1. η-mesic nucleus by d + d reaction ー how to deduce η-Nucleus int. ー
東北大ELPH拠点研究会、2016年12月1日（木）、2日（金）
「マルチフレーバーで探るエキゾチックハドロンとハドロン多体系の物理」
12月2日（金） 11: [Session 5] eta and etaprime in medium (II)
η-mesic nucleus by d + d reaction ー how to deduce η-Nucleus int. ー
Satoru Hirenzaki
Nara Women’s University
Collaborate with
Natsumi Ikeno (Tottori University)
Hideko Nagahiro (Nara Women’s University)
Daisuke Jido (Tokyo Metropolitan Univ.)
H. Nagahiro, D. Jido, S. Hirenzaki, PRC(09)
Kolomeitsev, Jido, Nagahiro, Hirenzaki, NPA(08)
H.Nagahiro., D.Jido and S.Hirenzaki, NPA761(05)92
H.Nagahiro., D.Jido, S.Hirenzaki, PRC68(03)035205
D.Jido, H.Nagahiro. and S.Hirenzaki, PRC66(02)045202

2. Introduction of h-mesic nuclei
properties of eta meson
h meson
hNN* system
-No I=3/2 baryon contamination
-Large coupling constant
-no suppression at threshold
(s-wave coupling)
h-N system
Strong Coupling to N*(1535),
eta-Nucleus system
Doorway to N*(1535)
Motivation and our aim
h-N system … strongly couples to the N*(1535) resonance
h-mesic nuculei … doorway to in-medium N*(1535)
N*(1535) … a candidate of the chiral partner of nucleon
chiral symmetry for baryons

3. h-Nucleus Interaction: general remark
~ 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 ?? ?

4. Chiral models for N and N* and h-nucleus interaction
Chiral doublet model
DeTar, Kunihiro, PRD39 (89)2805
Jido, Nemoto, Oka, Hosaka NPA671(00)471
Jido, Oka, Hosaka, PTP106(01)873
Jido, Hatsuda, Kunihiro, PRL84(00)3252
etc
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.

5. h -Nucleus optical potential
associated with mass reduction

6. Formation ofη-4He by d + d reaction at COSY
Today’s main topics
　　　　　　　Formation ofη-4He 　　　　by d + d reaction at COSY

7. Isospin dependence  only expected at decay process

9. A Simple Theoretical Model for
(COSY Proposal)
(P.Moskal, arXiv:nucl-ex/ )
Some remarks
Momentum transfer Large
pd = GeV/c, pa = ph= 0 at threshold in C.M.
Data of d d  4He h above threshold
Simple spectral structure is expected for light systems
System consists of
2 Nucleon + 2 Nucleon  4 Nucleon + 1 meson
Exp. was performed

10. High q transfer at each propagator
A Simple Theoretical Model for
Some remarks
Transition (h-production) part h
High q transfer at each propagator
Parameterize this part. Fix by h production data

11. with h-a optical potential
A Simple Theoretical Model for
Schematic picture d h
Green function method a d
with h-a optical potential
Correspond to ‘η Production EXP.’ s
total s
s(dd4Heh) data
escape
conversion
threshold
Etot
threshold
Etot
Correspond to the ‘Decay Product Observation’

12. F(q) ( f(r): r-space representation)… Assumed to be Gaussianh a
F(q)
Scattering Amplitude
F(q) ( f(r): r-space representation)… Assumed to be Gaussian

13. A Theoretical Model for
3 parameters in this model
h-a optical potential
h production part dd  4Heh
Exp. Data of dd  4Heh
Fig. taken from
slide by S. Schadmand
R.Frascaria et al., Rhys.Rev.C50 (1994) 573,
N. Wills et al., Phys. Lett. B 406 (1997) 14,
A.Wronska et al., Eur. Phys. J. A 26, (2005).

