1. Effects on the Vector Spectral Function from Vector-Axialvector mixing based on the Hidden Local Symmetry combined with AdS/QCD Masayasu Harada (Nagoya Univ.) @ × (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. Origin of Mass ? of Hadrons of Us 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 T critical 170 – 200 MeV critical a few times of normal nuclear matter density Change of Hadron masses ?

5. 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 T critical and/or ρ ρ critical 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)

6. Di-lepton data consistent with dropping vector meson mass KEK-PS/E325 experiment m = m 0 (1 - / 0 ) for = 0.09 m = m 0 (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 P T Analysis : J.Ruppert, C.Gale, T.Renk, P.Lichard and J.I.Kapusta, PRL100, 162301 (2008) NA60 CLAS R. Nasseripour et al. PRL99, 262302 (2007). M.H.Wood et al. PRC78, 015201 (2008)

7. Signal of chiral symmetry restoration other than dropping ? axial-vector current (A 1 couples) vector current (ρ couples) These must agree with each other e-e- e+e+ vector mesons (ρ etc.) e ν axial-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+ e-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 e-e- e+e+ A1 π + ρ e-e- e+e+ π ρ Effects of pion mass Enhancement around s 1/2 = m a – m π Cusp structure around s 1/2 = m a + m π V-A mixing originated from -A 1 - interaction

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

12. Vanishing V-A mixing (g a1 = 0) at Tc ? In quark level A1 Left chirality L L R We need to flip chirality once in a1- - coupling g a1 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 transverse and A 1 ex : for p = (p 0, 0, 0, p) no mixing between V 0,3 and A 0,3 (longitudinal modes) mixing between V 1 and A 2, V 2 and A 1 (transverse modes) Dispersion relations for transverse and A 1 + sign transverse A 1 [p 0 = m a1 at rest (p = 0)] - sign transverse [p 0 = m at rest (p = 0)]

15. Determination of mixing strength C An estimation from dominance A 1 interaction term an empirical value : (cf: N.Kaiser,U.G.Meissner, NPA519,671(1990)) NN interaction provides the condensation in dense baryonic matter an empirical value : Mixing term from dominance

16. An estimation in a holographic QCD (AdS/QCD) model Infinite tower of vector mesons in AdS/QCD models,,, … These infinite 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 mesons contribute ? This is related to a long-standing problem of QCD not clearly understood: The / meson dominance seems to work well. Here I would like to show some examples of the violation of / dominance meson dominance ; Example 1: EM form factor In an effective field theory for and based on the Hidden Local Symmetry EM form factor is parameterized as In Sakai-Sugimoto model (AdS/QCD model), infinite tower of mesons do contribute k=1 : meson k=2 : meson k=3 : meson … T.Sakai, S.Sugimoto, PTP113, PTP114 = 1.31 + (-0.35) + (0.05) + (-0.01) + …

18. Example 1: EM form factor meson dominance 2 /dof = 226/53=4.3 ; SS model : 2 /dof = 147/53=2.8 best fit in the HLS : 2 /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 meson dominance ! MH, S.Matsuzaki, K.Yamawaki, PRD82, 076010 (2010) cf : MH, K.Yamawaki, Phys.Rept 381, 1 (2003)

19. Example 2: Proton EM form factor M.H. and M.Rho, arXiv:1102.5489 meson dominance : 2 /dof=187 best fit in the HLS : 2 /dof=1.5 a = 4.55 ; z = 0.55 Violation of / 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: 2 /dof=20.2 a = 3.01 ; z = -0.042

20. An estimation in a holographic QCD (AdS/QCD) model Infinite tower of vector mesons in AdS/QCD models,,, … These infinite 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 × (n B /n 0 ) at n B = 5 n 0 C = 0.5 × (n B /n 0 ) at n B = n 0 This may be too big, but we can expect some contributions from heavier,, …

21. Dispersion relations meson A 1 meson C = 0.5 GeV : small changes for and A 1 mesons C = 1 GeV : small change for A 1 meson substantial change in meson

22. Vector spectral function for C = 1 GeV note : = 0 for s < 2 m low 3-momentum (p bar = 0.3 GeV) longitudinal mode : ordinary peak transverse mode : an enhancement for s < m and no clear peak a gentle peak corresponding to A 1 meson spin average (Im G L + 2 Im G T )/3 : 2 peaks corresponding to and A 1 high 3-momentum (p bar = 0.6 GeV) longitudinal mode : ordinary peak transverse mode : 2 small bumps and a gentle A 1 peak spin averaged : 2 peaks for and A 1 ; Broadening of peak

23. Effect of vector - axial-vector mixing (V-A mixing) in hot matter Effect of the dropping A 1 to the vector spectral function might be relevant through the V-A mixing. Note : The mixing becomes small associate with the chiral restoration. g a F 2 0 at T = Tc Observation of dropping A1 may be difficult 4. Summary

24. Effect of V-A mixing (violating charge conjugation) in dense baryonic matter for -A 1, -f 1 (1285) and -f 1 (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 : C = 0.3 GeV at n B = 3 n 0. This V-A mixing becomes relevant for n B > 3 n 0

25. Including dropping mass (especially dropping ) ? This mixing will not vanish at the restoration. (cf: V-A mixing in hot matter becomes small near Tc.) Future work Dropping may cause a vector meson condensation at high density. ex: m */m = ( 1 – 0.1 n B /n 0 ) suggested by KEK-E325 exp. C = 0.3 (n B /n 0 ) [GeV] just as an example Vector meson condensation ! vacuum longitudinal transverse p0p0 p n B /n 0 = 2 n B /n 0 = 3 n B /n 0 = 3.1