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Some Topics In Hot and Dense Matter in QCD

Some Topics In Hot and Dense Matter in QCD --- with a focus on the soft modes of QCD phase transitions ---. Teiji Kunihiro (Kyoto U.). The 34 th Reimei Workshop Physics of Heavy-Ion Collisions at J-PARC Aug. 8-9, 2016 @J-PARC. Contents.

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Some Topics In Hot and Dense Matter in QCD

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  1. Some Topics In Hot and Dense Matter in QCD --- with a focus on the soft modes of QCD phase transitions --- Teiji Kunihiro (Kyoto U.) The 34th Reimei Workshop Physics of Heavy-Ion Collisions at J-PARC Aug. 8-9, 2016 @J-PARC

  2. Contents 1.Precursory phenomena of Color superconductivity (CSC) 2. Phase diagram with the vector int. and axial anomaly: combined fluctuations of chiral and diquark fields 3. Functional RG amalysis of the soft mode of QCD CP: phonon mode v.s. sigma mesonic mode 4. Fate of density fluctuations near the QCD CP 5.Expected phenomena associated with (partial) chiral symmetry: a. vector-axial vector, b. scalar modes, c. parity doubling in baryon sector 6. A brief summary and concluding remarks

  3. Precursory Phenomena of color Superconductivity in Heated Quark Matter Ref. M. Kitazawa, T. Koide, T. K. and Y. Nemoto Phys. Rev. D70, 956003(2004); Prog. Theor. Phys. 114, 205(2005), M. Kitazawa, Y. Nemoto and TK, Phys. Lett.B 631(2005),157; PoS CPOD07 (2007)041 (arXiv.0711.4429)

  4. A conjectured QCD phase diagram QGP T RHIC/LHC FAIR, NICA, J-PARC Critical region cSB ? Various phases CSC CFL Ferromagnetism? m  0

  5. FAIR,NICA, J-PARC hadrons CSC Diquark pair fluctuations prior to CSC T The diquark excitations as the soft mode of CSC m ε→０ （Ｔ→ＴＣ） The strong coupling nature of CSC eads to a sharp peak even atε~ 0.2 electric SC： ε~ 0.005 even in 2d-SC Existence of large pair fluctuations M.Kitazawa, T. Koide, T. K., Y. Nemoto, PRD 65, 091504 (2002) It may affect various observables even well above Tc.

  6. Aslamasov-Larkin effects on lepton-pair production M.Kitazawa, Y. Nemoto and TK, PoS CPOD07 (2007) 041;arXiv:0711.4429 Photon Self-Energy P k Aslamasov and Larkin,Sov. Phys. SS 10,875(’68) collective pairing oscillation Vertex: factor 3 due to color degrees of freedom Pair field (T-matrix): p2 p1 cf) Maki-Thompson term AL term represents the effects of the virtual Cooper pairs on the photon self-energy.

  7. An enhancement of dilepton-pair production M. Kitazawa, Y. Nemoto and T.K., PoS CPOD07 (2007) 041;arXiv.0711.4429 with AL-term -per invariant mass dRee/dM2 [fm-4GeV-2] T=1.5Tc (40MeV) T=Tc (40MeV) Prominent enhancement at M<150MeV. from free quarks The peak becomes sharp as e 0. invariant mass M [MeV] c.f. other channel: anomalous absorption of sound; B.O. Kerbikov and M.S. Lukashov, arXiv:1607.00125 p-h p-h enhanced near CP! Unfortunately, a weak coupling calculation a la BCS theory.

  8. Phase diagram with CSC: combined effect of axial anomaly and the vector Interaction(and/or charge neutrality constraint) Z. Zhang and T. K., Phys.Rev.D80:014015,2009.; chiral di-quark vector anomaly for 2+1 flavors diquark-chiral density coupl. Fierts tr. Kobayashi-Maskawa(’70); ‘t Hooft (’76)

  9. Incorporating an anomaly term inducing the chiral and diquark mixing the anomaly-induced new CP in the low T region a la Hatsuda-Tachibana-Yamamoto-Baym (2006) chiral-diquark coupling (A) Flavor-symmetric case: Abuki et al, PRD81 (2010), 125010

  10. (B) Realistic case with massive strange quark; << H. Basler and M. Buballa, (2010) Notice! Without charge neutrality nor vector interaction.

