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Teiji Kunihiro (YITP, Kyoto)

Status of the chiral symmetry restoration and sigma-meson physics. Teiji Kunihiro (YITP, Kyoto). Dubna round table session July 7-9, 2005 JINR, Dubna, Russia. Contents.

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Teiji Kunihiro (YITP, Kyoto)

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  1. Status of the chiral symmetry restoration and sigma-meson physics TeijiKunihiro(YITP, Kyoto) Dubna round table session July 7-9, 2005 JINR, Dubna, Russia

  2. Contents • Introduction : vacuum structure v.s. elementary excitations • The sigma meson • Chiral restoration and the sigma meson • Chiral restoration as seen in other channels including chiral anomaly • Summary

  3. A condensed matter physics of vacuum (Y. Nambu; 1960)

  4. (Bogoliubov-Anderson) Gauge invariance Axial gauge (chiral) symm.

  5. Inter-deterministic property of the matter and vacuum in QFT The definition of vacuum: ; vacuum In the definition of vacuum in QFT, the definition of the particle picture is pre-requisite. Equivalence between what is the vacuum and what are the particles to be observed. Change of the vaccum Change of the particle picture Eg. Superconductivity

  6. Dispersion relation of electron-quasi particle in the normal metal and superconducting matterial 常伝導 超伝導 gap and Bogoliubov-Anderson mode Change in the elementary excitations Change of vacuum

  7. Chiral Transformation (left handed) (right handed) Chirality: For , the chiral transformation forms

  8. Chiral Invariance of Classical QCD Lagrangian in the chiral limit (m=0) invariant! not invarinat! Dirac mass term order parameter In the chiral limit (m=0), ; Chiral invariant Ｘ ;Chiral invariant!

  9. The notion of Spontaneous Symmetry Breaking the generators of a continuous transformation ; Noether current eg. Chiral transformationfor Notice; The two modes of symmetry realization in the vacuum : a. Wigner mode b. Nambu-Goldstone mode The symmetry is spontaneously broken. Now, Chiral symmetry is spontaneously broken!

  10. Non-perturbative properties of QCD vacuum: condensates QCD 真空の非摂動的性質（補） Gell-Mann-Oakes-Renner using We have QCD sum rules for heavy-quark systems,

  11. Confinement and chiral transion in Lattice QCD

  12. QCD phase diagram T QGP ~150MeV QCDcritical point cSB ? CSC CFL m  0 H matter? meson condensation?

  13. The sigma meson • Real or not? • If real, what is it?

  14. The significance of the  meson in low energy hadron physics and QCD • 1. The pole in this mass range observed in the pi-pi S-matrix. • As a compilation of the pole positions of the  obatined in the modern • analyses: Significance of respecting chiral symmetry,unitarity and crossing • symmetry to reproduce the phase shifts both in the  (s)- and , (t)-channels • with a low mass  pole;(Igi and Hikasa(1999)). • 2. Seen in decay processes from heavy particles; • E. M. Aitala et al, Phys. Rev. Lett. (86), 770 (2001) • 3. Responsible for the intermediate range attraction in the nuclear force. • 4. Accounts for  I=1/2 enhancement in K ->2 compared with K+->+0. • E.P. Shabalin (1988); T. Morozumi, C.S. Lim and I. Sanda (1990). • 5.-N sigma term 40-60 MeV (naively » 15 MeV) enhanced by thecollectiveness of the (.T.Hatsuda and T.K.(1990)) ; see the next slide. • 6. The  : of the chiral order parameter The Higgs particle in the WSG model

  15. Chiral Transition and the collective modes 0 c.f. Higgs particle in WSH model ; Higgs field Higgs particle

  16. K. Igi and K. Hikasa, Phys. Rev. D59, 034005(1999) The phase shifts in the sigma and rho channel in the N/D Method; resp. chiral symm., crossing symm and so on. Both with the  in the s- No  but r in the t-channel and the r in the t-channel

  17. 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)

  18. E. M. Aitala et al, Phys. Rev. Lett. (86), 770 (2001) Without sigma pole With a sigma pole: 24 23 42 40

  19. flavor mixing The numbers in ( , ) are those in the naive quark model. (T.K. and T. Hatsuda, Phys. Lett. B240 (1990) 209) The quark content (or the scalar charge of the quarks) is enhanced by the collective  mode in the scalar channel!