14. (V0,W0) = (−100, −10) MeV p0 = 500 MeV/c (Ideal case) 8 7 6 5
Numerical Results
(Ideal case) 8
stot [nb] 25 20 7 15 10 5 6 5
(V0,W0) = (−100, −10) MeV
p0 = 500 MeV/c
Arbitrary unit 4 3 2 1
−20
−15
−10 −5 5 10 15
Eh − mh [MeV]

15. How to know new info. on eta-Nucleus pot. ?
Theory – 3 parameters, Absolute size of σ -- difficult.
EXP – Above threshold -- η production cross section
Below threshold – Upper limit of ‘Peak heght’ on 　　　　
　　　　　‘Smooth spectrum (background)’

16. How to know new info. on eta-Nucleus pot. ?
Theory – 3 parameters, Absolute size of σ -- difficult.
EXP – Above threshold -- η production cross section
Below threshold – Upper limit of ‘Peak heght’ on 　　　　
　　　　　‘Smooth spectrum (background)’
Procedure
Data above threshold  size of cross section
Info. on eta-Nucleus pot. from data

17. How to know new info. on eta-Nucleus pot. ?
Theory – 3 parameters, Absolute size of σ -- difficult.
EXP – Above threshold -- η production cross section
Below threshold – Upper limit of ‘Peak heght’ on 　　　　
　　　　　‘Smooth spectrum (background)’
Procedure
Data above threshold  size of cross section
Info. on eta-Nucleus pot. from data
(Implicit assumption)
Structure of spectra around eta threshold is dominated by the eta-processes.

18. Numerical Results again. --- p0 dependence
We fix p0=500MeV/c.

19. Let’s remember Total, Conversion, Escape parts.

20. Comparison: Escape part vs. η production data
　　　( This is a good case.)

21. ＊Results for various combinations of V0 and W0 paranmeters
＊Results of Total spectra

22. -40
-20 -5
Total Spectra

23. ＊Results for various combinations of V0 and W0 paranmeters
＊Results of Total spectra
＊Results of Escape parts with η Production Data

24. Scaled escape part with data

25. ＊Results for various combinations of V0 and W0 paranmeters
＊Results of Total spectra
＊Results of Escape parts with η Production Data
　　Not so sensitive to V0 and W0 values. It seems
difficult to determine V0 and W0.

26. ＊Results for various combinations of V0 and W0 paranmeters
＊Results of Total spectra
＊Results of Escape parts with η Production Data
　　Not so sensitive to V0 and W0 values. It seems
difficult to determine V0 and W0.
＊Total spectra again with two modifications
(1) Scaled by η production data
(2) Flat contributions are removed

27. Scaled Total spectra,
Flat contributions are removed.

28. ＊Results for various combinations of V0 and W0 paranmeters
＊Results of Total spectra
＊Results of Escape parts with η Production Data
　　Not so sensitive to V0 and W0 values. It seems
difficult to determine V0 and W0.
＊Total spectra again with two modifications
(1) Scaled by η production data
(2) Flat contributions are removed
＊Conversion part of the spectra with the modifications before.  Corresponding to the EXP. upper limit below threshold.

29. Scaled conversion part, Flat contributions are removed.

30. Back to the experimental upper limits

31. Back to the experimental upper limits
Our results are Inclusive for decay process
Upper limit estimated to = = 45 nb

32. Back to Numerical results
Back to the experimental upper limits
Our results are Inclusive for decay process
Upper limit estimated to = = 45 nb
Assume Isospin
n+pi0 channel × (2+1) / 1 = Inclusive、
Upperlimit = 108 nb
p+pi- channel × (2+1) / 2 = Inclusive、
Upperlimit = 13.5 nb　（Smallest limit）
Back to Numerical results

33. Important numbers here are
13.5、 45、 and 108 nb

34. Summary for d+d reaction
Formation of h mesic nucleus
d + d  (4He-h)  N + p + 3He reaction
High momentum transfer (~1GeV/c)
h production data above threshold
Simple spectra are expected
A simple model with Green’s function
Provide estimation and interpretation of data.

35. Summary for d+d reaction
Formation of h mesic nucleus
d + d  (4He-h)  N + p + 3He reaction
High momentum transfer (~1GeV/c)
h production data above threshold
Simple spectra are expected
A simple model with Green’s function
Provide estimation and interpretation of data.
Combined analysis ( data above/below threshold and theoretical model) may provide strong limitation to eta-Nucleus interaction.