????????????? - A brief summary of current interests -

1
?????????????- A brief summary of current
interests -

• ??????
• ??? ?

2
Pionic Atom, Kaonic Atoms(?????????)
Meson ( Yukawa Particle )
B.E.
mp 300 me
p-
Radius
A(Z,N)
Electromagnetic Strong
Interactions
Strong Interacting Particle System!
3
Observation of Pionic Atom
Traditional Way Slow Pion Trap
X-ray Detector
X-ray
Absorption to Nucleus by Strong Interaction
Slow
Nucleus
4
4He
16O
40Ca
5
Pion Nucleus Optical Potential
In-Medium Dispersion Relation
Medium Effects
Ericson-Ericson, Ann. Phys. 36 (66)
323 Seki-Masutani, Phys. Rev. C27(83)2799
with
6
Toki, Hirenzaki, Yamazaki, Hayano (1989)
7
Toki, Hirenzaki, Yamazaki, Hayano (1989)
8
???
Energy and Width
Information on pion-nucleus interactions
9
Missing mass spectroscopy
proton
-hole
Incident particle
emitted particle
target
meson
10
Distortion effect
Eikonal approx.
distortion Factor reduction of the flux due to
absorption
These two reactions have different sensitivities
to systems.
11
Missing mass spectroscopy
proton
-hole
Incident particle
emitted particle
target
meson
12
Deeply bound p- states in the 208Pb(d,3He)
reaction
K. Itahashi et al.
PRC62(00)025202
Hirenzaki, Toki, Yamazaki PRC(1991)
13
Deeply bound 1s and 2p Pionic States in the
206Pb(d,3He) reaction
PRL88(02)122301
Hirenzaki, Toki PRC55(97)2791
14
Pionic 1s states of Sn nuclei
Umemoto, Hirenzaki, Kume, Toki
PRC62(00)024606
K. Suzuki et al. Phys. Rev. Lett. 92(2004) 072302
GOR relation Tomozawa-Weinberg Relation
15

• New method Observation of Meson-Nucleus states
• (????????????)
• Information on at finite r r0
• Eigen state observation Invariant
  Mass Method
• Quantum number fixed Selective
  information

Umemoto et al., PRC62 (2000)
16
Further Progresses

• 1. Exotic Many Body Physics
• 2. Hadron Physics at finite density
• Fundamental theory (QCD)
• Effective theory
• Hadron property at finite r
• ??? ???
• ?????? ???

Exotic few body systems.
(core, fermion, boson)
17
Meson Mass Spectrum
Jp 0-

• T.Kunihiro, T.Hatsuda, PLB206(88)385
• T. Kunihiro, PLB219(89)363
• R.D.Pisarski, R.Wilczek, PRD29(84)338
• K.Fukushima, K.Onishi, K.Ohta,
• 
  PRC63(01)045203
• P. Costa et al.,PLB560(03)171,
• 
  hep-ph/0408177
• etc

• Higgs mechanism

• Spontaneous
• Chiral Symmetry Breaking

• UA(1) Anomaly Effect

18
In-Flight (K-,p) Reactions for the formation of
Kaon-Nucleus bound systems

• Junko Yamagata (Nara Womens Univ.)
• H. Nagahiro (RCNP, Osaka Univ.)
• S. Hirenzaki (Nara Womens Univ.)

J. Yamagata, H. Nagahiro, Y. Okumura, S.
Hirenzaki, Prog.
Theor. Phys. 114 (2005) 301 Errata 114 (2005)
905 J. Yamagata, H. Nagahiro, S. Hirenzaki,
arXivenucl-th/0602021
19
Introduction for kaon
K

• Kaonic Nuclei
• K-Nucleus bound system ? strong interaction
• Binding Energy 10 100 MeV
• Formation Reaction
• (In-flight K,N) reaction Kishimoto Group (Exp.)
• (Stopped K,N) reaction Iwasaki, Suzuki Group
  (Exp.)
• (K light nuclei) system structure Akaishi,
  Yamazaki, Dote
• 
  (Theor.)
• Critical analysis E. Oset, H. Toki (Theor.)

Cf. Kaonic Atoms
Very deep!!

