensate Spontaneous Chiral Symmetry Breaking

  4. ☆ 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 ?

  5. M.H. and K.Yamawaki, PRL86, 757 (2001) ◎Vector Manifestation M.H. and C.Sasaki, PLB537, 280 (2002) M.H., Y.Kim and M.Rho, PRD66, 016003 (2002) ☆ Dropping mass of hadrons Masses of mesons become light due to chiral restoration ◎ NJL model T.Hatsuda and T.Kunihiro, PLB185, 304 (1987) ◎ Brown-Rho scaling G.E.Brown and M.Rho, PRL 66, 2720 (1991) for T → Tcritical and/or ρ → ρcritical T.Hatsuda, Quark Matter 91 [NPA544, 27 (1992)] ◎ QCD sum rule : T.Hatsuda and S.H.Lee, PRC46, R34 (1992)

  6. All PT ☆ Di-lepton data consistent with dropping vector meson mass 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) ◎KEK-PS/E325 experiment mf=m0 (1 -  /0) for  = 0.03 mr=m0 (1 -  /0) for  = 0.09 ☆ Di-lepton data consistent with NO dropping vector meson mass ◎CLAS ◎NA60 Analysis : J.Ruppert, C.Gale, T.Renk, P.Lichardand J.I.Kapusta, PRL100, 162301 (2008) R. Nasseripour et al. PRL99, 262302 (2007). M.H.Wood et al. PRC78, 015201 (2008) Analysis : H.v.Heesand R.Rapp, NPA806, 339 (2008)

  7. ◎ Signal of chiral symmetry restoration other than dropping r ? axial-vector current (A1couples)＝ vector current(ρ couples) e e- These must agree with each other axial-vector mesons vector mesons (ρetc.) ν e+ Impossible experimentally But, in medium, this might be seen through the vector – axial-vector mixing ! , w, … How these mixing effects are seen in the vector spectral function ? e- ρ etc etc e+

  8. Outline 1. Introduction 2. Effect of Vector-Axialvector mixing in hot matter 3. Effect of V-A mixing in dense baryonic matter 4. Summary

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

  10. ◎ Vector spectral function at T/Tc = 0.8 V-A mixing originated from r-A1-p interaction + e- π ρ A1 e+ π e- ρ A1 e+ Effects of pion mass ・Enhancement around s1/2 = ma – mπ ・ Cusp structure around s1/2 = ma + mπ

  11. ◎ T-dependence of the mixing effect ◎ V-A mixing → small near Tc

  12. ☆ Vanishing V-A mixing (ga1rp = 0) at Tc ? In quark level r L L R A1 p Left chirality We need to flip chirality once in a1-r-p coupling ga1rp∝ < qbar q > → 0 for T → Tc Vector – axial-vector mixing vanishes at T = Tc !

  13. 3. Vector – Axial-vector mixing in 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)

  14. ☆ A possible V-A mixing term violates charge conjugation but conserves parity generates a mixing between transverser 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)]

  15. ☆ Determination of mixing strength C ◎ An estimation from w dominance ・ r A1winteraction term (cf: N.Kaiser,U.G.Meissner, NPA519,671(1990)) ・ wNN interaction provides the w condensation in dense baryonic matter an empirical value : an empirical value : ・ Mixing term from w dominance

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

  17. 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 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 r meson dominance ⇒ ; • In Sakai-Sugimoto model (AdS/QCD model), • infinite tower of r mesons do contribute T.Sakai, S.Sugimoto, PTP113, PTP114 k=1 : r meson k=2 : r’ meson k=3 : r” meson … = 1.31 + (-0.35) + (0.05) + (-0.01) + … r’’’ r r’ r’’

  18. Example 1: p EM form factor MH, S.Matsuzaki, K.Yamawaki, PRD82, 076010 (2010) cf : MH, K.Yamawaki, Phys.Rept 381, 1 (2003) 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) • meson dominance • c2/dof = 226/53=4.3 ; best fit in the HLS : c2/dof=81/51=1.6 SS model : c2/dof = 147/53=2.8 Infinite tower works well as the r meson dominance !

  19. Example 2: Proton EM form factor M.H. and M.Rho, arXiv:1102.5489 • meson dominance : • c2/dof=187 • best fit in the HLS : • c2/dof=1.5 a = 4.55 ; z = 0.55 • Hong-Rho-Yi-Yee (Hashimoto-Sakai-Sugimoto) model: c2/dof=20.2 a = 3.01 ; z = -0.042 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

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

  21. ☆ 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

  22. ☆ 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

  23. 4. Summary • ◎ 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

  24. ◎ 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

  25. ☆ Future work ◎ 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.) ・ 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 nB/n0 = 2 nB/n0 = 3.1 nB/n0 = 3 p0 longitudinal r vacuum r transverse r p Vector meson condensation !

  26. The End

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