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Effects of vector – axial-vector mixing to dilepton spectrum in hot and/or dense matter

Effects of vector – axial-vector mixing to dilepton spectrum in hot and/or dense matter. Masayasu Harada (Nagoya Univ.). @ Heavy Ion Meeting 2010-12 at Yonsei (December 11, 2010). based on M.H. and C.Sasaki , PRD74, 114006 (2006)

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Effects of vector – axial-vector mixing to dilepton spectrum in hot and/or dense matter

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  1. Effects of vector – axial-vector mixing to dilepton spectrum in hot and/or dense matter Masayasu Harada (Nagoya Univ.) @ Heavy Ion Meeting 2010-12 at Yonsei(December 11, 2010) based on M.H. and C.Sasaki, PRD74, 114006 (2006) 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., S.Matsuzaki and K.Yamawaki, Phys. Rev. D 82, 076010 (2010)   M.H. and M.Rho, arXiv:1010.1971 [hep-ph]

  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. (S. Weinberg, 69’) ☆ Quark Structure and Chiral representation ◎coupling to currents and densities longitudinal components Note: ρ andA1（π and σ）are chiral partners？ These are partners …

  8. Chiral Restoration vector manifestation linear sigma model π, ρ degenerate: mρ → mπ σ, A1degenerate: mσ→ mA1 π、σ degenerate: mσ → mπ ρ, A1degenerate: mA1→ mρ Hybrid Scenario(π、ρ, A1, σdegenerate) : mσ = mA1 = mρ = mπ Either of 3 is expected to happen → dropping mass

  9. ◎ Signal of chiral symmetry restoration 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 ! ρ etc etc How these mixing effects are seen in the vector spectral function ? e- e+

  10. Outline 1. Introduction 2. Di-lepton spectrum from the dropping ρ in the vector manifestation (Effect of the violation of r meson dominance) 3. Effect of Vector-Axial-vector mixing in hot matter 4. Effect of V-A mixing in dense baryonic matter 5. Summary

  11. 2. Di-lepton spectrum from the dropping ρ in the vector manifestation (Effect of the violation of vector dominance)

  12. Chiral Restoration vector manifestation linear sigma model π, ρ degenerate: mρ → mπ σ, A1degenerate: mσ→ mA1 π、σ degenerate: mσ → mπ ρ, A1degenerate: mA1→ mρ Hybrid Scenario(π、ρ, A1, σdegenerate) : mσ = mA1 = mρ = mπ only p and r are taken into account : Dropping r mass

  13. ◎ Assumptions ・ Relevant d.o.f until near Tc-ε ・・・ only π and ρ ・ Other mesons (A1, σ, ...) ・・・ still heavy ・ Partial chiral restoration already at Tc-ε ☆ Formulation of the VM ◎ View of the VM in Hot Matter

  14. ☆ Formulation of the VM ◎ Hidden Local Symmetry ・・・ EFT for r and pbased on chiral symmetry of QCD 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) r = gauge boson of the HLS massive through the Higgs mechanism Systematic low-energy expansion including dynamical r 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) loop expansion ⇔ derivative expansion ◎ VM is protected by the VM fixed point ・ stable against the quantum corrections M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001) ・ stable against the thermal corrections M.H. and C.Sasaki, Phys. Lett. B 537, 280 (2002) ・ stable against the density corrections M.H., Y. Kim and M. Rho, Phys. Rev. D 66, 016003 (2002).

  15. e+ e- ☆ Key 1 : Strong Violation of r meson dominance in the VM ◎r meson dominance at T = 0 e+ e- 1 – a/2 a/2 a = 2 ⇒ vector dominance long standing problem not clearly explained in QCD ! ◎r dominance at T > 0 ? 0 → 1 1 → 1/2 ◎ a = 2 kept fixed in several analyses (No T-dependence on a)

  16. ☆ Key 2 : Dropping ρ occurs only forT > Tf ~ 0.7 Tc G.E.Brown, C.H.Lee and M.Rho, PRC74, 024906 (2006); NPA747, 530 (2005) (H.v.Hees and R.Rapp, hep-ph/0604269) ＋ Suppression by the violation of VD When the r meson coming from the region T < Tf gives dominant contribution to the dilepton spectrum, the dropping r scenario may not be excluded by NA60 data cf : “Hadronic freedom” leads to the small interactions for T > Tf, so that the r from T > Tf is highly suppressed. G.E.Brown, MH, J.W.Holts, M.Rho, C.Sasaki, PTP 121, 1209 (2009)

  17. T dependence of r with dropping mass for T > Tf = 0.7 Tc VM with VD T = 0.75 Tc ρ mass mρ → 0 VM VM ~ VM with VD /1.8 T = 0.8 Tc ◎violation of “Vector meson dominance” → Large suppression near Tc Tf/Tc We need to include other hadrons such as A1 to make a comparison with experiment. VM ~ VM with VD / 2

  18. 3. Effect of Vector-Axialvector mixing in hot matter MH, C.Sasaki and W.Weise, Phys. Rev. D 78, 114003 (2008) Using an Effective field theory including p, r, A1 based on the generalized hidden local symmetry