• quasi-stable K-Nuclear State
• Ultra high density state

Really Exist or not ?
20
Introduction for kaon

• Our Study
• Structure of Kaonic Atoms and Kaonic Nuclei
• (two different K-Nucleus optical
  potentials)
• Formation spectra of In-flight (K-,p) reactions
• Green Function Method
• The energy dependence of the optical potential
• The Quasi-Free Kaon production processes

21
Formulation -- Structure

• Klein-Gordon Equation

Chiral Unitary Model
A. Ramos, E. Oset, NPA671(00)481 Hirenzaki,
Okumura, Toki, Oset, Ramos, PRC61(00)055205
Phenomenological Model
Batty, Friedman, Gal, Phys. Rep. 287(97)385
22
Phase Space Factor (for the phenomenological
potential)
Phase Space Factor
threshold
threshold
23
Formulation -- Structure

• Klein-Gordon Equation

A. Ramos, E. Oset, NPA671(00)481 Hirenzaki,
Okumura, Toki, Oset, Ramos, PRC61(00)055205
Chiral Unitary Model
Phenomenological Model
Batty, Friedman, Gal, Phys. Rep. 287(97)385
24
Energy level (examples by the potential at E0)
Atomic State
Similar
25
Formulation Reaction

• Green Function Method

O. Morimatsu, K. Yazaki NPA435 (85)727 O.
Morimatsu, K. Yazaki NPA483 (88)493
Elementary cross section (Exp. data)
Green function for K interacting with the
nucleus
Previous work Effective Number Approach
(J. Yamagata et. al., PTP114(05)301)
12C is interesting !
26
Momentum Transfer q0
Kaon Binding Energy
B.E. 150 MeV
B.E. 100 MeV
B.E. 50 MeV
B.E. 0 MeV
27
Green vs. Effective (Energy Spectrum)
Nuclear States

• Phenomenological
• potential
• At E0

Target 12C
TK 600 MeV
28
Green vs. Effective (Energy Spectrum)
Nuclear States
Target 12C
TK 600 MeV
Bound region

• Phenomenological
• potential
• At E0

29
Energy Spectrum ( E0 potential )
12C (K-,p) reactions TK 600 MeV
Green
Effective Number
30
Energy Spectrum ( Energy dependence )
12C (K-,p) reactions TK 600 MeV
Structure?
Smooth
31
Effect of Branching Ratio of Decay Channel

• Phenomenological Potential

Phase Space Factor
80 20
32
Energy Spectrum

• Phenomenological Model (Energy Dependent)

80 90 20 10
33
Energy Spectrum

• Energy Dependent

Phenomenology
Chiral Unitary
Green
Green
Effective Number
Effective Number
J. Yamagata, H. Nagahiro, S. Hirenzaki,
arXivenucl-th/0602021
34
Energy Spectrum
Energy dependent
Chiral Unitary
Green Effective Number
Please ask Kishimoto san group.
Phenomenology
Comparison with Kishimoto groups data
35
Summary for kaon

• We studied the formation spectra of In-flight
  (K-,p) reactions.
• Target 12C, 16O TK 600 MeV
• Green Function Method (cf. Effective number
  approach)
• Interesting spectrum shape.
• No peak structure is expected in spectra for all
  cases
• 
  considered here.
• Nuclear structure change was not considered.

( not simple peaks )
36

• Formation of h-mesic nuclei
• Optical potential N(1535) dominance model
• Chiral Doublet model
• Chiral Unitary model
• Numerical Results of (d,3He) (g,p) reactions
• Formation of h(958)-mesic nuclei
• NJL model
• UA(1) anomaly in finite density
• Numerical Results of (g,p) reactions

Hideko Ngahiro, D.Jido and S.Hirenzaki,
NPA761(05)92 Hideko Nagahiro, D.Jido and
S.Hirenzaki, PRC68(03)035205 D.Jido, Hideko
Nagahiro and S.Hirenzaki, PRC66(02)045202 H
ideko Nagahiro, S. Hirenzaki, PRL94(05)232503 Hide
ko Nagahiro, M.Takizawa and S. Hirenzaki, in
preparation.
37
h(958)-Nucleus system
Hideko Nagahiro, S. H, Phys.Rev.Lett.94, 232503
(2005) Hideko Nagahiro, M.Takizawa and S. H, in
preparation.

• h(958) meson close connections with UA(1)
  anomaly
• some theoretical works
• the effects of the UA(1) anomaly on h properties
• at finite temperature/density
• T. Kunihiro, PLB219(89)363
• R.D.Pisarski, R.Wilczek, PRD29(84)338
• Y. Kohyama, K.Kubodera and M.Takizawa,
  PLB208(1988)165
• K.Fukushima, K.Onishi, K.Ohta, PRC63(01)045203
• P. Costa et al.,PLB560(03)171, hep-ph/0408177
  etc
• the possible character changes of h
• a poor experimental information on the
  UA(1) anomaly at finite density
• proposal for the formation reaction of the
  h-mesic nuclei
• UA(1) anomaly in medium from the viewpoint of
  mesic nuclei
• the h properties, especially mass shift, at
  finite density

