『ストレンジネスとエキゾティクス・理論の課題』
3 Mar. 2007 @ 鳥羽, 三重
Formation spectra of h-mesic nuclei by (p+,p) reaction
at J-PARC
永廣 秀子 (阪大RCNP)
H.Nagahiro, D.Jido and S.Hirenzaki, NPA761(05)92
H.Nagahiro, D.Jido and S.Hirenzaki, PRC68(03)035205
D.Jido, H.Nagahiro and S.Hirenzaki, PRC66(02)045202
E.Kolomeitsev, D.Jido, H.Nagahiro, S.Hirenzaki, in preparation
H.Nagahiro, D.Jido, S.Hirenzaki, in preparation
Collaborators :
慈道 大介 (京大基研)
比連崎 悟 (奈良女)
1
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
Introduction

h 中間子原子核
» works for h-mesic nuclei
› (p+,p)
›
›
›
›
* Liu, Haider, PRC34(1986)1845 [theo]
* Chrien et al., PRL60(1988)2595 [exp]
negative result
* Chiang, Oset, and Liu, PRC44(1988)738 [theo]
* Kohno et al., NPA519(1990)755 [theo]
(d,3He) * Hayano, Hirenzaki, Gilltzer, EPJ.A6(1999)99 [theo]
* Jido, Nagahiro, Hirenzaki, PRC66(2002)045202 [theo]
* Exp. at GSI (Yamazaki, Hayano group) 2005-6 [exp]
(g,p)
* Nagahiro, Jido, Hirenzaki, NPA761(2005)92 [theo]
h-light-nucleus system : TAPS @ MAMI(2004) [exp]
etc… (ex. (g,h) @ Tohoku, etc …)
» strong coupling to N*(1535) [JP= ½-] resonance
› 有限密度中における N*(1535) の性質  h 中間子原子核
– カイラル二重項模型 … N* mass reduction in medium
– カイラルユニタリー模型 … no change N* mass in medium

formation of h-mesic nuclei induced by meson beam
»
p and K beams are available at J-PARC  (p+,p) reaction
› カイラル模型を用いたスペクトラム
› 運動学的な考察
» “(p+,p) experiment at 1988” の再考
› “negative result” の意味するところ。
2
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
Chiral doublet model
DeTar, Kunihiro PRD39(89)2805
Jido, Nemoto, Oka, Hosaka NPA671(00)471
Jido, Oka, Hosaka PTP106(01)873
Kim, Jido, Oka NPA640(98)77
mass
核媒質中の N*(1535) に対するカイラル模型
N* : Chiral partner of nucleon
mass difference of N* and nucleon
C ~ 0.2 : strength of chiral restoration at the saturation density r0
reduction of mass difference in the nuclear medium
Kaiser, Siegel, Weise PLB362(95)23
Waas, Weise NPA625(97)287
Garcia-Recio, Nieves, Inoue, Oset PLB550(02)47
Inoue, Oset NPA710(02)354
Chiral unitary model
N* : resonance dynamically generated
in meson-baryon scattering
 quasi bound state of KS
T
no Pauli blocking for S in nuclear medium
=
V
+
V
V
+…
coupled channel Bethe-Salpater eq. in medium
No mass shift of N* is expected in the nuclear medium
3
optical potential
+ (cross term)
potential nature
Chiang, Oset, Liu PRC44(1991)738
N* - N
Jido, Nagahiro, Hirenzaki, PRC66(2002)045202
48 MeV
attractive
h
medium effect
associated with mass
reduction
repulsive
energy w
mN*-mN
mh
level crossing
Kolomeitsev, Jido, Nagahiro, Hirenzaki
in preparation
r/r0
1
2
3
4
r [fm]
5
6
7
4
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
h self-energy
h-nucleus interaction ~ N* dominance model ~
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
Energy dependence of the h self-energy
bound region
Chiral unitary model
Inoue, Oset, NPA710(02) 354, fig.6
5
150
100
bound region
0
0
-50
-50
V(r) [MeV]
50
-100
-150
150
unitary
100
-100
-150
150
50
0
0
-50
-50
w - mh = -100 MeV
-100
-150
unitary
100
50
-100
doublet
100
50
w - mh = +100 MeV
-150
150
doublet
100
-100
150
50
-100
-150
150
unitary
100
w - mh = -70 MeV
2
4
6
r [fm]
8
-150
unitary
100
-50
-50
-100
-150
150
0
0
-50
-100
50
50
0
50
-50
V(r) [MeV]
unitary
100
V(r) [MeV]
-150
150
doublet
100
Chiral unitary model
Inoue, Oset, NPA710(02) 354, fig.6
-50
-100
150
0
0
-50
-150
50
0
100
doublet
w [MeV]
50
0
-100
-50
100
50
V(r) [MeV]
V(r) [MeV]
150
doublet
w - mh = 0 MeV
-100
w - mh = -50 MeV
2
4
6
r [fm]
8
-150
2
6
4
r [fm]
8
6
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
Energy dependence of the optical potentials
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
Missing mass spectroscopy : one nucleon pick-up
Incident particle
nucleon -hole
emitted particle
target
meson

