# Presentation: 855901

## Hideko Nagahiro
Research Center for Nuclear Physics (RCNP), Osaka University

Makoto Takizawa
Showa Pharmaceutical University
Satoru Hirenzaki
Nara Women’s University

- Research Center for Nuclear Physics (RCNP), Osaka University
- Makoto Takizawa
- Showa Pharmaceutical University
- Satoru Hirenzaki
- Nara Women’s University

**PANIC05 **
- Particles and Nuclei International Conference
- Santa Fe, NM - October 24, 2005

- H.Nagahiro, S.Hirenzaki, Phys.Rev.Lett.94 (2005) 232503

- and UA(1) anomaly at finite density

**’(958)-mesic nuclei formation

## Introduction

- Interests of meson bound systems : _**mesic nuclei**_
- important information on in-medium hadron physics and QCD symmetries
- our previous work : **-mesic nuclei with chiral models : (d,3He), (,p) reactions
********’****(958) meson**
-  close connections with  _U__A__(1) anomaly_
- heavy **’ mass due to the existence of anomaly term
- many theoretical works
- in vacuum / at finite temperature / _at finite density_
- R. D. Pisarski, R. Wilczek, PRD29(84)338
- T. Kunihiro, T. Hatsuda, PLB206(88)385 / T. Kunihiro, PLB219(89)363
- V. Bernard, R.L.Jaffe and U.-G.Meissner, NPB308(1988)753
- Y. Kohyama, K.Kubodera and N.Takizawa, PLB208(1988)753
- K. Fukushima, K.Onishi, K.Ohta, PRC63(01)045203
- P. Costa *et al.*,PLB560(03)171, PRC70(04)025204, etc;                         etc...

- - partial restoration of chiral sym. in medium

- D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202,
- H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205,
- H.N., D.Jido,S.Hirenzaki, NPA761(05)92

## Our Motivation & present work

- a _poor experimental__ information _		           on the UA(1) anomaly effect at finite density
- proposal for the formation reaction of the **’-mesic nuclei
- _U__A__(1) anomaly effect in medium__ from the viewpoint of __“mesic nuclei”_
- the **’ properties, especially **mass shift**, at finite density
- new information on the properties of UA(1) anomaly ?
**Nambu-Jona-Lasinio model** with the **KMT interaction **
- unified treatment of the ** and **’ meson

- explicit breaking the UA(1) sym.

- Kobayashi, Maskawa Prog.Theor.Phys.44, 1422 (70)
- G. ’t Hooft, Phys.Rev.D14,3432 (76)

## Masses in finite T/ with NJL

- Masses in finite T/ with NJL

- T. Kunihiro, PLB219(89)363
- P. Costa *et al.*,PLB560(03)171
- etc...

## SU(2) symmetric matter

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

_**__ __and __**__’__ mass shifts @ ____0_

*We can see the large medium effect even *_*at normal nuclear density*_*.*

- anomaly term effect

## anomaly effect in the finite density

- We simulate an extreme case.

-  m**’ ~ -150 MeV @ 0

-  m** ~  +20 MeV @ 0

- gD = gD() ??

- gD = gD(=0) exp(-(/0)2)

## - & ’-Nucleus optical potential

- _Real Part  V__0_
- evaluated by possible _**__’__ mass shift_ at **0

- ~ potential description

## - & ’-Nucleus optical potential

- _Real Part  V__0_
- evaluated by possible _**__’__ mass shift_ at **0
- _Imaginary Part W__0 __for __**__’_
- estimated from nucl-th/0303044 (A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth)analysis of p     **’p data

- ~ phenomenological estimation

- ~ potential description

## Missing mass spectroscopy

## (,p) reaction : Parameters

- (,p) reaction @ E=2.7 GeV
- target ... 12C
- Forward ( ~ 0 deg.)
- Elementary cross section for p  **’p
_****__**-mesic nuclei**_
- _m__**__ ~ 547 MeV      __ __**m**__******__** ~ 783 MeV **__    __ m__**__’__ ~ 958 MeV _
- _plan of experiment for the formation of ____-mesic nuclei @ SPring-8, 2005_
- two different predictions for optical potentials
- 【attractive】 V= - (156 + 29 i) /0 MeV  [Klingl, Waas, Weise NPA650(99)299]
- 【repulsive】 V= - ( - 42.8 + 19.5i) /0 MeV   [Lutz, Wolf, Friman NPA706(02)431]
- elementary cross section ~ 150 nb/sr
- event # [**] ~ [] ~ [**’]@ test experiment at SPring-8                                                              [N.Muramatsu, private communication]
**-mesic nuclei
- elementary cross section ~ 150 nb/sr

## Numerical results : 12C(,p)11B,,’

- Numerical results : 12C(,p)11B**,,**’

