Hadrons in nuclei
and
possible chiral restoration
in nuclear medium
Teiji Kunihiro (YITP, Kyoto)
Workshop on Hadron Structure at
J-PARC
November 30 – December 2, 2005
KEK
Contents
Mostly a review on the subject:
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 and N*(1535)
 Summary

A condensed matter physics of vacuum (Y. Nambu; 1960)
Inter-deterministic property of the matter and vacuum in QFT
The definition of vacuum:
a 0  0 
0

; 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
Eg. Superconductivity
Change of the particle picture
Dispersion relation of electron-quasi particle in the normal metal
超伝導
and 常伝導
superconducting matterial
E
E
gap

2   2


and Bogoliubov-Anderson mode
Change of vacuum
Change in the elementary
excitations
Non-perturbative
properties of QCD vacuum: condensates
QCD 真空の非摂動的性質（補）
Gell-Mann-Oakes-Renner
using
We have
QCD sum rules for heavy-quark systems,
Chiral condensate at finite density
For nuclear matter,
at nB  n0
(Drukarev and Levin(’90)
The scalar mesononic
mode in nuclei
• The sigma meson, real or
not?
• If real, what is it?
• What would happen
in nuclear media
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.
No  but r in the t-channel
Both with the  in the sand the r in the t-channel
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)
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 diquarks? (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
The Scalar mesons on the Lattice
---- A full QCD calculation -----
The Scalar Collaboration:
S. Muroya,A. Nakamura,C. Nonaka,M. Sekiguchi,
H. Wada,T. K.
(Phys. Rev. D70, 034504(2004))
The meson masses
m
_
Chiral Transition and the collective modes
0
c.f. Higgs particle in WSH model
; Higgs
field
Higgs particle


the softening of
the  with increasing
T
and
What is the significance of the  in hadron physics?
T dependence of the (`para’) sigma and (`para’) pion masses
T. Hatsuda and T. K., Phys. Rev. Lett. 55 (1985), 158
Large
T
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)
Softening !
T. Hatsuda, H. Shimizu, T.K. ,
Phys. Rev. Lett. 82 (1999), 2840
Spectral function
in the  channel
P. Camerini et al, Phys. Rev. C64, 067601
(2001). (CHAOS coll.)
This ratio represents the
net effect of nuclear
matter on the interacting
system.
CB: Phys. Rev. Lett. 85, 5539 (2000).
CHAOS:Phys. Rev. C60, 018201 (1999).
A’=2 !
208
CHAOS (1996)
E = 400 - 460 MeV
 A  o o X
 A  +/- o X
o o angular distribution




J.G.Messchendorp et al., PRL 89, 222302
L. Roca, et a l., PLB 541 (2002) 77, priv. comm.
m(oo) for isoscalar channel only:
• drops with increasing A
• consistent with isotropic
angular distribution
©: S.Shadmand @ Chiral05, RIKEN
S.Schadmand
The spectral enhancememnt
in the nonlinear ｒealization
D. Jido, T. Hatsuda and T. K.,Phys. Rev. D63} (2000), 011901(R).
In the polar decomposition M=SU,
fixed
In the heavy S-field limit,
;
The renormalization of the wave function
Due to the new vertex:
C.f. Importance of the w.f. renormalization in
other physics:
U. Meissner, J. Oller and A. Wirzba, Ann. Phys. 297 (2002) 27
E. Kolomeitzev, N. Kaiser and W. Weise, P.R.L. 90 (2003)092501
Deeply bound pionic nuclei
w.f. renormalization
Softening of the in-medium pi-pi cross section
In the non-linear realization
D. Jido et al (2000)
Chiral Lagrangian in the Medium
Chiral Lagrangian:
The pion field:
Pion decay constants:
In the vacuum:
Normalization of the 
the pion mass:
( =
)
In the medium: Thorsson-Wirzba Lagrangian (1996)
The normalization of 
and
Then,
The pion mass:
m*2  ( f 2  4c1r )m2 / a 2
 m [1  2(2c1 - c2 - c3 
2
 m2 - 4 (1  mmN )a r
qq
The quark condensate:
qq
r
0
g 2A
8 mN
) fr2 ]
( a  ; isoeven scatt. Length )
 1  4c1
r
f
2
r
 1 - 0.35
r0
 -  Scattering amplitude in the medium:
T
I 0
( s; r ) 
i
6 f
( t )*2
(2 s - m )
2
Enhancement of the scattering amplitude in the
sigma-meson channel!
Owing to the wave-function renormalization
as desribed by the pion-decay const. in the medium.
(Jido, Hatsuda, T.K.(2000))
A unified picture of the physics of the deeply
bound pionic nuclei and the pi-pi scattering in
I=J=0 channel of nuclei.
(D. JIdo, T. Hatsuda and T.K. ;in preparation)
Deeply-bound pionic nuclei and missing repulsion
○
●
△
LO+EE without w.f.r.
LO+EE with w.f.r.
NNLO with w.f.r.
K. Suzuki et al., Phys. Rev. Lett. 92,
072302 (’04)
Kolomeitsev, Kaiser, & W. Weise,
Phys.Rev.Lett. 90 (’03)
P.Kienle and T.Yamazaki,Prog. Part.
Nucl. Phys. 52 (2004), 85
Gell-Mann-Oakes-Renner relation in the nuclear medium
2
r
holds up to
:
f(t )*2 ( r )m*2 ( r )  - mu 2md qq

