Transcript 博士后中期考核汇报 - Shandong University

Hiden symmetry and
strongly interacting
fermions correlations
at Finite T and ρN
Ji-sheng Chen
Central China Normal Univ.
Wuhan 430079
[email protected]
With P.-F Zhuang (Tsinghua Univ.) ,J.-R Li
(CCNU) and M. Jin
2015/7/16
Contents
1.
2.
Introduction
Dyson-Schwinger Equations: RHA+RPA
3.
A.
B.
C.
4.
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
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Phase or Correlation in strongly
interaction field theory with Continuous
Field theory
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1. Introduction
1. Heavy ion collisions
•
High T/ρ Physics
QGP-deconfinement
Chiral symmetry (partial) restoration phase transition
•
Medium effects?
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Phase diagram of strongly interacting matter
Superfluidity
as well as BEC
Superconducti
vity
CERN-SPS, RHIC, LHC: high temperature, low baryon density
AGS, GSI (SIS200) & CSR:
(moderate) baryon density
moderate temperature, high
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2.
Experiments
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
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3、Space-time Evolution
Loosely
pairs of
quasiparticl
es (BEC)?
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4. 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
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Dilepton production



Background
Partial chiral symmetry
restoration (CSR)
Adv. Nucl. Phys. 25 (2000) 1
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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+eHELIOS-3, +  DLS (BEVALAC), e+e-
Believed to be observed in CSR certainly!
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Experiment results
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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!


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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.

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


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
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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 (Selfconsistency?)
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Addressing
1.
2.
3.
4.
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)
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2.QHD-I &RHA+RPA

The simplest renormalizble QHD-I
Adv. Nucl. Phys.16 (1986)1
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Attributed to calculation
of self-energies

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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

NPA 292 (1977) 413;
PRC 42 (1990) 1416.
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Meson property and RPA

Determined by the full propagator:
using the relativistic random phase
approximation (RPA)
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
To discuss the effective meson
masses, spectral function, and
dispersion relation of meson
excitations
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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
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1.
2.
3.
Back interaction of in-medium meson
with nucleon ~Improvement of the
solution consistency?
EOS of nuclear matter.
The relation of MN*, m* , m* etc.
Research-III
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•Along a single direction(?)
MN*, μN*
Research-III
m* , m* ,
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Improvement of selfconsistency
Research-III
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Results
1.
2.
Softer EOS with compressibility
K=318.2 MeV (acceptable 250
MeV~350 MeV)
Relation between m* , m* , mρ*
and MN* more closer to BrownRho scaling law.
Research-III
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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?

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Pressure vs density at T=0
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Binding Energy vs density
At T=0. Dot-dashed to MFT, dashed to RHA and solid
to RHA+RPA
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LG phase transition still exists
Pressure vs scaled density for fixed
temperature
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Eff. masses vs scale density
Dotted to σ, Dot-dashed to , Solid to N
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Masses vs T at ρ=0
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II Dybe screening effects of
mesons on 1S0 correlation with
Dyson-Schwinger Equation
Nucl-th/0309033, Phys. Lett.B 585,
85 (2004)
“Original work” ?
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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)
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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).
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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 selfconsistent Dyson-Schwinger equations2015/7/16
?
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
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Coupled propagators of in-medium
nucleon and meson
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Gap equation for 1S0 correlation
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Debye Screening effects in the in-medium
particle-particle interaction potential
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Crucial: potential medium dependent
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Numerical Results
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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)
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III Broken U(1) EM symmetry
related with LG phase
transition and breached
pairing strengths
nucl-th/0402022
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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?
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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
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Why?
Non empty of realistic ground state with mean field theory
approach!

Nonzero electric charge of protons

Infrared singularity of photon propagator even with Fock term;
Almost uncontrollable contribution of EM contribution to the EOS of
nuclear matter within the existed model(s).

Nonrelativistic empirical knowledges: quite different negative
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)

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How?


Simplest mean field approximation
Thermodynamics effective potential
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Constructed a model

Lagranrian (Proca-lika: not EM?) with a
parametric photon mass
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Thermodynamic effective
potential
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Pressure and energy density
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Pressure
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EOS for charged nuclear
matter in Heavy ion Collision
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Coulomb Correlation Energy
(Compression Modulus)
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An old figure interesting but
important?
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EOS for charge neutralized Protoneutron star through betaequilibrium
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Proton fraction ratio
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Solid limit for photon parameter
mass: supercharge conservation
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1,Weak is mixed with “stronger”
2,Weak is Strong for many-body
effects
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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) !
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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!
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Relevant topics

Strongly coupling electrons correlations. Not Trivial screening
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 Theories
Authors: Edward V. Shuryak, Ismail Zahed
… G.E. Brown et al.’s

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Non-perturbative characteristic.


Highlighting: Color charged and electric
charged!
Non-perturbative characteristic.
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• 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?
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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”.
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4.Conclusions and Prospects
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1.More application value of relativistic
field nuclear theory (Green function)
under extreme conditions?



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
law.
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2.Superfluidity with in-medium meson
effects
Improvements of the description for the nuclear property
Significantly at ρ=0?

Reducing the difference between relativistic and non-relativistic
theory

In-medium effects more self-consistently?
But more important in methodology?
Beyond Mean Field Theory (mean field
dynamics~fluctuation)?

Consistent with “polarization~fluctuation effects suppress the
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.

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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.
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


Apply into finite nuclei structure or neutron
star structure esp. the mirror nuclei would
give many exciting results (tensor or spinorbit force, splitting).
Hidden Local symmetry(HLS) and Many-body
Theory
fluctuations and correlations (self-consistency
of Non-perturbative approaches)
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Hope

Welcome comments and suggestions
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Thank You!
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