  11. g_V varied with the coefficients of the anomaly terms (K’ /K ) fixed at 1 Z. Zhang and T. K., Phys.Rev.D80:014015,2009.; 1. Effects of mismatched Fermi sphere by charge-neutrality 2. Then effect of g_V comes in to make ph. tr. at low T cross over. Cf. Significance of g_V in CSC: M. Kitazawa, T. Koide, Y. Nemoto and T.K., PTP (’02); See also, TK, PLB271 (1991),395

  12. Implications to HI collisions: a speculation .The message to be taken in the present MF calculation: It seems that the QCD matter is very soft along the critical line where the diquark condensate with partially restored chiral symmetry exists. There can be a good chance to see large fluctuations of various observables like chiral-diquark-density mixed fluctuations, Can make seeds for baryon creation Thus, since the preformed diquarks may become seeds for creation of baryons with chiral symmetry being partially restored, and thus we may expect possible proliferation of baryons with (incoplete) parity doubling as a signal of the coexistence phase of chiral symmetry breaking and diquark condensate. Z. Zhang and TK, arXiv:1510.04417, to be published in an special issue on the physics of NICA in EPJ.

  13. Novel picture of the soft modes at the QCD critical point based on the FRG method Takeru Yokota, Kenji Morita and TK, PTEP (2016) 073D01(arXiv:1603.02147) Teiji Kunihiro (Dept. of Phys., Kyoto Univ.) Kenji Morita (YITP, Kyoto Univ.)

  14. A conjectured QCD phase diagram QGP T The universality class, Z2, the same as that of Liq.-Gas. QCD CP cSB ? Various phases CSC CFL m  0 Fluctuations of conserved quantities such as the number and energy are the soft mode of QCD critical point! The sigma mode is a slaving mode of the density.

  15. What is the soft mode at CP? Sigma meson has still a non-zero mass at CP. This is because the chiral symmetry is explicitly broken. What is the soft mode at CP? At finite density, scalar-vector mixing is present. Spectral function of the chiral condensate T-dependence (m=mCP) Phonon mode in the space-like region softens at CP. T>Tc H. Fujii (2003)H. Fujii and M.Ohtani(2004) P=40 MeV See also, D. T. Son and M. Stephanov (2004) does not affect particle creation in the time-like region. s-mode (non-soft mode) It couples to hydrodynamical modes, leading to interesting dynamical critical phenomena. Space-like region (the soft modes)

  16. Functional RG approach with meson-quark model Takeru Yokota, Kenji Morita and TK, PTEP (2016) 073D01(arXiv:1603.02147) R. Tripolt, L. Smekal, J. Wambach, PRD90 (2014) Vacuum value

  17. Time-like momentum region Peak of sigma mesonic mode Dispersion relation of sigma mesonic mode Bump of particle-hole mode Ⓢ Ⓟ Dispersion relation of particle-hole mode Space-like momentum region Space-like momentum region

  18. Development of the phonon mode near the QCD CP ● Ⓟ Ⓟ Ⓟ Ⓢ Ⓢ Space-like momentum region ●The particle-hole mode becomes soft.

  19. Anomalous softening of the sigma once located in the time-like region to merge into the phonon mode ● Merge ●As the system approaches the QCD CP, the dispersion relation of sigma mesonic mode shifts to low-energy region and merges with the bump of the particle-hole modes in the space-like momentum region.

  20. Fate of density fluctuations as the soft mode ofQCD CP---- Brillouin v.d. Rayleigh modes--- Y. Minami and TK, PTP,122(2010),881 Notice: The 1st-order can be valid for describing the hydrodynamic modes with a long wave-length without encountering the causality problem.

  21. We apply for the first time relativistic hydrodynamic equations to analyze the spectral properties of density fluctuations, and examine possible critical phenomena. The density fluctuation depends on the transport as well as thermodynamic quantities which show an anomalous behavior around the critical point. Notice: The 1st-order can be valid for describing the hydrodynamic modes with a long wave-length without encountering the causality problem. Fornon-relativistic case with use of Navier-Stokes eq. L.D. Landau and G.Placzek(1934), L. P. Kadanoff and P.C. Martin(1963), R. D. Mountain, Rev. Mod. Phys. 38 (1966), 38 H.E. Stanley, `Intro. To Phase transitions and critical phenomena’ (Clarendon, 1971)

  22. Spectral function of density fluctuations as calculated with the dissipative rela. fluid dynamics in the Landau frame ：sound velocity ：specific heat ratio sound modes In the long-wave length limit, k→0 thermal mode Rel. effects appear only in the width of the peaks. Rel. effects appear only in the sound mode. rate of isothermal exp. thermal expansion rate： Long. Dynamical ： enthalpy Notice: As approaching the critical point, the ratio of specific heats diverges! The strength of the sound modes vanishes out at the critical point.

  23. Critical behavior of the density-fluctuation spectral functions Critical opalescence In the vicinity of CP, only the Rayleigh peak stay out, while the sound modes (Brillouin peaks) die out. The dynamical critical exponent. c.f. So, the divergence of and the viscosities therein can not be observed, unfortunately.

