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) H.N.,D.Jido,S.Hirenzaki, PRC68(2003) H.N.,D.Jido,S.Hirenzaki, in preparation (( ,p)) H.N.,S.Hirenzaki, hep-ph/ (  ’ ) › 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. RIKEN +  ’ (958)

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) * 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 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  -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 -Nucleus optical potential -Nucleus optical potential associated with mass reduction

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

7 What should we observe ?

8 Missing mass spectroscopy

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

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

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 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 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 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 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) – P. Costa et al.,PLB560(03)171, hep-ph/ » 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/

16  ’-Nucleus optical potential Real Part V 0 › evaluated by possible  ’ mass shift at  0 Imaginary Part W 0 › estimated from nucl-th/ (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) P. Costa et al., Phys. Lett. B560(03)171 ~ a rough estimation › in analogy with  -hole model for the  -nucleus system

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 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?

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

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

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

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

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 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 Spectra of 12 C target (d, 3 He)

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 E ex -E 0 [MeV]

27 Spectra of 12 C target

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

29 Chiral Doublet : Mirror vs. Naive

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

31 Momentum transfer