1. 1  - mesic nuclei and baryon chiral symmetry in medium Hideko Nagahiro (Nara Women’s Univ.) collaborators: Daisuke Jido (Tech. Univ. Muenchen) Satoru Hirenzaki (Nara Women’s Univ.) D.Jido,H.N.,S.Hirenzaki, PRC66(2002)045202 H.N.,D.Jido,S.Hirenzaki, PRC68(2003)035205 H.N.,D.Jido,S.Hirenzaki, in preparation (( ,p)) H.N.,S.Hirenzaki, hep-ph/0412072 (  ’ ) › Introduction › Formation of  -mesic nuclei » Optical Potential ~ N*(1535) dominance model ~ » Chiral Doublet model » Chiral Unitary model › Numerical Results of (d, 3 He) & (  p) reactions » 12 C target » 40 Ca target › Summary ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ›  ’ (958)-nucleus system › our next interest International Workshop on "Chiral Restoration in Nuclear Medium" CHIRAL05 16 Feb. 2005 @ RIKEN +  ’ (958)

2. CHIRAL05@RIKEN 2 Introduction :  -Nucleus system  meson  -N system Strong Coupling to N*(1535), » » » » works for eta-mesic nuclei * Liu, Haider, PRC34(1986)1845 * Chiang, Oset, and Liu, PRC44(1988)738 * Chrien et al., PRL60(1988)2595 » * Hayano, Hirenzaki, Gilltzer, Eur.Phys.J.A6(1999)99 * D. Jido, H.Nagahiro, S.Hirenzaki PRC66(2002)045202 * Exp. at GSI (2005?) (Yamazaki, Hayano group) » (d, 3 He) properties of eta meson system -No baryon contamination -Large coupling constant -no suppression at threshold (s-wave coupling) eta-Nucleus system Doorway to N*(1535)  mesic nuclei as a probe of the in-medium modification of N*(1535)

3. CHIRAL05@RIKEN 3 Chiral models : two different predictions for N* Chiral doublet model DeTar, Kunihiro, PRD39 (89)2805 Jido, Oka, Hosaka, Nemoto, PTP106(01)873 Jido, Hatsuda, Kunirhiro, NPA671(00)471 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 a resonance generated dynamically * the N* is introduced as a resonance generated dynamically from meson-baryon scattering.

4. CHIRAL05@RIKEN 4  -Nucleus Interaction  -Nucleus Interaction (Chiang, Oset, Liu PRC44(1991)738) (D.Jido, H.N., S.Hirenzaki, PRC66(2002)045202) ~ N* dominance model ~ potential nature optical potential In free space attractive to reproduce the partial width at tree level. N & N* properties in medium evaluated by two kinds of Chiral Models General feature medium effect Repulsive ?? m N & m N* change ?? ?

5. CHIRAL05@RIKEN 5 -Nucleus optical potential -Nucleus optical potential associated with mass reduction

6. CHIRAL05@RIKEN 6 Chiral unitary model Inoue, Oset, NPA710(02) 354, fig.6 Energy dependence of self-energy

7. CHIRAL05@RIKEN 7 What should we observe ?

8. CHIRAL05@RIKEN 8 Missing mass spectroscopy

9. CHIRAL05@RIKEN 9 Distortion factor distortion Factor reduction of the flux due to absorption [Eikonal approx.] These two reactions have different sensitivity to the system.

10. CHIRAL05@RIKEN 10 Missing mass spectroscopy to calculate the formation cross section of the quasi-stable eta-nucleus system

11. CHIRAL05@RIKEN 11 Spectra of 12 C target (d, 3 He) Bound state It seems impossible to observe b.s. from the spectrum. These two models provide the significantly different spectra with 12 C target case. binding region quasi-free region

12. CHIRAL05@RIKEN 12 Spectra of 12 C target ( ,p) Bound state enhanced It seems impossible to observe b.s. as a peak from the spectrum. We can see the difference between two models more clearly.

13. CHIRAL05@RIKEN 13 Spectra of 40 Ca target heavy target case heavy target case Chiral Doublet model Chiral Doublet model C=0.0 vs. C=0.2 C=0.0 vs. C=0.2 Whole spectra change reflecting the reduction of mass difference of N & N*.

14. CHIRAL05@RIKEN 14 Summary of  -mesic nuclei  mesic nuclei as a probe of N*(1535) in nuclear medium › N* properties in-medium » Chiral Doublet Model – N* mass reduction … repulsive  -nucleus potential » Chiral Unitary Model – No mass shift of N* … attractive  -nucleus potential formation cross section with (d, 3 He) and ( ,p) reactions » We can deduce the new information of V opt from these experiments. » By knowing the nature of V opt, we will be able to study the in- medium properties of N*. » ( ,p) : sensitive to the potential nature – But large background ? S/N ~ 1/20 ?? [ref. K.Baba et al., NPA415(84)462] Future view » (d, 3 He) experiment at GSI (2005?)

