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QCD phase transitions and possible change of the particle picture in hot and/or dense media : 

QCD phase transitions and possible change of the particle picture in hot and/or dense media Teiji Kunihiro (YITP) KEK 研究会「通常核から離れた核物理の新展開」 2004年3月15 --- 17 日 於 KEK

Introduction continued: 

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


Chiral Transition = a phase transition of QCD vacuum, 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, 9 soft 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 and sigma) exisit even in the ``QGP” phase.


The spectral function of the degenerate ``para-pion” and the ``para-sigma” at T>Tc for the chiral transition: Tc=164 MeV T. Hatsuda and T.K. (1985)


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


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 the collectiveness 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


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 !


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. No  but r in the t-channel and the r in the t-channel Both with the  in the s-

Issues with the low-mass  meson in QCD: 

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 mass; (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.


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! in the constituent quark model They all should be in the same mass range 1.2 – 1.6 GeV


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


The Scalar mesons on the Lattice The Scalar Collaboration: S. Muroya, A. Nakamura, C. Nonaka, M. Sekiguchi, H. Wada, T. K. (Ref. hep-ph/0310312) ---- A full QCD calculation -----


Simulation parameters Lattice size : 83 × 16 b = 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 ) Number of the Z 2 noise = 1000 Wilson Fermions & Plaquette gauge action



meson propagators                     Connected Part & Disconnected Parts ( k = 0.1891 ): 

meson propagators                     Connected Part & Disconnected Parts ( k = 0.1891 )


 = .1874



mp/mr : 

mp/mr nearly equal


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) isenhanced by the collective  mode in the scalar channel! C.f. The empirical value of -N Sigma term is reproduced due to the enhancement of the scalar charge due to the -mesonic collective mode!


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 in a 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


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). P. Camerini et al, Phys. Rev. C64, 067601 (2001). (CHAOS coll.) A’=2 ! 208 CHAOS (1996)


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


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


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.


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


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)

Chiral Lagrangian in the Medium: 

Chiral Lagrangian in the Medium Chiral Lagrangian: The pion field: Pion decay constant: In the vacuum: pion mass, quark condensate,


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


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) A:  model B:  model C:  -  model D:


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)


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


Summary The  meson as the quantum fluctuation of the order parameter of the chiral transition may account for various phenomena in hadron physics which otherwise remain mysterious. There have been accumulation of experimental evidence of the  pole in the pi-pi scattering matrix. ( chiral symmetry, analyticity and crossing symmetry. A full lattice QCD suggests the existence of the  Partial restoration of chiral symmetry in hot and dense medium as represented by the decreasing f leads to a softening of the  and the  pole in the 2nd Riemann sheet in various chiral models.


Even a slight restoration of chiral symmetry in the hadronic matter leads to a peculiar enhancement in the spectral function in the  channel near the 2m threshold. Such an enhancement might have been observed in the reaction The decrease of the of w.f. renormalization of the pion commonly seen in the deeply bound pionic nuclei, suggesting a strongly coupled system of the pion and nuclear medium. Other channels: simultaneous softening of the  and  c.f. KEK, CERES, STAR N* and parity doublets of other baryons (De Tar and T.K.; 1989)

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