The sigma meson and chiral transition in nuclear medium

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?????????QCD????????(?)
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How firmly established is the phase structure
at small temperature but at finite density?
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Possible Phase diagram in weak coupling
adapted from
T. Schaefer arXivhep-ph/0509068
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L.McLerran and R. Pisarski NPA796, 83 (2007)
Chiral symmetry is restored but still baryons are
there, Creating baryon density.
Supports K. Fukushima, PRD77, 114028 (2008),
K. Miura and A. Ohnishi, arXiv0806.3357 nucl-th
etc.
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Smooth variation of the quark condensate with
baryon density?
S. Klimt, M. Lutz and W. Weise, PLB249 (90)
?
As we will see, strong vector coupling and/or
the axial anomaly make the chiral transition
crossover at finite density!
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Effects of GV on Chiral Restoration
GV?Large
T.Hatsuda and T.K.(85) without vector coupling
First Order
As GV is increased,
Cross Over
Chiral restoration is shifted to higher
densities. The phase transition is weakened.
Asakawa,Yazaki 89 /Klimt,Lutz,Weise 90 /T.K.
90/ Buballa,Oertel 96
What would happen when the CSC joins the game?
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With color superconductivity transition
incorporated Two critical end point!
M. Kitazawa, T. Koide, Y. Nemoto and T.K. (02)
(4)
Another end point appears from lower
temperature, and hence there can exist two end
points in some range of GV !
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T22MeV
15MeV
Large fluctuations scalar-diquark mixed mode.
12MeV
M. Kitazawa, T. Koide, Y. Nemoto and T.K. (02)
5MeV
m
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Possible role of U_A(1) anomaly on the QCD phase
diagramenhancement of the coexisting of CSC and
chiral SB
No
Hatsuda, Tachibana, Yamamoto and Baym, PRL97
(2006)
COECoexistence phase
Remark Conjectured possible QCD phase diagram
with parameters varied by hand. A serious
quantitative calculation is needed to confirm or
disconfirm this.
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Talk presented in Quark Nuclear Physics with GeV
Photons and Symmetry Problems, Osaka, Japan, 7-9
Mar 1996. (arXivnucl-th/9604019)
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Other Issues and interesting observables

• Vector-axial vector degeneracy
• hadron realizatin of chiral symmetry vector
  manifestation
• N(1535)-eta
• Magnetic moments
• in nuclei K-N v.s. in the
  nuclear medium

As chiral symmetry is restored,
Violence of Vector Dominance (Harada) then OZI
rule in hot/sense matter(?)
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Meson

• Related to

Anomaly otherwise
ideal mixing realized
with N(1535)
Also selective coupling of
chiral dynamics v.s. Chiral doublet (a la
DeTar-Kunihiro(89) )type? a funny density
dependence of the opt. pot. in the latter.
(Nagahiro et al) Near future experiment in GSI
and J-PARC?
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Issues on Vecotr Mesons
Hatsuda-Lee, Brown-Rho vacuum change (chiral
tr.) leads to a mass shift of the vector mesons.
KEK-PS (Yokkaichi)
show a mass drop!
However,
Lorentz invariance is lost in the medium, and the
spectral function should be used, not simply
by mass and width.
Vector modes decompose into longitudinal and
transvere modes, and moreover , the longitudinal
modes is coupled with the scalar mode. Spectral
Function in the whole plane.
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What is the Vector Mesons, especially, What is
their chiral properties?
An answer Hidden local Symmetry approach (Bando
et al)
Vector Manifestation occurs at critical
point? (1/2, 1/2) ((3.1)(1,3))
representation Pure (3,1)(1,3) pi and rho
get degenerated?! Yes, according to C. Sasaki,
Harada.
Lattice calculations and testing the many
interesting predictions with experiment
will tell.
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The softening of the ?-like excitation around
the critical temperature of chiral transition
(F.Karsch, Lect. Notes 583 (2002), 209)
The generalized mass
?
degenerated
?
Remark is not the dynamical mass as a
pole of the time-correlator.
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Experimental check !
How about creating the baryon in a nucleus? The
nuclear medium may act as a filter changing the
particle contents of the resonances.