Restoration of UA1 Symmetry and Eta Meson at Finite Density

1
Restoration of UA(1) Symmetry and Eta Meson at
Finite Density

• Makoto Takizawa, Showa Pharm. Univ.
• Collaborators
• Hideko Nagahiro, RCNP, Osaka Univ.
• Satoru Hirenzaki, Nara Womens Univ.

MENU2007 11th International Conference on
Meson-Nucleon Physics and the Structure of the
Nucleon September 13, 2007, IKP,
Forschungzentrum Juelich, Germany
2
UA(1) problem
Pseudoscalar meson nonet
Vector meson nonet
3
UA(1) anomaly
Spontaneous chiral symmetry breaking in QCD
Number of the Goldstone boson is 8

• Dynamical mechanism of the U(1) symmetry breaking
  
• has not been understood yet!
• 1/Nc expansion approach
• Instanton approach

4

• Three energy scales are similar.
• 1. Dynamical chiral symmetry breaking
• 2. Strange quark mass
• 3. UA(1) anomaly
• It is important to treat these energy scales
• on an equal footing.

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Partial restoration of UA(1) symmetry at finite
density

• If dynamical origin of the UA(1) symmetry
  breaking is instanon induced quark detarminant
  interaction derived by t Hooft,
• At finite density, it is natural that UA(1)
  breaking interaction becomes weaker.

6
3 flavor Nambu-Jona-Lasinio Model
explicit breaking the UA(1) sym.
Kobayashi, Maskawa Prog.Theor.Phys.44, 1422
(70) G. t Hooft, Phys.Rev.D14,3432 (76)
For a review, T. Hatsuda and T. Kunihiro, Phys.
Rep. 407, 205 (1994).
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Pseudoscalar meson masses in NJL Model
M. Takizawa, et al., Nucl. Phys. A 507, 611 (1990)
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NJL model at finite density
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SU(2) symmetric matter
H. Nagahiro, M. Takizawa and S. Hirenzaki, Phys.
Rev. C 74, 045203 (2006)
anomaly term effect
h and h mass shifts _at_ r0
We can see the large medium effect even at normal
nuclear density.
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Problem How to observe this effects!

• Eta mass reduction --gt Strong N - eta
  attractive force
• Formation of the eta-mesic nuclei
• Formation cross section of the eta-mesic nuclei
  by (gamma, p) reaction

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?- ?-Nucleus optical potential
potential description

• Real Part V0
• evaluated by possible ?, ? mass shift at ?0
• Imaginary Part W0 for ?
• estimated from nucl-th/0303044 (A.Sibirtsev,Ch.Els
  ter, S.Krewald, J.Speth)analysis of ?p ?p
  data

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c Parameters

• (?,p) reaction _at_ E?2.7 GeV
• target 12C
• Forward (q 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 _at_ SPring-8, 2005
• predictions for optical potentials
• ?repulsive? V - ( - 42.8 19.5i) ?/ ?0 MeV
  Lutz, Wolf, Friman NPA706(02)431
• elementary cross section 150 nb/sr
• event ? ? ? _at_ test experiment at
  SPring-8
  N.Muramatsu, private
  communication
• ?-mesic nuclei
• elementary cross section 150 nb/sr

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Numerical results 12C(?,p)11B?,?,?
gD -12.36/?5
quasi-free
V0 - (- 42.8 19.5i) MeV (Lutz)
?
quasi-free
quasi-free
?
?
H. Nagahiro, M. Takizawa, S. Hirenzaki, Phys.
Rev. C 74, 045203 (2006)
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Summary

• We have a chance to observe the effective
  restoration of the UA(1) symmetry at finite
  density by formations of the ?-mesic nuclei.
• Our estimation is based on the naïve chiral quark
  modelwith the constituent quark gas. ----gt
  Further study is needed.
• Strength of the UA(1) breaking interaction gD may
  be density dependent. ----gt Further study is
  needed.
• Dr. Sumihama is now doing the analysis of LEPS
  (?,p) data. We hope we will find some evidences
  of the partial restoration of the UA(1) symmetry
  .