23/4/20

Hiden symmetry and strongly interacting fermions correlations at Finite T and ρN

Ji-sheng ChenCentral China Normal Univ.

Wuhan 430079Chenjs@iopp.ccnu.edu.cn

With P.-F Zhuang (Tsinghua Univ.) ,J.-R Li (CCNU) and M. Jin

23/4/20

Contents1. Introduction2. Dyson-Schwinger Equations: RHA+RPA3. A. In-medium meson effects on EOSB. Superfluidity with Debye screening effectsC. Model of broken U(1) Em symmetry and EM i

nteraction on the correlations of nucleons in nuclear matter

4. Conclusions

23/4/20

Phase or Correlation in stronglyinteraction field theory with

ContinuousField theory

23/4/20

1. Introduction

1. Heavy ion collisions• High T/ρ Physics

QGP-deconfinement

Chiral symmetry (partial) restoration phase transition

• Medium effects?

23/4/20

PPhase diagram of strongly interacting matterhase diagram of strongly interacting matter

CERN-SPS, RHIC, LHC: high temperature, low baryon density

AGS, GSI (SIS200) & CSR: moderate temperature, high (moderate) baryon density

Superfluidity as well as BEC

Superconductivity

23/4/20

2. Experiments

<0.2~0.5~10 (fm/c)

4-101.5-4.0<1QGP (fm/c)

2x1047x103103Vf(fm3)

15-403.52.5 (GeV/fm3)

3-8 x103650500dNch/dy

550020017s1/2(GeV)

LHCRHICSPSCentral collisions

23/4/20

3 、 Space-time Evolution

Loosely pairs of quasiparticles (BEC)?

23/4/20

4. Signals of QGP Probes of EOS: Effective member of d

egrees of freedom, Collective flows (transverse & epileptic flows)

EM signals (background) Probes of Color Deconfinement Signatures of Chiral Symmetry

23/4/20

Dilepton production

Background Partial chiral symmetry

restoration (CSR) Adv. Nucl. Phys. 25 (2000) 1

23/4/20

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!

23/4/20

Experiment results

23/4/20

Physics

Has QGP been produced?

From hadronic view, if without medium effects, the data can not be explained.

Broadening (R. Rapp 　 et al.) Mass decreasing of (Brown-Rho, G. Q. Li)

Too many works in the literature!

23/4/20

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 of hadronic matter under the hot/dense extreme conditions.

23/4/20

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

23/4/20

PRL 67 (1991) 961; PRC 63 (2001) 025206Phys. 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?)

23/4/20

1. EOS of hot/dense nuclear matter 2. Relation between mN*, mσ* , m*, m* etc. i

mproved3. Superfluidity with relativistic nuclear theo

ry more self-consistently (screening effects)

4. U(1) EM symmetry and the correlations of nucleons in nuclear matter (emphasis on the mechanism and Model)

Addressing

23/4/20

2.QHD-I &RHA+RPA

The simplest renormalizble QHD-I

Adv. Nucl. Phys.16 (1986)1

23/4/20

23/4/20

Attributed to calculation of self-energies

23/4/20

23/4/20

RHA result=MFT+εvac The saturation condition at normal d

ensity at T=0 fixes the coupling constants.

The EOS is hard. Nonlinear σ - and ZM model

NPA 　 292 (1977) 413; PRC 　 42 (1990) 1416.

23/4/20

Meson property and RPA

Determined by the full propagator: using the relativistic random phase approximation (RPA)

23/4/20

To discuss the effective meson masses, spectral function, and dispersion relation of meson excitations

23/4/20

I. In-medium Meson Effects on the EOS of Hot and dense Nuclear MatterNucl-th/0209074, Phys. Rev. C 68, 045209 (2003) .

The origin of “Hidden Local Symmetry” suggested by one of the referees

Research-III 23/4/20

1. Back interaction of in-medium meson with nucleon

~Improvement of the solution consistency?

2. EOS of nuclear matter.3. The relation of MN

*, m* , m

* etc.

Research-III 23/4/20

•Along a single direction(?)

MN*, μN

* m* , m

* ,

Research-III 23/4/20

Improvement of self-consistency

Research-III 23/4/20

Results

1. Softer EOS with compressibility K=318.2 MeV (acceptable 250 MeV~350 MeV)

2. Relation between m* , m

* , mρ* an

d MN* more closer to Brown-Rho sc

aling law.

23/4/20

23/4/20

Similar work at T=0 in the literature:PRC60 (1999) 044903But numerical results might be incorr

ect K ~ 380 MeV?

Compared with existed result in literature

23/4/20

Pressure vs density at T=0

23/4/20

Binding Energy vs density

At T=0. Dot-dashed to MFT, dashed to RHA and solid to RHA+RPA

23/4/20

LG phase transition still exists

Pressure vs scaled density for fixed temperature

23/4/20

Eff. masses vs scale density

Dotted to σ, Dot-dashed to , Solid to N

23/4/20

Masses vs T at ρ=0

23/4/20

II Dybe screening effects of mesons on 1S0 correlation with Dyson-Schwinger Equation

Nucl-th/0309033, Phys. Lett.B 585, 85 (2004)

“Original work” ?

23/4/20

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)

23/4/20

Superfluidity in nuclear matter Phys. Rev. 110, 936 (1958).Bohr, B.R. Mottelson, and D. Pines Field theory with Nambu-Gorkov formalismH. Kucharek and P. Ring, Z. Phys. A 339, 23 (199

1)

“standard” but non-relativistic: J. Decharge and D. Gogny, Phys. Rev. C 21, 1568 (1980).

