1. Missing mass spectroscopy
neutron
-hole
emitted proton
Incident p+
nucleus
meson
Candidate reactions : recoil-free production
(d,3He) reaction …established method p atom formation (96, 98, 01)
S.Hirenzaki, H.Toki, T.Yamazaki, PRC44(91)2472, …
K.Itahashi, et al., PRC62(00)025202, …
First, I’d like to explain the the missing mass spectroscopy used in this work.
In this reaction, the incident particle reacts with a proton inside a target nucleus and produces a meson there. The meson may be trapped into a certain bound state in the nucleus, if there exist bound states. The proton is ejected from the nucleus,
we observe this emitted proton in the final state, and obtain a spectrum like this.
Such a spectrum should reflect this in-medium dispersion relation, then we can study medium effects from spectra.
A candidate reaction is, for example, (d,3He) reaction, which originally has been studied theoretically on the deeply bound pionic atom studies, and proved to be powerful tool experimenaly.
And (gamma,p) reaction is another experimental tool for formation of the hadron-nucleus system and it is originally proposed in these references.
(g,p) reaction … smaller distortion effect
M.Kohno, H.Tanabe PLB231(89)219
E.Marco, W.Weise, PLB502(01)59 … etc.
(p,N) reaction … pion beam at J-PARC
Chrien et al., PRL60(1988)2595
Liu, Haider, PRC34(1986)1845

2. meson production in recoil-free kinematics
magic momentum in (p,N) reaction
h-mesic nuclei
pp ~ 1 GeV/c
N*(1535)-hole ... N*(1535) in medium
900
800
w-mesic nuclei
pp ~ 2-3 GeV/c
700
w mass shift / N(1520)-hole coupling
600
h’-mesic nuclei
pp ~ 3-5 GeV/c
500
momentum transfer q [MeV/c]
UA(1) anomaly effect in medium
400 h w
h’(958)
300 h
200 h’ w
100
mh’ – 100 MeV
1.0
2.0
3.0
4.0
5.0
incident pion momentum pp [GeV/c]
~ 0.9 GeV/c
~ 2.7 GeV/c
~ 1.8 GeV/c  mw – 80 MeV

3. What causes the level crossing
What causes the level crossing ? : partial restoration of chiral symmetry
DeTar, Kunihiro PRD39(89)2805
Jido, Nemoto, Oka, Hosaka NPA671(00)471
Jido, Oka, Hosaka PTP106(01)873
Kim, Jido, Oka NPA640(98)77
Chiral doublet model
650
600
550
500
450
400
w [MeV]
sh(0,k0)
r = 0.8 r0
mass
N* : Chiral partner of nucleon
mass difference of N* and N
C ~ 0.2 : strength of chiral restoration at the saturation density r0
reduction of mass difference in the nuclear medium
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 T V = + …
 quasi bound state of KS
No mass shifts of N* is expected in the nuclear medium
coupled channel Bethe-Salpater eq. in medium
no Pauli blocking for S in nuclear medium
N* : resonance dynamically generated in meson-baryon scattering
Inoue, Oset NPA710(02)354 50
100
-50
-100
sh(0,k0)
r = 0.3 r0
There is one scenario which causes the mass reduction, chiral doublet model. This model has been developed by these authors, and this model is an extension of SU(2) linear sigma model for the nucleon sector. In this model, N* is regarded as the chiral partner of nucleon.
In this model, the mass difference of N and N* is expressed like this, where the parameter C represents the strength of the partial restoration of the chiral symmetry at the nuclear saturation density rho0. Empirically, its value is around 0.2, this means 20% mass reduction at rho0 as shown in previous slide. Thus this model predicts the reduction of the mass difference, considering the restoration of the chiral symmetry in the nuclear medium, and yields the level crossing.
---
One the other hand, there is another model describing the N*(1535), which is the chiral unitary model.
The chiral unitary model has quite different picture from the chiral doublet model. This approach in developed by these authors. In this model, N* is introduced as a resonance generated dynamically in meson baryon-scattering and is regarded as quasi-bound state of K Sigma. Since there is no Pauli-blocking effect for Sigma in nucleus, then almost no mass shift is expected in the nuclear medium in this model. [In this study we directly use the eta-self-energy shown in this reference and use it to obtain the eta-nucleus optical potential.]
In this talk, I am going to compare the consequences of these two models as extreme cases for N* behavior.
In order to see these phenomena in physical observables, we should discuss in the finite size nucleus.

