1. Formation of Meson-Nucleus Bound Systems by (g,p) reactions
@Japan-US Workshop on
Electromagnetic Meson Production and
Chiral Dynamics
9 Apr. ’05
S. Hirenzaki (Nara Women’s Univ.)

2. Features ( cf Invariant Mass Methods)
Objects
Hadron – Nucleus bound systems.
Coulomb + Strong … Exotic Atoms
(Deeply Bound) atom, Kaonic atom, atom …
Strong … Exotic Nuleus
Mesic Nucleus, Hypernuclei, …
Exotic Many Body Systems.
In Medium Hadron Properties.
Spectroscopic Methods ( Peak structure)
Quasi-Static Systems around
Interests
Features ( cf Invariant Mass Methods)

3. Basic Concepts In-Medium Dispersion Relation look carefully !! initial
: Missing Mass ( Invariant Mass)
Bound States
look carefully !!
Peaks!!
initial
final N
Zoom In
meson
Medium Effects
In-Medium Dispersion Relation

4. Formation Cross Section by ‘pick-up’ reactions, (g, N), (d,3He), (K,N), …
Effective Number approach
Recoilless
Substitutional States formation
For large widths systems;
Green function Method by O. Morimatsu, K. Yazaki,
NPA 435, 727 (85), NPA 483, 493 (88)
:smaller distortion, background large?
Experimental data
or Theoretical model

5. Pionic 1s states of Sn nuclei
Umemoto, Hirenzaki, Kume, Toki PRC62(00)024606
K. Suzuki et al. PRL (04)

6. There are active discussions
K. Suzuki et al., Phys. Rev. Lett. 92(2004)072302
observation
Kolomeitsev, Kaiser, Weise (PRL90(2003)092501)
in two-loop chiral perturbatio
Energy dependent of
Gauge coupling of
Phenomenological pieces, ( , p-wave terms)
Discussion on rn (n>1) ?… (Garcia-Recio, Nieves, Oset,
PLB541(2002)64)
E. Friedman and A. Gal, PLB578(2004)85
G. Chanfray, M. Ericson, M. Oertel, PLB563(2003)61
‘Chiral Restoration in nonlinear realization’ D. Jido, T. Hatsuda, T. Kunihiro, PRD63(2000)011901
U.-G. Meissner, J. Oller, A. Wirzba, … Ann. Phys. 297 (2002) 27
are important

7. Kinematics of (g, N) at forward angles
500
400
q [MeV/c]
300
200
100
500
1500
2000
2500
3000
p atom
w mesic Nuclei
S. Hirenzaki, E. Oset
E. Marco, W. Weise
Phys. Lett. B527 (2002) 69
Phys. Lett. B502 (2001) 59

8. We consider here (g,p) – (K,N) – K nucleus (K,p) – nucleus
D. Jido, H. Nagahiro, S. Hirenzaki : PRC66(02)045202
H. Nagahiro, D. Jido, S. Hirenzaki : PRC68(03)035205
H. Nagahiro, S. Hirenzaki : hep-ph/
H. Nagahiro, D. Jido, S. Hirenzaki : in preparation
J. Yamagata, H. Nagahiro, Y. Okumura, S. Hirenzaki
: nucl-th/
H. Nagahiro, S. Hirenzaki, E. Oset, M.J. Vicente-Vacas
: nucl-th/ , v2

9. h -Nucleus system : Introduction
works for eta-mesic nuclei
D. Jido and H. Nagahiro
* Liu, Haider, PRC34(1986)1845
* Chiang, Oset, and Liu, PRC44(1988)738
* Chrien et al., PRL60(1988)2595
* Hayano, Hirenzaki, Gilltzer, Eur.Phys.J.A6(1999)99
* D. Jido, H.Nagahiro, S.Hirenzaki PRC66(2002)045202
* Exp. at GSI (2005?) (Yamazaki, Hayano group)
(d,3He)
properties of eta meson
eta meson
system
-No baryon contamination
-Large coupling constant
-no suppression at threshold
(s-wave coupling)
eta-N system
Strong Coupling to N*(1535),
eta-Nucleus system
Doorway to N*(1535)

10. h -Nucleus Interaction
~ N* dominance model ~
optical potential
(Chiang, Oset, Liu PRC44(1991)738)
(D.Jido, H.N., S.Hirenzaki, PRC66(2002)045202)
to reproduce the partial width
at tree level.
potential nature
In free space
attractive
N & N* properties in medium evaluated
by two kinds of Chiral Models
General feature
medium effect
Repulsive ??
mN & mN* change ?? ?