23/4/20

1. Quite unacceptable results of superfluidity with frozen meson propagators (MFT and RHA) even with additional parameters Improvement: with external potential (Bonn) as input?

2. Important topic in contemporary physics screening effects on 1S0 correlation widely discussed within the frame of nonrelativistic frame!

Improvement of description for fundamental 1S0 correlation with self-consistent Dyson-Schwinger equations ?

23/4/20

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

23/4/20

Coupled propagators of in-medium nucleon and meson

23/4/20

Gap equation for 1S0 correlation

23/4/20

Debye Screening effects in the in-medium particle-particle interaction potential

23/4/20

23/4/20

Crucial: potential medium dependent

23/4/20

Numerical Results

23/4/20

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)

23/4/20

III Broken U(1) EM symmetry related with LG phase transition and breached pairing strengthsnucl-th/0402022

23/4/20

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?

23/4/20

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

23/4/20

Why? Non empty of realistic ground state with mean field theory a

pproach! Nonzero electric charge of protons Infrared singularity of photon propagator even with Fock ter

m;Almost uncontrollable contribution of EM contribution to the E

OS of nuclear matter within the existed model(s). Nonrelativistic empirical knowledges: quite different negativ

e scattering lengths between various nucleons (through the work nucl-th/0311065 citing ours, Phys.Rev. C69 (2004) 054317. There are many sentences commenting our work)

23/4/20

How? Simplest mean field

approximation Thermodynamics effective

potential

23/4/20

Constructed a model Lagranrian (Proca-lika: not EM?) with a pa

rametric photon mass

23/4/20

Thermodynamic effective potential

23/4/20

Pressure and energy density

23/4/20

Pressure

23/4/20

23/4/20

EOS for charged nuclear matter in Heavy ion Collision

23/4/20

Coulomb Correlation Energy (Compression Modulus)

23/4/20

An old figure interesting but important?

23/4/20

EOS for charge neutralized Proto-neutron star through beta-equilibrium

23/4/20

Proton fraction ratio

23/4/20

23/4/20

23/4/20

Solid limit for photon parameter mass: supercharge conservation

23/4/20

1,Weak is mixed with “stronger”2,Weak is Strong for many-body effects

23/4/20

Crucial problem EM breaking (U(1) Charge Symmetry Breaking CSB)

~ SU(2) isospin breaking. They should be taken into account simultaneously.

There is some kind competition bet them for phase space distribution function deformation- (supercharge)!

“Weak” interaction is “strongly” one in many-body environment.

Not important for bulk EOS, but important for transport coefficients (~ flows in heavy ion collisions) !

23/4/20

Why interesting?

Astro-particle physics; Glitches’s origin?

Vs Landau’s 4He two-components super fluidity theory. There are different energy spectrum (many gaps-Landau levels) in a system!

23/4/20

Relevant topics Strongly coupling electrons correlations. Not Trivial screenin

g effects! How to beyond MFT or RHA approaches?

QGP, How to solve the Puzzle? hep-ph/0307267:Edward V. Shuryak, Ismail Zahed, Rethinking

the Properties of the Quark-Gluon Plasma at $T\sim T_c$? BEC (quasiparticles into pair or cluster);

hep-th/0310031, Spin-Spin and Spin-Orbit Interactions in Strongly Coupled Gauge TheoriesAuthors: Edward V. Shuryak, Ismail Zahed

… G.E. Brown et al.’s

23/4/20

Non-perturbative characteristic. Highlighting: Color charged and electr

ic charged! Non-perturbative characteristic.

23/4/20

• J. Ekman et al., “The hitherto overlooked electromagnetic spin-orbit term is shown to play a major role ” (To appear in PRL)(Comm., no arxiv file)

• Compact star as Type-I superconductor? Rule completely the magnetic field out of the star!

• Charged stars? Vortex phenomena?

23/4/20

Lasting

1S0 Proton and Neutron Superfluidity in beta-stable Neutron Star Matter W. Zuo et al., nucl-th/0403026, “It is found that the three-body force has only a small effect on the neutron 1S0 pairing gap, but it suppresses strongly the proton 1S0 superfluidity in $\beta$-stable neutron star matter”.

23/4/20

4.Conclusions and Prospects

23/4/20

Softer EOS with in-medium meson effects. Smaller K, comparable with nonlinear σ- model or ZM model

LG phase transition still exists. Approach more the Brown-Rho scaling l

aw.

1.More application value of relativistic field nuclear theory (Green function) under extreme conditions?

23/4/20

2.Superfluidity with in-medium meson effects

Improvements of the description for the nuclear propertySignificantly at ρ=0? Reducing the difference between relativistic and non-relativi

stic theory In-medium effects more self-consistently?But more important in methodology?Beyond Mean Field Theory (mean field dynamics~fluctuatio

n)? Consistent with “polarization~fluctuation effects suppress t

he pairing gaps by a fact of 3~4 and not sensitive to a special parameters set ” A long standing problem:

A. Schwenk, B. Friman and G.E. Brown with other approaches PRL92,082501(2004), NPA 713, 191(2003),703, 745 (2003) etc.

23/4/20

3. Now addressing

Asymmetric nuclear matter (NP correlation).

P-wave pairing (crystalline maybe is more important or useful for realistic issue) and d pairing?

Following Shuryak et al.’s proposal.

23/4/20

Apply into finite nuclei structure or neutron star structure esp. the mirror nuclei would give many exciting results (tensor or spin-orbit force, splitting).

Hidden Local symmetry(HLS) and Many-body Theory

fluctuations and correlations (self-consistency of Non-perturbative approaches)

23/4/20

Hope

Welcome comments and suggestions

23/4/20

Thank You!