38
Model for h and h meson in medium

• Nambu-Jona-Lasinio model with the KMT interaction
  
• unified treatment of the h and h meson

explicit breaking the UA(1) sym.
Kobayashi, Maskawa Prog.Theor.Phys.44, 1422
(70) G. t Hooft, Phys.Rev.D14,3432 (76)
39
Masses in finite r/T with NJL
T. Kunihiro, PLB219(89)363, P. Costa et
al.,PLB560(03)171. etc
40
SU(2) symmetric matter

• we consider the SU(2) sym. matter as the sym.
  nuclear matter.

anomaly term effect
h and h mass shifts _at_ r0
We can see the large medium effect even at normal
nuclear density.
41
anomaly effect in the finite density

• We simulate an extreme case.

gD gD(r) ??
gD gD(r0) exp(-(r/r0)2)
Dmh -150 MeV _at_ r0
Dmh 20 MeV _at_ r0
42
h- h-Nucleus optical potential
potential description

• Real Part V0
• evaluated by possible h, h mass shift at r0

43
h- h-Nucleus optical potential
potential description

• Real Part V0
• evaluated by possible h, h mass shift at r0
• Imaginary Part W0 for h
• estimated from AIP Conf.Proc.717
  (04)837(A.Sibirtsev,Ch.Elster, S.Krewald,
  J.Speth)analysis of gp hp data

phenomenological estimation
44
(g,p) reaction Parameters

• (g,p) reaction _at_ Eg2.7 GeV
• target 12C
• Forward (q 0 deg.)
• Elementary cross section for gp ? hp
• w-mesic nuclei
• mh 547 MeV mw 783 MeV mh 958
  MeV
• plan of experiment for the formation of w-mesic
  nuclei _at_ SPring-8, 2005
• two different predictions for optical potentials
• ?attractive? V - (156 29 i) r/r0 MeV Klingl,
  Waas, Weise NPA650(99)299
• ?repulsive? V - ( - 42.8 19.5i) r/r0 MeV
  Lutz, Wolf, Friman NPA706(02)431
• elementary cross section 150 nb/sr
• event h w h _at_ test experiment at
  SPring-8
  N.Muramatsu, private
  communication
• h-mesic nuclei
• elementary cross section 150 nb/sr

45
Numerical results 12C(g,p)11Bh,w,h
no medium effect
We only observe the quasi-free h peak
46
Numerical results 12C(g,p)11Bh,w,h
no medium effect
quasi-free
V0 - (- 42.8 19.5i) MeV (NPA706(02)431)
w
47
Numerical results 12C(g,p)11Bh,w,h
no medium effect
w
48
Numerical results 12C(g,p)11Bh,w,h
gD -12.36/L5
w
49
Numerical results 12C(g,p)11Bh,w,h
gD -12.36/L5
mass reduction due to the medium effect
throughanomaly term
w
50
Numerical results 12C(g,p)11Bh,w,h
gD -12.36/L5
quasi-free
Quasi-free w overlap with bound h
V0 - (- 42.8 19.5i) MeV (NPA706(02)431)
w
51
Numerical results 12C(g,p)11Bh,w,h
density dependent gD
quasi-free
quasi-free
V0 - (- 42.8 19.5i) MeV (NPA706(02)431)
quasi-free
w
52
Numerical results 12C(g,p)11Bh,w,h
density dependent gD
quasi-free
quasi-free
w
53
Summary for h and h mesic nuclei hadron
properties in finite r

• h-mesic nuclei by (d,3He) and (g,p) reactions
• Chiral doublet model
• Chiral unitary model
• Different pictures for the N(1535) in medium
• h-mesic nuclei by (g,p) reactions
• NJL model
• UA(1) anomaly in finite density
• Future works
• h-mesic nuclei
• (d,3He) experiment for h-mesic nuclei formation _at_
  GSI
• h-mesic nuclei
• (g,p) experiment for w-mesic nuclei _at_ SPring-8 ?
  Coming soon ?
• What is the density dependence of gD ??
• Other treatment ?
• relation with other models for h h
• chiral doublet model chiral unitary approach
  for the h-mesic nuclei

54
Summary

• Mesic Atoms and Mesic Nuclei
• A finite density Laboratory
• ??????????????????
• ???????????????????????????????
• h by (d,3He) Hayano (Tokyo group) _at_GSI
• w (h,h) by (g,p) Muramatsu (LEPS group)
  _at_SPring8
• k by In-Flight (K,p) Kishimoto (Osaka group)
• Many Others
• ?????????????????????

??????