15. CHIRAL05@RIKEN 15 our next interest :  ’(958)-Nucleus system  ’ (958) meson … close connections with U A (1) anomaly  ’ (958) meson … close connections with U A (1) anomaly › some theoretical works » the effects of the U A (1) anomaly on  ’ properties » at finite temperature/density – T. Kunihiro, PLB219(89)363 – R.D.Pisarski, R.Wilczek, PRD29(84)338 – K.Fukushima, K.Onishi, K.Ohta, PRC63(01)045203 – P. Costa et al.,PLB560(03)171, hep-ph/0408177 » the possible character changes of  ’ a poor experimental information on the U A (1) anomaly at finite density proposal for the formation reaction of the  ’ -mesic nuclei › discuss the possibility of the  ’ -nucleus bound states (Previous estimation of b.s. by K.Tushima, NPA670(00)198c : But,  is fixed to be 0) › the  ’ properties, especially mass shift, at finite density H.N.,S.Hirenzaki, hep-ph/0412072

16. CHIRAL05@RIKEN 16  ’-Nucleus optical potential Real Part V 0 › evaluated by possible  ’ mass shift at  0 Imaginary Part W 0 › estimated from nucl-th/0303044 (A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth) analysis of  p  ’ p data fix a coupling g NN*(1535) ’’g (only one resonance included) T. Kunihiro, Phys.Lett.B219(89)363 K. Fukushima et al., Phys.Rev.C63(01)045203 P. Costa et al., Phys. Lett. B560(03)171 ~ a rough estimation › in analogy with  -hole model for the  -nucleus system

17. CHIRAL05@RIKEN 17 Numerical Results : 12 C( ,p) 11 B  ’ V 0 = -100 MeV W 0 = -5 MeV V 0 = 0 W 0 = -5 MeV V 0 = -100 MeV W 0 = -20 MeV V 0 = 0 W 0 = -20 MeV

18. CHIRAL05@RIKEN 18 Summary of  ’(958) -mesic nuclei  ’ (958) meson formation in nuclei » Information on U A (1) anomaly in nuclear medium the ( ,p) reaction with the 12 C target reasonable magnitude of the cross section » We can obtain the information on the optical potential Future › What the peak position means? » more microscopic estimation for the  ’ -nucleus optical potential – repulsive?? attractive?? – the relation with the  meson ? – effect of U A (1) anomaly?

19. Effective quark interaction (KMT) Phys. Rep. 247 (94) 221 by T. Hatsuda, T. Kunihiro Case I : const Case II T 0 =100 MeV u ds u d s

20. Phys. Lett B560 (2003) 171 by P. Costa, M. C. Ruivo, Yu. L. Kalinovsky hep-ph/0408177 by P.Costa, M. C. Ruivo, C. A. de Sousa, Yu. L. Kalinovsky PRC63 (2001) 045203 by K. Fukushima, K. Ohnishi, K. Ohta

21. CHIRAL05@RIKEN 21 Momentum transfer ( ,p) reactions (d, 3 He) reaction SPring-8 energy ’’ ’’

22. CHIRAL05@RIKEN 22 Reaction parameters :  ’ (958) mesic nuclei ( ,p) reaction @ E  = 3 GeV (around SPring-8 energy) Target 12 C Forward (  ~0 deg.) Elementary cross section Data:SAPHIR collaboration PLB444(98)555-562 Fig: Chiang, Yang, PRC68(03)045202 0.02 ~ 0.04  b/sr

23. CHIRAL05@RIKEN 23 Background in ( ,p) reactions We estimate the background roughly to be We estimate the background roughly to be 1.5 [  b/sr MeV]. 1.5 [  b/sr MeV]. S/N = 1/15 – 1/20. S/N = 1/15 – 1/20. Exact background of ( ,p) still unknown… Exact background of ( ,p) still unknown…

24. CHIRAL05@RIKEN 24 Background in 12 C(d, 3 He) reactions calculated SIGNAL ~ 1 [nb/sr MeV] calculated SIGNAL ~ 1 [nb/sr MeV] experimental BACKGROUND ~ 10 [nb/sr MeV] experimental BACKGROUND ~ 10 [nb/sr MeV] (from test experiment at GSI) (from test experiment at GSI) “real” experiment in this year ?

25. CHIRAL05@RIKEN 25 Spectra of 12 C target (d, 3 He)

26. CHIRAL05@RIKEN 26 eta binding regionquasi-free region (s-wave)  -production threshold  -production threshold For s-state contribution, the eta-production threshold is shifted 18MeV corresponding to the difference of the separation energy. 18 MeV -20 0 20 40 60 E ex -E 0 [MeV]

27. CHIRAL05@RIKEN 27 Spectra of 12 C target

28. CHIRAL05@RIKEN 28 N* width (in Mirror assignment) (Effective coupling of  NN* through  meson) The terms change according as the restoration of Chiral sym.small

29. CHIRAL05@RIKEN 29 Chiral Doublet : Mirror vs. Naive

30. CHIRAL05@RIKEN 30 Peaks become to be sharp if imaginary potential becomes small. Chiral Doublet Model (C=0.2) Chiral Unitary Model

31. CHIRAL05@RIKEN 31 Momentum transfer