  19. Chiral Restoration vector manifestation linear sigma model π, ρ degenerate: mρ → mπ σ, A1degenerate: mσ→ mA1 π、σ degenerate: mσ → mπ ρ, A1degenerate: mA1→ mρ Hybrid Scenario(π、ρ, A1, σdegenerate) : mσ = mA1 = mρ = mπ ρ mass is invariant → dropping A1& σ masses

  20. ☆ T – dependence of ρ and A1 meson masses A simple assumption for the parameters of the GHLS Lagrangian no-dropping dropping

  21. ◎ Vector spectral function at T/Tc = 0.8 + 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

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

  23. Chiral Restoration vector manifestation linear sigma model π, ρ degenerate: mρ → mπ σ, A1degenerate: mσ→ mA1 π、σ degenerate: mσ → mπ ρ, A1degenerate: mA1→ mρ Hybrid Scenario(π、ρ, A1, σdegenerate) : mσ = mA1 = mρ = mπ Either of 3 is expected to happen → dropping mass

  24. ☆ Dropping A1 withdropping ρ T/Tc = 0.8 Effect of A1meson s1/2 = 2 mρ Effect of dropping A1 ・ Spectrum around the ρ pole is suppressed ・ Enhancement around A1-πthreshold ・ Cusp structure around s1/2= 2mρ

  25. ☆ 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 !

  26. 4. 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, Phys. Rev. D 82, 076010 (2010) M.H. and M.Rho, arXiv:1010.1971 [hep-ph]

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

  28. ☆ 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)]

  29. ☆ Determination of mixing strength C ◎ An estimation from w dominance + w e- Cw～ 0.1 GeV × (nB / n0) ρ A1 n0 : normal nuclear matter density e+ a very rough estimation ◎ An estimation in a holographic QCD (AdS/QCD) model ・ Infinite tower of vector mesons (w, w’, w”, …) in AdS/QCD models ・ These effects of 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)

  30. Can infinite tower of w mesons contribute ? This is related to a long-standing problem of QCD not clearly understood: Why does the r/w meson dominance work well ? n n t p Example 1: vector form factor int -> KpKbarnt at CLEO t K p a1 a1 CLEO, PRL92, 232001 (2004) r, r’ K* K K K K K n n t t p K p r, r’, r’’ w r, r’, r’’ K* K CLEO results : • : 1/(1+l+d) = 1.27 • ‘ : l/(1+l+d) = - 0.40 • ‘’ : d/(1+l+d) = 0.13

  31. Example 2: 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 T.Sakai, S.Sugimoto, PTP113, PTP114 k=1 : r meson k=2 : r’ meson k=3 : r” meson … r meson dominance ⇒ ; r a1(1260) r’(1450) PDG 776 1230 1465 SS 776(input) 1190 1607 Note: AdS/QCD model is for large Nc limit = 1.31 + (-0.35) + (0.05) + (-0.01) + … r’’’ r r’ r’’

  32. Example 2: p EM form factor MH, S.Matsuzaki, K.Yamawaki, arXiv:1007.4715 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 !

  33. Example 3: wp transition form factor MH, S.Matsuzaki, K.Yamawaki, arXiv:1007.4715 cf : MH, K.Yamawaki, Phys.Rept 381, 1 (2003) • Sakai-Sugimoto model : c2/dof=45/31=1.5 1 Exp data: CMD-2, PLB613, 29 (2005) NA60, PLB677, 260 (2009) • best fit in the HLS : • c2/dof=24/30=0.8 r meson dominance : c2/dof=124/31=4.0

  34. Example 4: Proton EM form factor M.H. and M.Rho, arXiv:1010.1971 [hep-ph] • meson dominance : • c2/dof=187 • best fit in the HLS : • c2/dof=1.5 a = 4.55 ; z = 0.55 • Sakai-Sugimoto: Hong-Rho-Yi-Yee 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

  35. ◎ 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 ・・・

  36. ☆ 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

  37. ☆ 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

  38. ☆ Di-lepton spectrum at T = 0.1 GeV with C = 1 GeV 2 mp note : Gr = 0 for √s < 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

  39. ☆ 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

  40. ◎ f meson spectral function spin 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

  41. ☆ Integrated rate with r, w and f mesons for C = 0.3, 0.5, 1 GeV (at T = 0.1GeV) ・ 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

  42. 5. Summary ◎ chiral symmetry restoration in hot and/or dense medium → mass change of either ρ, A1 (or both) can be expected ◎ Dilepton spectrum from the dropping r in the VM ・In the VM, strong violation of the vector (ρ) meson dominance is expected → large suppression of dilepton spectrum ◎ Effect of axial-vector (A1) meson ・ In the standard scenario, dropping A1 is expected. Through the V-A mixing, we may see the dropping A1. Note : The mixing becomes small associate with the chiral restoration. ga1rp～ Fp2 → 0 at T = Tc → Observation of dropping A1 may be difficult ・ In case of dropping A1 with dropping ρ, effect of A1 suppress the di-lepton spectrum cusp structure around s1/2= 2mr

  43. ◎ 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

  44. ☆ 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 !

  45. The End

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