Ji-sheng Chen Central China Normal Univ. Wuhan 430079 Chenjs@iopp.ccnu.edu.cn With P.-F Zhuang (Tsinghua Univ.) ,J.-R Li (CCNU) and M. Jin Hiden symmetry and strongly interacting fermions correlations at Finite T and ρN
Contents • Introduction • Dyson-Schwinger Equations: RHA+RPA • In-medium meson effects on EOS • Superfluidity with Debye screening effects • Model of broken U(1) Em symmetry and EM interaction on the correlations of nucleons in nuclear matter • Conclusions
Phase or Correlation in strongly interaction field theory with Continuous Field theory
1. Introduction • Heavy ion collisions • High T/ρ Physics • QGP-deconfinement • Chiral symmetry (partial) restoration phase transition • Medium effects?
Phase diagram of strongly interacting matter Superfluidity as well as BEC Superconductivity CERN-SPS, RHIC, LHC: high temperature, low baryon density AGS, GSI (SIS200) & CSR: moderate temperature, high (moderate) baryon density
Central collisions SPS RHIC LHC s1/2(GeV) 17 200 5500 dNch/dy 500 650 3-8 x103 e (GeV/fm3) 2.5 3.5 15-40 Vf(fm3) 103 7x103 2x104 tQGP (fm/c) <1 1.5-4.0 4-10 t0 (fm/c) ~1 ~0.5 <0.2 • Experiments
3、Space-time Evolution Loosely pairs of quasiparticles (BEC)?
Signals of QGP • Probes of EOS: Effective member of degrees of freedom, Collective flows (transverse & epileptic flows) • EM signals (background) • Probes of Color Deconfinement • Signatures of Chiral Symmetry
Dilepton production • Background • Partial chiral symmetry restoration(CSR) • Adv. Nucl. Phys. 25 (2000) 1
Light vector mesons • EM signal of QGP：Dilepton and photons; background? ~ , , • The partial Chiral Symmetry Restoration(CSR): The property of esp. meson in hot/dense nuclear environment(?). CERES/NA45, e+e- HELIOS-3, + - DLS (BEVALAC), e+e- Believed to be observed in CSR certainly!
Physics • Has QGP been produced? • From hadronic view, if without medium effects, the data can not be explained. • Broadening (R. Rappet al.) • Mass decreasing of (Brown-Rho, G. Q. Li) • Too many works in the literature!
Framework Review • QHD The saturation property of nuclear matter and to finite nuclei successfully (MFT) • Following the proposal of Brown-Rho scaling law (PRL 66, (1991) 2720), QHD is used to discuss the property ofhadronic matter under the hot/dense extreme conditions.
No chiral symmetry explicitly Lagrangian • Hides and reflects the vacuum effect , short and long range correlation effects etc.? • Argued: the obtained result is consistent with(?) the result of partial chiral symmetry restoration
PRL 67 (1991) 961; PRC 63 (2001) 025206 Phys. Rep. 363, 85 ( 2002); 347, 289 (2001) Modified QHD? Nuclear matter: effective theory? Refinement of microscopic description for nuclear matter theory with in-medium meson (Self-consistency?)
Addressing • EOS of hot/dense nuclear matter • Relation between mN*, mσ* , m*, m* etc. improved • Superfluidity with relativistic nuclear theory more self-consistently (screening effects) • U(1) EM symmetry and the correlations of nucleons in nuclear matter (emphasis on the mechanism and Model)
2.QHD-I &RHA+RPA • The simplest renormalizble QHD-I Adv. Nucl. Phys.16 (1986)1
Attributed to calculation of self-energies
RHA result=MFT+εvac • The saturation condition at normal density at T=0 fixes the coupling constants. • The EOS is hard. • Nonlinear σ- and ZM model NPA292 (1977) 413; PRC42 (1990) 1416.
Meson property and RPA • Determined by the full propagator: using the relativistic random phase approximation (RPA)
To discuss the effective meson masses, spectral function, and dispersion relation of meson excitations
I.In-medium Meson Effects on the EOS of Hot and dense Nuclear Matter Nucl-th/0209074, Phys. Rev. C 68, 045209 (2003) . The origin of “Hidden Local Symmetry” suggested by one of the referees
Back interaction of in-medium meson with nucleon~Improvement of the solution consistency? • EOS of nuclear matter. • The relation of MN*, m* , m* etc.
Along a single direction(?) • MN*, μN*m* , m* ,
Results • Softer EOS with compressibility K=318.2 MeV (acceptable 250 MeV~350 MeV) • Relation between m* , m* , mρ* and MN* more closer to Brown-Rho scaling law.
Compared with existed result in literature • Similar work at T=0 in the literature: PRC60 (1999) 044903 But numerical results might be incorrect K ~ 380 MeV?
Binding Energy vs density At T=0. Dot-dashed to MFT, dashed to RHA and solid to RHA+RPA
LG phase transition still exists Pressure vs scaled density for fixed temperature
Eff. masses vs scale density Dotted to σ, Dot-dashed to , Solid to N
II Dybe screening effects of mesons on 1S0 correlation with Dyson-Schwinger Equation Nucl-th/0309033, Phys. Lett.B585, 85 (2004) “Original work” ?
S-wave pairing correlation: Important in physics • A theoretical long-standing problem. • Background of other pairing correlations (P,D –waves etc. ) • How to beyond MFT approach? A hot topic in temporary physics (condensed physics, nuclear theory)
Superfluidity in nuclear matter • Phys. Rev. 110, 936 (1958). Bohr, B.R. Mottelson, and D. Pines • Field theory with Nambu-Gorkov formalism H. Kucharek and P. Ring, Z. Phys. A 339, 23 (1991) • “standard” but non-relativistic: J. Decharge and D. Gogny, Phys. Rev. C 21, 1568 (1980).
Quite unacceptable results of superfluidity with frozen meson propagators (MFT and RHA) even with additional parametersImprovement: with external potential (Bonn) as input? • Important topic in contemporary physics screening effects on1S0 correlation widely discussed within the frame of nonrelativistic frame! • Improvement of description for fundamental 1S0 correlation with self-consistent Dyson-Schwinger equations ?
Formalism • Solution of gap equations for full nucleon and meson propagators as well as the that for superfluidity pairing • Diagrammatic representations for the coupled equations
Debye Screening effectsin the in-medium particle-particle interaction potential
Main results • Numerical results, two respects. One is crucial. • The numerical results are not sensitive again to the concrete coupling constants and the momentum cutoffs as well as the bulk EOS (very mandatory)
III Broken U(1) EM symmetry related with LG phase transition and breached pairing strengthsnucl-th/0402022
Motivation • Inspired by the low temperature superconductivity • The article citing our previous work (Phys. Lett.B) tells us one important fact: the quite different scattering lengths of nucleons! But no works addressing this problem either in nonrelativistic or relativistic frame?
Frame: relativistic field theory • Symmetry in physics • QHD hidden Chiral symmetry • How about EM symmetry? • Coulomb interaction role on the EOS? Multi-canonical formalism just published in PRL (2003), the theoretical background to be explored as clearly pointed out by the authors