- We only observe the quasi-free **’ peak

- no medium effect

## Numerical results : 12C(,p)11B,,’

- Numerical results : 12C(,p)11B**,,**’

- V0= - (- 42.8 + 19.5i) [MeV]
- (Lutz)

- quasi-free

- no medium effect

****

## Numerical results : 12C(,p)11B,,’

- Numerical results : 12C(,p)11B**,,**’

****

- no medium effect

## Numerical results : 12C(,p)11B,,’

- Numerical results : 12C(,p)11B**,,**’

****

- gD = -12.36/5

- W0**’ = -5 MeV

## Numerical results : 12C(,p)11B,,’

- Numerical results : 12C(,p)11B**,,**’

****

- mass reduction
- due to the medium effect throughanomaly term

- gD = -12.36/5

- W0**’ = -20 MeV

****

- Numerical results : 12C(,p)11B**,,**’

- gD = -12.36/5

- quasi-free

- V0= - (- 42.8 + 19.5i) [MeV]
- (Lutz)

- Quasi-free  overlap with bound **’

## Numerical results : 12C(,p)11B,,’

- Numerical results : 12C(,p)11B**,,**’

- quasi-free

- V0= - (- 42.8 + 19.5i) [MeV]
- (Lutz)

- density dependent gD

## Numerical results : 12C(,p)11B,,’

- Numerical results : 12C(,p)11B**,,**’

****

- density dependent gD

## Summary

- UA(1) anomaly effect in finite density			through the view point of _**“mesic nuclei”**_
- possibility of observation of anomaly effects in-medium
* *** and **’ mesic nuclei with NJL model
-  response to the environment change
- (,p) reaction for the mesic nuclei formation
- Reasonably large cross sections predicted
- S/N ~ 1/10 ... N.Muramatsu, private communication
- the experiment for the formation of -mesic nuclei
-     	    @ SPring-8  Coming soon
-                	    (information on ** & **’ also expected)
- (d,3He) experiment for ** mesic nuclei formation @ GSI  Coming soon
- Future
- What is the density dependence of gD ?
- Other treatment ?
- relation with other models for ** & **’
- chiral doublet model & chiral unitary approach for the **-mesic nuclei

## simple quark matter
Mixed phase
Quark droplet (confine) ... chiral sym. restored
Quark gas ... constituent quark

- Mixed phase
- Quark droplet (confine) ... chiral sym. restored
- Quark gas ... constituent quark

## Omega potentials

- Attractive potential
- one loop approximation with an effective Lagrangian based on the SU(3) chiral symmetry incorporating vector mesons.
- Repulsive potential
- in a relativistic and unitary approach for meson-baryon amplitudes.
- Repulsive due to a subthreshold effect of the N(1520).

## pseudo-scalar meson masses with KMT term

## anomaly effect in the finite density

- We simulate extreme cases.

-  m**’ ~ -150 MeV @ 0

-  m** ~  +20 MeV @ 0

- ex.) w/o KMT term

- gD = gD(=0) exp(-(/0)2)

*no change*

- anomaly term effect

## Optical potentials : 11B

## Mu

- Mu

- Ms

## SU(2) symmetric matter

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

- baryon density

- chemical potential

- constituent quark mass
- (result of Gap eq.)

## For s-state contribution, the eta-production threshold is shifted 18MeV corresponding to the difference of the separation energy. 

- For s-state contribution, the eta-production threshold is shifted 18MeV corresponding to the difference of the separation energy.

- -20               0                  20               40               60

- Eex-E0 [MeV]

## P. Costa et al., PLB560(03)171, Fig.2

## -nucleus optical potential

**-nucleus optical potential

## Elementary Cross Section

- PRD9(1974)1917
- H.Brody, et al.

- PLB72(1977)144
- R. W. Clifft et al.

## Reaction Parameters

- (,p) reaction @ E = 2.7 GeV (around SPring-8 energy)
- Target 12C
- Forward (0 deg.
- Elementary cross section

- Data:SAPHIR collaboration
- PLB444(98)555-562

- Fig: Chiang, Yang, PRC68(03)045202

## formation of mesic-nuclei

- momentum transfer
- (,p) reaction
- missing mass spectroscopy
- small distortion effect
- nearly(?) recoilless condition

- (,p) reaction

- (d,3He) reaction

- SPring-8 energy

**’

**’

- -nucleus (Marco, Weise, PLB502(01)59)
- -atom (Hirenzaki, Oset, PLB527(02)69)
- //-nucleus (Nagahiro, Jido, Hirenzaki, NPA in press)

-  Green function method
-                [O.Morimatsu, K.Yazaki, NPA435, 727(85)
-                                                         NPA483,493(88)]
-      to calculate the formation cross section
-              of the quasi-stable **, **’-nucleus system

-  ~ E=2.7 GeV

## Distortion factor

**distortion Factor **** **reduction of the flux due to absorption

- [Eikonal approx.]