4. h-mesic nuclei formation spectra
(K.Itanashi, H.Fujioka, S.Hirenzaki, D.Jido, H.Nagahiro, Letter of Intent for J-PARC 2007)
h-mesic nuclei formation spectra
Tp = 650 MeV (pp = 777 MeV/c) : q = 0 deg. (Lab)
Chiral doublet model [C=0.2]
Chiral unitary model 80 60 40 20
0s : (B.E.,G) =
(9.7,35.0) [MeV]*
* 12C
Garcia-Recio et al.,
PLB550(02)47
shallow b.s.
left figure shows the chiral doublet model and right is the chiral unitary model case.
First, let me focus the behavior around the threshold.
At threshold, the real part of the optical potentials in doublet model and unitary model are like this. In the chiral unitary case, we can see one bound state in s-wave here. But, unfortunately, at the same energy, there is quasi-free eta contribution from p-wave eta, the green line, so we cannot separate the bound state peak from the quasi-free contribution in the total spectrum.
And secondly, we can see the deep bound state in the chiral doublet model here, because of the attractive potential. But strength is very small, we cannot expect to observe this bound state as a peak.
Unlike the pionic atom formation, for the eta mesic nuclei case, we should observe not peak structures but whole spectrum shape itself in order to get some information.
[added after talk at INPC2007]
And third point we would like to focus here, is about this bump structure,
Eex – E0 [MeV] 50
100
150
-50
-100
elementary cross section
S.Prakhov et al., [Crystal Ball Collaboration]
PRC72, (2005).
deep b.s.
0s : (B.E., G) = (91.3, 26.3) [MeV]

5. w mesic nuclei formation
w meson properties in medium
various models/approaches
scaling rule
Brown and Rho, PRL66, 2720 (1991)
QCD sum rule
Hatsuda and Lee, PRC46, 34 (1992).
SU(3) chiral Lagrangian
Klingl, Kaiser and Weise, NPA624, 527 (1997)
Klingl, Waas, Weise, NPA650(99)299
Marco, Weise, PLB502(01)59
couples to N*(1520)-hole
Lutz, Wolf, Friman, NPA706, 431 (2002)
w/ Walecka model (s-w mixing)
Saito, Tsushima, Thomas, Williams, PLB433(1998)243
Saito, Tsushima, Lu, Thomas, PRC59(1999)1203
experimental works
invariant mass
p + A  w + X at KEK E325 : (M.Naruki at al., PRL96(06) etc.)
g + A  w + X  p0g +X’ by ELSA-TAPS : (D.Trnka et al., PRL94(05)192303)
missing mass
(g,p) reaction at SPring-8 LEPS (N.Muramatsu, LEPS group)
(p,N) reaction at J-PARC (K.Ozawa and R.S.Hayano, LoI for J-PARC, ’07) r p w N r p w N : w w
N(1520) N N
Brown-Rho scalling
m*/m = 0.8 at rho = rho0
QCD Sum Rule by Hatsuda & Lee ('92)
m*/m = rho/rho0 for rho/omega
m*/m = rho/rho0 for phi
KEK E325 : 9% deduction
ELSA/TAPS : MeV/c^2 rho = 0.6 rho0

6. w-mesic nuclei formation spectra by (p,N) reaction
(K.Ozawa and R.S.Hayano, LoI for J-PARC, ’07)
w-mesic nuclei formation spectra by (p,N) reaction
reaction : 12C(p+,p)11Cw
elementary cross section
incident pion momentum : pp = 1.8 GeV/c
G.Penner and U.Mosel, PRC65(02) data: J.S.Danburg et al., Lawrence Radiation Lab.
PRD2(1970)2564
proton angle : 0 degree 4
(a) V0 = − (156,29i) MeV
(b) V0 = − (100,50i) MeV
(c) V0 = − (0,50i) MeV
1/10 of h case 3 2
excess from
large imaginary part
smooth 1
-100
-50 50
-100
-50 50
-100
-50 50
100
Eex – E0 [MeV]
Eex – E0 [MeV]
Eex – E0 [MeV]

7. ? N(1520)-hole coupling w mode mw mN* -mN N*-hole mode N*(1520)-h w
900
400
600
700
800
500
[MeV] 1 2
0.5
1.5
r/r0 mw
mN* -mN
w mode
N*-hole mode
N(1520)-hole coupling ? w
gwNN*
hole
N*(1520)
gwNN* w 4 3 2 1
N*(1520)-h
-200
-300
-150
-250
-100
-50 50
100
Eex – E0 [MeV]

8. h’(958) meson in medium h’ h p
T. Kunihiro, PLB219(89)363
P. Costa et al.,PLB560(03)171, etc.
h’(958) meson in medium
H.N., M.Takizawa, S.Hirenzaki, PRC74(06)045203
we consider the SU(2) sym. matter as the sym. nuclear matter.
anomaly term effect
Kunihiro, Hatsuda, PLB206(88)385, Fig.3 h’ h p
Anomaly effect in vacuum
NJL model + KMT int.
... reproduce
the heavy h’ mass
h and h’ mass r0
Dmh’ ~ -150 r0
Dmh ~ +20 r0
We can see the large medium effect even at normal nuclear density.

9. h’-mesic nuclei formation by (g,p) reaction at Eg = 2.7 GeV
H.N., S.Hirenzaki, PRL94(05)232503
H.N., M.Takizawa, S.Hirenzaki, PRC74(06)045203
gD = /L5
quasi-free
quasi-free
V0= - (156+29i) [MeV]
(Klingl et al., NPA650(99)299) h h’
W0 = – 20 MeV w
And this is the broader imaginary part case, -20 MeV.
Even in the broader case, we can see the mass reduction due to the medium effect through the anomaly term.