(d,3He) : established by studies of pionic atom formation
– theory … S.Hirenzaki, H.Toki, T.Yamazaki, PRC44(91)2472, …
– experiment … K.Itahashi et al., PRC62(00)025202, …
› h-mesic nuclei formation : D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202,
H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205.

(g,p) : smaller distortion effect
– w-nucleus … Marco, Weise, PLB502(01)59
– p-atom … Hirenzaki, Oset, PLB527(02)69
› h-mesic nuclei formation : H.N., D.Jido,S.Hirenzaki, NPA761(05)92.

(p+,p) : could be possible at J-PARC ?
› secondary meson beam, p, K, …
7
h
reaction
momentum transfer : forward angle (0 degree)
J-PARC で可能になると期待されるエネルギー領域
w = mh – 100 MeV
w = mh – 50 MeV
elementary cross section
S.Prakhov et al., [Crystal Ball Collaboration]
PRC72,015203 (2005).
として見積もり
total cross section
w = mh
total
angular distribution
~ flat
Tp = 650 MeV (pp ~ 777 MeV/c)
Tp = 820 MeV (pp ~ 950 MeV/c)
8
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
12C(p+,p)11B
(p+,p) spectra : 12C target
by Green function method*
recoilless at h threshold
Tp = 820 MeV (pp = 950 MeV/c) : q = 0 deg.
h production
threshold
Chiral doublet model [C=0.0]
(t-r approx.)
Chiral doublet model [C=0.2]
Chiral unitary model
20
15
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
* Morimatsu, Yazaki NPA435(85)727
NPA483(88)493
bound region
quasi-free
10
5
pion
0
-100
-50
0
50
100
Eex – E0 [MeV]
150 -100
-50
0
50
Eex – E0 [MeV]
100
150 -100
proton
-50
0
50
100
150
Eex – E0 [MeV]
h production
threshold (s-state proton-hole)
9
150
V(r)
V(r)
doublet
unitary
target
: Green
function
method
100
50
recoilless at h threshold
0
Tp = 820 MeV (pp = 950 MeV/c)
: q = 0 deg. (Lab)
-50
w - mh = -100 MeV
-100
-150
2
4
Chiral doublet model [C=0.0]
(t-r approx.)
6
8
r [fm]
2
4
6
8
r [fm]
Chiral doublet model [C=0.2]
Chiral unitary model
20
quasi-free h
15
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
spectra :
12C
V(r) [MeV]
(p+,p)
10
shallow b.s.
deep b.s.
5
0
-100
-50
0
50
100
150 -100
-50
0
50
150Eex – E0 [MeV]
V(r)
Eex – E0 [MeV]
150 -100
doublet
100
V(r) [MeV]
* Total spectrum shape : 顕著な違い
* 束縛状態の存在
- 浅い束縛状態 : CUM
- 深い束縛状態 : CDM
* ピーク構造は見えない。
- 幅が広い
100
-50
0
50
100
150
Eex – E0 [MeV]
V(r)
unitary
50
0
-50
-100
at threshold
-150
2
4
6
r [fm]
8
2
4
6
r [fm]
8
10
Tp = 820 MeV (pp = 950 MeV/c)
80
Tp = 650 MeV (pp = 777 MeV/c)
Chiral doublet model [C=0.2]
recoilless position
60
Chiral doublet model [C=0.2]
20
Chiral unitary model
40
15
20
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
(p+,p) spectra : 12C target : 入射 p+ エネルギー依存性
10
0
20
Chiral unitary model
5
60
15
0
10
-100
-50
0 40 50
Eex – E0 [MeV]
5
20
0
0
-100
100
150 -100
-50
0
50
100
150
Eex – E0 [MeV]
-50
0
50
100
Eex – E0 [MeV]
150
11
momentum transfer
500
400
Chrien et al., PRL60(1988)2595
15 deg.
[MeV]