r
-1
a  -.1m
c2  3.2  .25
c3  -4.7  1.16
(GeV^(-1))
 ( ')
• Related to
Meson:
U A (1)
 8

uu  dd ,
 ' ss
Anomaly; otherwise
 ' 0
; ideal mixing realized
Current divergences and Quantum Anomalies
SUV ( N f )
SU A ( N f )
U A (1)
(
)
Chiral Anomaly
Quantum effects!
Dilatation
Dilatation(scale)
Anomaly
; energy-momentum tensor of QCD
U A (1) Problem
G= U L (3) U R (3)
# of the generators
2x(8+1)=18
H= UV (1)  SU f (3)
1+8=9
# of NG-bosons= dim G - dim H = 18 – 9 = 9 (?)
Nambu-Goldstone Theorem
# of the lightest pseudo-scalar mesons
  ,  0(140) K  , K 0 , K 0 (500)  (550)
3
Why is
+
4
+
'
so massive ?
1
<<
 ' (958)
=89 !
------ UA(1) Problem

Anomaly
even in the chiral limit!
0
Operator
Equation!
 ( ')
or chiral anomaly in the medium at finite T and
r
T.K. (1989), Ohnishi et al(1998), Ruivo et al (‘00)
Also selective coupling of

with N*(1535)
Jido, Hirenzaki and Nagahiro
chiral dynamics v.s. Chiral doublet
a la DeTar-Kunihiro(Phys. Rev. D39,2805 (‘89) )type?
gives different optical potential for eta!
experiment done in GSI (Hayano et al)
Summary
•The  meson as the quantum fluctuation of the order parameter
of the chiral transition may account for various phenomena in
hadron physics which otherwise remain mysterious.
• There have been accumulation of experimental evidence of the
 pole in the pi-pi scattering matrix.
( chiral symmetry, analyticity and crossing symmetry.
• A full lattice QCD suggests the existence
of the 
•Partial restoration of chiral symmetry in hot and dense medium
as represented by the decreasing f leads to a softening
of the  and the r pole in the 2nd Riemann sheet in
various chiral models.
•Even a slight restoration of chiral symmetry in the hadronic
matter leads to a peculiar enhancement in the spectral function
in the  channel near the 2m threshold.
•Such an enhancement might have been observed in the
reaction
•The decrease of the of
w.f. renormalization of the pion
commonly seen in the deeply bound pionic nuclei,
suggesting a strongly coupled system of the pion and nuclear
medium.
Also pi-A scattering at low energies. (E.Friedman et al(2004))
• eta (eta’) meson and N* and parity doublets of other baryons
(DeTar and T.K. (1989); Jido, Hosaka and Oka, Hirenzaki, Nagahiro …. )
Back Ups
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 r, (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  I=1/2 enhancement in K ->2 compared with K+->0.
E.P. Shabalin (1988); T. Morozumi, C.S. Lim and I. Sanda (1990).
5.-N sigma term 40-60 MeV (naively » 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
E. M. Aitala et al, Phys. Rev. Lett. (86), 770 (2001)
Without sigma pole
With a sigma pole:
24
23
42
40
Chiral Transition = a phase transition of QCD vacuum,
being the order parameter. Lattice QCD;
eg. F. Karsch, Nucl. Phys. Proc. Suppl. 83, 14 (2000).
The wisdom of many-body theory tells us:
If a phase transition is of 2nd order or weak 1st order,
9 soft modes » the fluctuations of the order parameter
For chiral transition,
The  meson becomes the soft mode of chiral transition at
T. Hatsuda and T. K. , Phys. Rev. Lett.; Prog. Theor. Phys (1985):
It was also shown that hadronic excitations (para pion and sigma)
exisit even in the ``QGP” phase.
A
C; A-dependence of 