11. Chiral models for N and N*
Chiral doublet model
DeTar, Kunihiro, PRD39 (89)2805
Jido, Oka, Hosaka, Nemoto, PTP106(01)873
Jido, Hatsuda, Kunirhiro, NPA671(00)471
Lagrangian
Physical fields
N* : chiral partner of nucleon
Mass difference
* reduction of mass difference
* C~0.2 :the strength of the Chiral restoration
at the nuclear saturation density
Chiral unitary model
Kaiser, Siegel, Weise, PLB362(95)23
Waas, Weise, NPA625(97)287
Garcia-Recio, Nieves, Inoue, Oset, PLB550(02)47
Inoue, Oset, NPA710(02) 354
A coupled channel Bethe-Salpeter eq.
* No mass shift of N* is expected in the nuclear medium.
* In this study, we directly take the eta-self-energy in the ref.NPA710(02)354
* the N* is introduced as a resonance generated dynamically from meson-baryon scattering.

12. h -Nucleus optical potential
associated with mass reduction

13. (g,p) Spectra of 12C target Bound state @Japan_US Workshop, 9 Arp. ‘05
enhanced
It seems impossible to observe b.s. as a peak from the spectrum.
(g,p)
We can see the difference between two models clearly.

14. h’(958)-Nucleus System : Introduction
H. Nagahiro
h’(958) meson
Close relation to UA(1) anomaly
heavy h’ mass due to the existence of anomaly term
some theoretical works
in vacuum / at finite temperature / at finite density
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/
etc…

15. Models with NJL Lagrangian + KMT interaction
Anomaly effect in vacuum
KMT term
T.Kunihiro, T.Hatsuda, PLB206(88)385, Fig.3 u d s
Meson Mass u s d
flavor mixing vertex
 Large h and h’ mass due to anomaly

16. Anomaly effect @ finite T / r
at finite Tempereture
P. Costa, M. C. Ruivo, Yu. L.Kalinovsky
PLB560(03)171, Fig.2
at finite density
: const
T.Kunihiro, PLB219(89)363, Figs.2, 3
: const
T0=100 MeV
Case I
Case II

17. Our motivation & present work
a poor experimental information on the UA(1) anomaly at finite density
h’(958)-mesic Nucleus formation reaction
UA(1) anomaly in medium
h, h’ mass shift observation
new information on the properties of UA(1) anomaly ?
We consider …
NJL Lagrangian + KMT term
h’ spectra
h and h’ in the same framework cf. chiral doublet, chiral unitary models.
h and h’ mesic nuclei formation cross section

18. h- & h’-Nucleus optical potential
~ phenomenological estimation
Real Part V0
evaluated by possible h, h’ mass shift at r0
Imaginary Part W0 for h’
estimated from nucl-th/ (A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth) analysis of gp h’p data N
N*(1535) h’ g
(only one resonance included)
fix a coupling g ’
in analogy with D-hole model for the p-nucleus system ’

19. mass shifts of h and h’ mesons
(1) Constant gD in medium P. Costa et al., PLB560(03)171, Fig.2 
Dmh’ ~ -150 r = r0
Dmh ~ +20 r = r0
(2) Smaller gD in medium
… no information …
 An estimation from the fig. in
T.Kunihiro, T.Hatsuda, PLB206(88)385, Fig.3  (Notice : This fig. shows the results in Vacuum.)
Dmh’ ~ -150 MeV
Dmh ~ -100 MeV
@ r = r0

20. Reaction Parameters w-mesic nuclei (g,p) reaction @ Eg=2.7 GeV
target … 12C
Forward (q ~ 0 deg.)
Elementary cross section for gp  h’p
w-mesic nuclei
mh ~ 547 MeV mw ~ 783 MeV mh’ ~ 958 MeV
plan of experiment for the formation of w-mesic SPring-8, 2005
two different predictions for optical potentials
【Attractive】 V= - ( i) r/r0 MeV [Klingl, Waas, Weise NPA650(99)299]
【Repulsive】V= - ( i) r/r0 MeV [Lutz, Wolf, Friman NPA706(02)431]
elementary cross section ~ 150 nb/sr
event # [h] ~ [w] ~ [h’] @ test experiment at SPring [N.Muramatsu, private communication]
h-mesic nuclei
Data:SAPHIR collaboration, PLB444(98)
Chiang, Yang, PRC68(03)045202

21. Numerical results : 12C(g,p)11Bh,w,h’
quasi-free
V0= - (150+5i) [MeV]
V0= - (156+29i) [MeV]
(Weise)
V0 = - (100+40i) [MeV]
mass  small

22. Numerical results : 12C(g,p)11Bh,w,h’
quasi-free h w h’
V0= - (150+20i) [MeV]
V0= - (156+29i) [MeV]
(Weise)
V0 = - (100+40i) [MeV]
mass  small