300
» pp = 800 MeV/c
200
» proton angle : 15 deg. (Lab.)
» search for predicted narrow bound state ( ex. G ~ 10 MeV)
100
 negative results (bound state was not observed)
0
0 deg.
0.4
0.6
0.8
1
1.2
1.4
pp [GeV/c]
hole
Chrien at al., PRL60(88)2595, Fig.1
h
Li
C
Liu, Haider, PRC34(86)1845, Fig.7
b.s. + quasi-free
O
quasi free h
bound state
Al
(B.E, G/2) = (2.65, 4.77) [MeV]
12
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
(p+,p) spectra : past experiment in 1988
momentum transfer
500
400
quasi-free の取り扱い
[Also commented in Kohno et al, NPA519(90)755]
» virtual h absorption (due to Imaginary potential)
 The peak structure is hidden in quasi-free contribution

Difference of nucleon separation energy in 16O
»
1p1/2  1p3/2  1s1/2
~ 6 MeV
~ 23 MeV
[MeV]

15 deg.
300
200
100
0 deg.
0
0.4
0.6
0.8
1
1.2
1.4
pp [GeV/c]
Liu, Haider, PRC34(86)1845
green function method (V0,W0) = -(34,15)
-(34,23) [MeV]
Liu, Haider, PRC34(86)1845, Fig.7
50
bound region
40
b.s. + quasi-free
30
20
quasi free h
bound state
10
0
100
80
60
40
20
0
Eex – E0 [MeV]
-20
-40
-60
(B.E, G/2) = (2.65, 4.77) [MeV]
13
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
(p+,p) spectra : past experiment in 1988

Chrien et al., PRL60(1988)2595
» pp = 800 MeV/c
» proton angle : 15 deg. (Lab.)
Chrien at al., PRL60(88)2595, Fig.1
chiral doublet model
chiral unitary model
80
Li
0 deg.
bound region
0 deg.
bound region
15 deg.
bound region
15 deg.
bound region
40
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
(p+,p) spectra : comparison of our calc. with the exp. data
C
0
30
O
20
Al
10
0
-100 100-50
500
050 -50100 -100 -100
EE
– –EE
[MeV]
[MeV]
exex
00
100
-50
50
0
50
0
-50
100
Eex
ex – E00 [MeV]
14
-100
Chiral doublet model
Chiral unitary model

Chrien et al., PRL60(1988)2595
• どちらの模型も実験データとは矛盾しない。
[Also commented in Kohno et al, NPA519(90)755]
» pp = 800 MeV/c
» proton angle : 15 deg. (Lab.)
Chrien at al., PRL60(88)2595, Fig.1
proton angle ~ 0 degree
chiral doublet model
chiral unitary model
80
Li
0 deg.
bound region
0 deg.
bound region
15 deg.
bound region
15 deg.
bound region
40
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
(p+,p) spectra : comparison of our calc. with the exp. data
C
0
30
O
20
Al
10
0
100
50
0
-50
Eex – E0 [MeV]
-100
100
50
0
-50
Eex – E0 [MeV]
-100
16
「ストレンジネスとエキゾティクス・理論の課題」 3 Mar. 2007 @ 鳥羽
Summary

formation of h-mesic nuclei
» In-medium properties of N*(1535) resonance
› Chiral doublet model : deep bound state
– pocket-like potential, level crossing of h and N*-hole modes
› Chiral unitary model : shallow bound state

(p+,p) reaction
» incident pion kinetic energy
› Tp = 820 MeV (pp ~ 950 MeV/c) : recoilless at h threshold
› Tp = 650 MeV (pp ~ 777 MeV/c) : recoilless at h threshold – 50 MeV
» possible at J-PARC ?

(p+,p) 実験結果(Chrien at al., 1988)の再考
» 15°proton angle は妥当か?
› It is hard to observe the peak structures of the bound states, even if it exist.
» We should discuss the whole shape itself in the case that the imaginary part
might be large like h-mesic nuclei

The proton angle ~ 0 deg.
17