  24. Spectral function of density fluctuation at CP See also, Fujii and Ohtani;Dam.T. Son and Stephanv 0.4 The sound mode (Brillouin) disappears Only an enhanced thermal mode remains. Furthermore, the Rayleigh peak is enhanced, meaning the large energy dissipation. Spectral function at CP Suggesting interesting critical phenomena related to sound mode. Eg. Attenation of a Mach cone The soft mode around QCD CP is thermally induced density fluctuations, but not the usual sound mode.

  25. Phenomena expected when chiral symm. is (partially) restored. Chiral restoration implies that correlators in the positive/negative parity get degenerate. • Chiral symmetry in Baryon sector; parity doubling? What is the nature of N*(1535)? C. De Tar and TK,PRD (1989) Axialanomaly: η’ in hot and dense matter πv.s. a_0 Scalar-Pseudoscalar Axial vector-Vector Possible charcter change of the sigma meson as T and/or density Is raised; tetra to q-qbar? A recent lattice calculation of the screening masses shows an increase (decrease) of the negative (positive) parity modes. (Y. Maezawa et al) Heinz, Strueber, Giacosa and Rischke, PRD 79 (09),037502

  26. Another role of the hot and/or dense medium for hadron physics ---- Filtering Effect of the medium -------

  27. Hadron structure as suggested by Dynamical Coupled Channel Approach Talk by H. Kamano @ MENU2016

  28. |H>=c_q|qqq>_B+∑c_i|M_iB_i> In dense and/or hot medium C_q(T,ρ) C_i(T,ρ) symbolically. (Spectral functions should be used, for describing hadronic modes in the medium.) The dense and/or hot medium may play a role of a filter of the Hilbert space for the hadron sector, and may well reveal the structure of the hadrons: Eg. Compositeness or elementariness may change in the medium!

  29. ・Magnetic field B induces isospin asymmetry due the different charges of u and d. EM field v.s. Chiral symm. Breaking ;eg. S. Klevansky,RMP (1992) and many many others. ・Hadron-`QGP’ transition at finite T is crossover! What is the physical picture of `hadrons’ around the crossover region? Swelled? Quarks/gluons are percolated? Super-multi quark hadrons? Tetraquarks or diquarks play significan roles? Implications to finite density systems? H-dibaryon matter in the intermediate stage? R. Tamagaki, PTP85 (1991) Hadron-quark transition at finite μalos crossover? Masuda, Hatsuda and Takatsuka, ApJ764(2013) The role of the vector interaction gVfor the crossover important? TK, PLB271 (1991), As well as the axial anomaly; Kitazawa et al,PTP108(2002); Hatsuda et a; PRL97 (2006)

  30. Brief summary and concluding remarks • Even if the CSC state may not be created in HI collisions, the precritical region • of CSC may be hit by HI collisions, and the pairing soft mode may affect the various • current-current correlations through A-L terms, which may lead to an enhancement • of lepton-pair production, and other observables. • 2. The phase boundary of CSC and the hadronic phase may be a coexistence phase • of ChiSB and CSC with a large fluctuations of the pairing, chiral and density fields, • which may lead to a proliferation of baryon excitations with parity doubling. • 3. The soft mode of QCD CP is primarily fluctuations of the conserved quantities, • but an FRG calculation shows that the sigma mesonic mode once existing in the • time-like region may merge with the phonon mode and constitute the soft • mode of QCD CP. • 4. Another aspect of the dynamical properties of QCD CP is an attenuation of the • phonon mode, which may affect, say, the strength of possible Mach cone created • by jets, for instance. • 5. Listed some expected phenomena associated with chiral restoration: • vector-axial-vector, scalar mode, baryons and • filtering effects of the hot and dense matter. • 6. EM effect and Confinement: isospin symmetry breaking, crossover ? Needs more study.

  31. Karsch, Maezawa, Mukhrjee, Petereczky, In preparation ----------------------------------------------------------------------------------------------------------------------- Positive parityとnegative parity states が互いに「歩み寄る」（positive parityが より積極的） Dynamicalmasses?And/or@finiteρ At relatively low T and/or ρ, a decrease of the constituent quark masses might overwhelm the symm. restoration. T.K., Nucl. Phys. B351(1991)

  32. 0 para sigma para pion Chiral Transition and the collective modes The low mass sigma in vacuum is now established: pi-pi scattering; Colangero, Gasser, Leutwyler(’06) and many others Full lattice QCD ; SCALAR collaboration (’03) q-qbar, tetra quark, glue balls, or their mixed st’s? M.Wakayamaetal（SCALARCollab.),PRD91(2015) c.f. The sigma as the Higgs particle in QCD ;a composite particle ; Higgs field Higgs particle (discovered @2012) with mass=125 GeV Is the Higgs a structureless elementary particle? Recent anomalous events in LHC?

  33. :Screening masses a0  U1(A)  the softening of the  with increasing T and a_0 meson in the medium would be interesting to explore the effective restoration of U_A(1) symmetry.