23. Numerical results : 12C(g,p)11Bh,w,h’
quasi-free h w h’
V0= - (150+20i) [MeV]
V0= - (156+29i) [MeV]
(Weise)
V0 = - (-20+40i) [MeV]
mass  large

24. Numerical results : 12C(g,p)11Bh,w,h’
quasi-free h w h’
V0= - (150+20i) [MeV]
V0= - ( i) [MeV]
(Lutz)
V0 = - (-20+40i) [MeV]
mass  large

25. Numerical results : 12C(g,p)11Bh,w,h’
quasi-free h w h’
V0= - (150+20i) [MeV]
V0= - ( i) [MeV]
(Lutz)
V0 = - (100+40i) [MeV]
mass  small

26. Summary (g,p) spectra of both h and h’ with w meson h mesic nuclei in
Chiral doublet (N*(1535) dominance)
Chiral Unitary
h and h’ in the same framework (NJL+KMT)
Reasonably large cross sections observation
S/N ~ 1/10 … N.Muramatsu, private communication
the experiment for the formation of w-mesic nuclei
@ SPring-8 (planned)
(information on h & h’ as byproducts ?)
in Future
What the peak position means?
more microscopic treatment for h and h’-nucleus interaction

27. Kaonic Bound States Formation by In-flight (K-,N) reaction
J. Yamagata
J. Yamagata H. Nagahiro Y. Okumura S. Hirenzaki
nucl-th/

28. Energy Spectrum – 16O(In-flight K-,p)
Comparison Exp. vs Calculated results
16O(In-flight K,n) PK = 930 MeV/c
16O(In-flight K-,ｐ) PK = 976 MeV/c
Bound region
Data by
Kishimoto group.
(Osaka Univ.) ?
[ T.Kishimoto et al., Prog. Theor. Phys. Suppl. 149 (2003)264 ]
[ Fig. taken from the seminar by Dr. Hayakawa ]

29. Q Hyper Nuclei formation
H. Nagahiro, S. Hirenzaki, E. Oset, M.J. Vicente-Vacas, nucl-th/ , v2
Interaction of the Q+ with the nuclear medium
Working Hypothesis
Q+ : , belongs to SU(3) antidecuplet
SU(3) symmetric Lagrangian
N*(1710) also belongs to antidecuplet
N*(1710) Npp decay deta fix the coupling const.
D. Cabrera et al., PLB 608(2005)231
A. Hosaka et al., hep-ph/
PRC in print
: antidecuplet states
: octet of ½+ baryons
: octet of 0- mesons
H. Nagahiro
S. Hirenzaki
E. Oset
M.J.
Vicente-Vacas
where
: a vector current for two mesons
attractive interaction diagram Q+ N p K
In the nuclear medium, new channels are open.

30. Q+ hypernuclei formation reaction
Possible process
Reported process in Prof. Nakano’s experiment
(g, K–) Q+ g K– n
Proposal at J-Lab reaction
(R. J. Feuerbach(spokesperson))
theoretical vertices, Q+ into MMB, in the SU(3) Lagrangian
[D. Cabrera et al., PLB 608(2005)231, A. Hosaka et al., hep-ph/ , PRC in print.]
Q K+ p– p
K0 p0 p
K0 h p
K+ p0 n
K+ h n
K0 p+ n
charged
Q K+ p– p
K0 p0 p
K0 h p
K+ p0 n
K+ h n
K0 p+ n Q+ B M
(K+,p+)
(p–, K–)
Notice : (p-,K-) could be
very small (KEK exp.)

31. 12C target case : VQ= -60 r/r0 [MeV]
free Q+ production threshold
(s-state proton pick-up case)
free Q+ production threshold
TK=300MeV
pK~620MeV/c
quasi-free Q+ region
clear peak separated from each other.
Reasonable cross section of the order of [micro b/sr MeV]
not too small

32. 12C target case : VQ= -120 r/r0 [MeV]
TK=300MeV
pK~620MeV/c
We can see clear peaks.
quite different spectrum from V=-60 r/r0 MeV case.
more bound states for V=-120 r/r0 MeV
narrower peaks due to the deeper bound states
we may be able to distinguish these two type potentials by the spectrum, if we can see.

33. 12C target case : energy dependence
We also calculate TK=500MeV(pK=863MeV/c) case.
momentum transfer q doesn’t change drastically.

34. Summary on Q+ hypernuclei
Summary on K
Narrow K-Nuclear state, Ultra high density matter,
Really exists ??
In flight (K,p) reaction
theoretical results Kishimoto exp.
Need systematic comparison of theoretical results and exp. data
Summary on Q+ hypernuclei
Q+ hypernuclei formation by (K+,p+) reaction
New frontier of S=+1 hypernuclei ?
(or just a dream)
Many Unknowns … Let’s try !