The sigma meson and chiral transition in nuclear medium

1

Status of the chiral symmetry restoration
and
sigma-meson physics
Teiji Kunihiro (YITP, Kyoto)
Dubna round table session
July 7-9, 2005 JINR, Dubna,
Russia
2
Contents

• Introduction vacuum structure v.s. elementary
  excitations
• The sigma meson
• Chiral restoration and the sigma meson
• Chiral restoration as seen in other channels
• including chiral anomaly
• Summary

3
A condensed matter physics of vacuum (Y. Nambu
1960)
4
(Bogoliubov-Anderson)
Gauge invariance
Axial gauge (chiral) symm.
5
Inter-deterministic property of the matter and
vacuum in QFT
The definition of vacuum
vacuum
In the definition of vacuum in QFT, the
definition of the particle picture is
pre-requisite.
Equivalence between what is the
vacuum and what are the particles to be observed.
Change of the vaccum
Change of the particle picture
Eg. Superconductivity
6
Dispersion relation of electron-quasi particle in
the normal metal and superconducting matterial
???
???
gap
and Bogoliubov-Anderson mode
Change in the elementary excitations
Change of vacuum
7
Chiral Transformation
(left handed)
(right handed)
Chirality
For
, the chiral transformation forms
8
Chiral Invariance of Classical QCD Lagrangian
in the chiral limit (m0)
invariant!
not invarinat!
Dirac mass term
order parameter
In the chiral limit (m0),
Chiral invariant
X
Chiral invariant!
9
The notion of Spontaneous Symmetry Breaking
the generators of a continuous transformation

Noether current
eg. Chiral transformation for
Notice
The two modes of symmetry realization in the
vacuum
a. Wigner mode
b. Nambu-Goldstone mode
The symmetry is spontaneously broken.
Now,
Chiral symmetry is spontaneously broken!
10
QCD ?????????(?)
Non-perturbative properties of QCD vacuum
condensates
Gell-Mann-Oakes-Renner
using
We have
QCD sum rules for heavy-quark systems,
11
Confinement and chiral transion in Lattice QCD
12
(No Transcript)
13
(No Transcript)
14
QCD phase diagram
T
QGP
150MeV
QCD critical point
cSB
?
CSC
CFL
m
?
0
H matter?
meson condensation?
15
The sigma meson

• Real or not?
• If real, what is it?

16

• 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 ? I1/2 enhancement in K -gt2?
  compared with K-gt??0.
• E.P. Shabalin (1988) T. Morozumi, C.S. Lim
  and I. Sanda (1990).
• 5.?-N sigma term 40-60 MeV (naively ｻ 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
17
Chiral Transition and the collective modes
0
c.f. Higgs particle in WSH model
Higgs field
Higgs particle
18
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.
Both with the ?
in the s-
No ?
but r
in the t-channel
and the r
in the t-channel
19
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)
20
E. M. Aitala et al, Phys. Rev. Lett. (86), 770
(2001)
Without sigma pole
With a sigma pole
24
23
42 40
21
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) is enhanced by the
collective ? mode in the scalar channel!
22
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 with 600
  MeV
• (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.

. (vi) a mixed state of scalar glue ball
and
states
23

in the constituent quark model

• I0
• I1
• 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