  20. Issues with the low-mass  meson in QCD • In the constituent quark model; the mass in the 1.2 --- 1.6 GeV region. Some mechanism needed to down the masswith ~ 600 MeV; • (i) Color magnetic interaction between the di-quarks? (Jaffe; 1977) • (ii) The collectiveness of the scalar mode as the ps mode; a superposition of states. Chiral symmetry (NJL) • (iii) The - molecule as suggested in -  scatt. . (vi) a mixed state of scalar glue ball and states

  21. in the constituent quark model • I=0 ; I=1; a 0 = 0 ++ ,a 1 = 1 ++ , a 2 =2 ++ , b 1 = 1 +- 3P0 3P1 3P2 1P1 We need some nontrivial dynamics to down the mass as low as 500 – 600 MeV! They all should be in the same mass range 1.2 – 1.6 GeV

  22. Scalar Mesons in the Di-quark picture (Jaffe(1977), Alford and Jaffe (2000))

  23. The Scalar mesons on the Lattice ---- A full QCD calculation ----- The Scalar Collaboration: S. Muroya,A. Nakamura,C. Nonaka,M. Sekiguchi, H. Wada,T. K. (Phys. Rev. D70, 034504(2004))

  24. Simulation parameters Lattice size : 83 × 16 • = 4.8 k = 0.1846, 0.1874, 0.1891 CP-PACS well established light meson with large lattice a = 0.197(2) fm ,kc = 0.19286(14) ( CP - PACS, Phys. Rev. D60(1999)114508 ) Wilson Fermions & Plaquette gauge action Disconnected diagram Number of the Z2 noise = 1000

  25. Disconnected diagram Connected diagram - Vacuum contribution Propagator for s meson (2) Where

  26. The meson masses m_

  27. ms/mr

  28. meson propagatorsConnected Part & Disconnected Parts (k = 0.1891 )

  29. Chiral Transition = a phase transition of QCDvacuum, being the order parameter. Lattice QCD; eg. F. Karsch, Nucl. Phys. Proc. Suppl. 83, 14 (2000). The wisdom of many-body theory tells us: If a phase transition is of 2nd order or weak 1st order, 9soft modes» the fluctuations of the order parameter For chiral transition, The  meson becomes the soft mode of chiral transition at T. Hatsuda and T. K. , Phys. Rev. Lett.; Prog. Theor. Phys (1985): It was also shown that hadronic excitations (para pion andsigma) exisit even in the ``QGP” phase.

  30. Chiral Transition and the collective modes 0 c.f. Higgs particle in WSH model ; Higgs field Higgs particle

  31. T dependence of the (`para’) sigma and (`para’) pion masses T. Hatsuda and T. K., Phys. Rev. Lett. 55 (1985), 158 T Large

  32.  the softening of the  with increasing T and What is the significance of the  in hadron physics?

  33. Wait! Is the pole observed in the pi-pi phase shift really the  as the quantum fluctuation of the order parameter of the chiral transition? A change of the environment a change of the mode coupled to the order parameter Production of the -meson ina nuclear medium Useful for exploring the existence of the  and the possible restoration of chiral symmetry at finite density. (T. K., Prog. Theor. Phys. Suppl. 120 (1994), 75) What is a good observables to see the softening in the sigma channel in nuclear medium? Notice:A particle might loose it identity when put in a medium. Need of a calculation of the Spectral function lepton pairs at as seen by ,2 and 4 ;

  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 !