N.Grion (talk at
Chiral05)
TAPS
CHAOS
00 I=0
- I~0
0 I=1
 I=2
E~420 MeV
E~420 MeV
r ~ 2/3r0
r ~ 1/3r0
Oset and Vicente,
PRC60(1999)064621
Oset: Full model of the 
,- process, standard nuclear effects discussed,
P-wave pionic modes included and the -meson dynamically generated.
Muhlich: Model based on Oset’s developed for the 
00 and  0,- reactions,
better treatment of FSI of pions with the nucleus, no medium modifications.
Muhlich et al.,
PLB595(2004)216
Differential cross sections of the reaction A(,0 0)A'
----- phase space
L. Roca et al (2002)
without softening
TAPS experiment:
J.G. Messchendorp et al, Phys. Rev. Lett.
89 (2002), 222302.
P. Muelich, L. Alvarez-Ruso, O. Buss and U. Mosel,
( nucl-th/0401042).
 -N FSI lowers the spectral function in the pi-pi invariant mass.
The spectral enhancement
in the nonlinear realization
D. Jido, T. Hatsuda and T. K.,Phys. Rev. D63} (2000), 011901(R).
In the polar decomposition M=SU,
fixed
In the heavy S-field limit,
;
In the medium: Thorsson-Wirzba Lagrangian (1996)
L(
f2
4
 c23 r )Tr[ U U  ]  ( c22 - 16gmAN ) rTr[ 0U 0U  ]  ...
The movement of the sigma pole in the complex
Energy plane in the N/D method with MFA
K. Yokokawa,
T. Hatsuda,
A. Hayashigaki,
And T.K.(2002)
A: r model
B:  model
C: r -  model
D:
The T matrix in the N/D method.
The in-medium - cross sections in I=J=0 channel.
The upper (lower) panel shows the case of small (large)
restoration corresponding to
K. Yokokawa,
T. Hatsuda,
A. Hayashigaki
and T.K. (2002)
Vector Mesons
QCD sum rules, effective theories as NJL model and
Brown-Rho scaling
suggest that
The vector mesons mass/width,
or more precisely,
their spectral functions may change
in hot and/or dense matter
The softening in the
K. Yokokawa et al (2002)
meson channel
Vector mesons in nuclei as seen by photon
mV ( r )  m0 (1 - r / r0 )
KEK-PS (Naruki et al): r ,  , 
r ,  show a mass drop!   0.1
ELSA@Bonn (Metag); CB/TAPS 4

  0.15
for

Experiment should be made and is being anallyzed:
Spring-8
Softening of the spectral function in
the Vector channel
Softening of the vector mesons in
Nuclear media (H. En’yo et al)
QCD phase diagram
T
precursory (T. Hatsuda and T.K. (’84, ’85)
hadronic modes?
QGP
QCD c.p.
SB
?
r0
CSC
CFL

H matter?
meson condensation?