  34. The poles of the S matrix in the complex mass plane for the sigma meson channel: complied in Z. Xiao and H.Z. Zheng (2001) G.Colangero, J. Gasser and Leutwyler (2001) Softening ! See also, I. Caprini, G. Colangero and H. Leutwyler, PRL(2006); H. Leutwyler, hep-ph/0608218 ; M_sigma=441 – i 272 MeV

  35. In the constituent quark model; the mass in the 1.2 --- 1.6 GeV region. Problem with the low-mass  meson in QCD Scalar Mesons as Tetraquarks (Jaffe(1977), Alford and Jaffe (2000))

  36. QCD phse diagram with tetra-quark codensate as well as the q-qbar, and a possible crossover of the tetra-sigma and q-qbar sigma. N_f=2: AHeinz, S. Strueber, F. Giacosa and D.R. Rischke, PRD 79 (09),037502 c.f. For N_f>2, R.D. Pisarski and V.V. Skokov, arXiv:1606.04111[hep-ph] Quarknium-tetraquark mixing model D. Black, A.H. Fariborz and J. Schechter, PRD 61 (2000, 074001, and References cited in A. H。 Fariborz et al, PRD 91 (2015) 073013 Significance of the U(1)_A anomaly term for the coupling between the chiral (q-q-bqr) fieldand tetraquark field as known in the physics of colorsuperconductivity.

  37. Possible character change of the sigma meson at hot and dese medium • Heinz, S. Strueber, F. Giacosa and D.R. Rischke, PRD 79 (09),037502 N_f=2 Condensates Masses Crossover from the tetera-dominated system to q-qbar system(chiral fluctuation). How about in nuclear medium? Mixing angle

  38. Possible crossover of tetraquark(σ) to diquark-pair condensation in hot and dense matter R.D. Pisarski and V.V. Skokov, arXiv:1606.04111[hep-ph The diquark fields introduced is almost identical to the operators which condense when the colorsuperconductivity occurs.

  39. Baryons and Chiral Symmetry and Filtering effect of dense hadronic medium

  40. The masses: The axial charge Matrix of N and N*(1535) sector

  41. Interplay between Electromagnetic and Storng interactions and Confinement/deconfinement in Hot and/or dense medium?

  42. Back Ups

  43. A conjectured QCD phase diagram T RHIC/LHC FAIR, NICA, J-PARC QCD CP QGP cSB ? Various phases CSC CFL Ferromagnetism? m  0 H-dibaryon matter? superconducting phases various meson condensation?

  44. p-wave Neutral Pion-condensed Baryonic Matter; pion-induced tensor-force dominating phase A.B. Migdal, Sawyer-Scalapino (’72) z Pion condensed phase =Alternating-Layer Spin(ALS)structure of the nucleonSystem (R.Tamagaki et al (1976~)) Pi ：longitudinal spin-isospin density wave PTP suppl.112(1993) c.f. ρ meson condensation： transversespin-isospin density wave T.K., PTP 60 (1978), 1229

  45. Relativistic shock adiabat run through by heavy-ion collisions with the presence of pion condensation T.Takatsuka, R. Tamagaki and T.K. PTP 79 (1988) 120 Taub shock adiabat (rel. fluid dynamics) : normal state Mixed phase：

  46. S.Carignano, D. Nickel and M. Buballa, arXiv:1007.1397 E. Nakano and T.Tatsumi, PRD71 (2005) Interplay between G_V and Polyakov loop is not incorporated; see also P. Buescher, Mater thesis submitted by Darmstadt University,where Ginzburg-Levanyuk analysys shows also an existence of Lifschitz point at finite G_V. Spatial dependence of Polyakov loop should be considered explicitly.

  47. Realistic treatment of π con. with the isobar Δand Short-range int. and correlations Effective Force (G0-force) with the resonance EOS for pion-condensed N=Z Matter ＊ R.Tamagakiand T.K. PTP. 61 (’79)1107 OPEP+g’ N ＊D.W.L.Sprung and P.K. Banerjee,NPA168(’71); D.W.L. Sprung,NPA182(’72),97.

  48. Rho meson condensation T.K., PTP 60 (1978), 1229; master thesis . • The nuclear spin direction oscillates at higher densities, • And then bend down, which is a rho meson condensed state. z Rho meson condensation Transverse spin-isospin ordered baryonic matter c.f. H. Toki and J.R. Comfort, PRL 47, (1981), 1716.

  49. Similarity of the effect of temperature and pairing gap on the chiral condensate. M. Kitazawa et al. PTP, 110 (2003), 185: arXiv:hep-ph/0307278 T Δ

  50. (A’) Role of 2SC in 3-flavor quark matter H. Basler and M. Buballa, PRD 82 (2010),094004 with

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