  35. T. Hatsuda, H. Shimizu, T.K. , Phys. Rev. Lett. 82 (1999), 2840 Spectral function in the  channel

  36. A’=2 ! 208 P. Camerini et al, Phys. Rev. C64, 067601 (2001). (CHAOS coll.) CHAOS (1996) This ratio represents the net effect of nuclear matter on the interacting system. CB: Phys. Rev. Lett. 85, 5539 (2000). CHAOS:Phys. Rev. C60, 018201 (1999).

  37. Cpp; A-dependence of pp p A TAPS CHAOS p0p0 I=0 p0p+ I=1 E~420 MeV r ~ 2/3r0 p+p- I~0 p+p+ I=2 E~420 MeV r ~ 1/3r0 Muhlich: Model based on Oset’s developed for the gp0p0and gp0p+,-reactions, better treatment of FSI of pions with the nucleus, no medium modifications. Oset and Vicente, PRC60(1999)064621 Oset: Full model of the p+p+p+,- process, standard nuclear effects discussed, P-wave pionic modes included and the s-meson dynamically generated. Muhlich et al., PLB595(2004)216

  38. Differential cross sections of the reaction A(,00)A' ----- phase space L. Roca et al (2002) without softening TAPS experiment: J.G. Messchendorp et al, Phys. Rev. Lett. 89 (2002), 222302.

  39. S.Schadmand E = 400 - 460 MeV o o angular distribution  A  o o X  A  +/- o X     preliminary J.G.Messchendorp et al., PRL 89, 222302 L. Roca, et a l., PLB 541 (2002) 77, priv. comm. • m(oo) for isoscalar channel only: • drops with increasing A • consistent with isotropic • angular distribution

  40. P. Muelich, L. Alvarez-Ruso, O. Buss and U. Mosel, ( nucl-th/0401042).  -N FSI lowers the spectral function in the pi-pi invariant mass.

  41. The spectral enhancememnt in thenonlinear ｒealization D. Jido, T. Hatsuda and T. K.,Phys. Rev. D63} (2000), 011901(R). In the polar decomposition M=SU, fixed In the heavy S-field limit, ;

  42. Softening of the in-medium pi-pi cross section In the non-linear realization D. Jido et al (2000)

  43. The renormalization of the wave function Due to the new vertex: C.f. Importance of the w.f. renormalization in other physics: U. Meissner, J. Oller and A. Wirzba, Ann. Phys. 297 (2002) 27 E. Kolomeitzev, N. Kaiser and W. Weise, P.R.L. 90 (2003)092501 Deeply bound pionic nuclei w.f. renormalization E-dependece of opt. pot. c.f. Freidman and Gal (04)

  44. ○LO+EE without w.f.r. ●LO+EE with w.f.r. △NNLO with w.f.r. Deeply-bound pionic nuclei and missing repulsion K. Suzuki et al., Phys. Rev. Lett. 92, 072302 (’04) P.Kienle and T.Yamazaki,Prog. Part. Nucl. Phys. 52 (2004), 85 Kolomeitsev, Kaiser, & W. Weise, Phys.Rev.Lett. 90 (’03)

  45. The movement of the sigma pole in the complex Energy plane in the N/D method with MFA • K. Yokokawa, • T. Hatsuda, • Hayashigaki, • And T.K.(2002) model A:  B:  model  C:  - model D:

  46. The T matrix in the N/D method. The in-medium - cross sections in I=J=0 channel. The upper (lower) panel shows the case of small (large) restoration corresponding to • K. Yokokawa, • T. Hatsuda, • Hayashigaki • and T.K. (2002)

  47. Vector Mesons QCD sum rules, effective theories as NJL model and Brown-Rho scaling suggest that The vector mesons mass/width, or more precisely, their spectral functions may change in hot and/or dense matter

  48. The softening in the meson channel K. Yokokawa et al (2002)

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