h - mesic nuclei and baryon chiral symmetry in medium

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

2. system -No baryon contamination -Large coupling constant -no suppression at threshold (s-wave coupling) Doorway to N*(1535) eta-Nucleus system h mesic nuclei as a probe of the in-medium modification of N*(1535) Introduction : h-Nucleus system works for eta-mesic nuclei • Strong Coupling to N*(1535), * Liu, Haider, PRC34(1986)1845 * Chiang, Oset, and Liu, PRC44(1988)738 * Chrien et al., PRL60(1988)2595 • (d,3He) * 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) properties of eta meson h meson h-N system

3. Chiral unitary model Chiral doublet 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 DeTar, Kunihiro, PRD39 (89)2805 Jido, Oka, Hosaka, Nemoto, PTP106(01)873 Jido, Hatsuda, Kunirhiro, NPA671(00)471 A coupled channel Bethe-Salpeter eq. Lagrangian Physical fields N* : chiral partner of nucleon Mass difference * the N* is introduced as a resonancegenerated dynamicallyfrom meson-baryon scattering. * No mass shift of N* is expectedin the nuclear medium. * C~0.2 :the strength of the Chiral restoration at the nuclear saturation density * reduction of mass difference * In this study, we directly take the eta-self-energy in the ref.NPA710(02)354 Chiral models : two different predictions for N*

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

5. associated with mass reduction -Nucleus optical potential

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

7. What should we observe ?

8. Missing mass spectroscopy

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

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

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

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

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

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

15. our next interest : h’(958)-Nucleus system H.N.,S.Hirenzaki, hep-ph/0412072 • h’(958) meson …close connections with UA(1) anomaly • some theoretical works • the effects of the UA(1) anomaly on h’ 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 possiblecharacter changes of h’ • a poor experimental information on the UA(1) anomalyatfinite density • proposal for the formation reaction of theh’-mesic nuclei • discuss the possibility of the h’-nucleus bound states (Previous estimation of b.s. by K.Tushima, NPA670(00)198c : But, G is fixed to be 0) • the h’ properties, especially mass shift, at finite density

16. h’ N g N*(1535) h’-Nucleus optical potential ~ a rough estimation • Real Part V0 • evaluated by possible h’ mass shift at r0 • Imaginary Part W0 • estimated from nucl-th/0303044 (A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth)analysis of gp h’p data 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 (only one resonance included) fix a coupling g • in analogy with D-hole model for the p-nucleus system

17. V0 = 0 W0 = -20 MeV V0 = -100 MeV W0 = -20 MeV Numerical Results : 12C(g,p)11Bh’ V0 = 0 W0 = -5 MeV V0 = -100 MeV W0 = -5 MeV

18. Summary of h’(958)-mesic nuclei • h’(958) meson formation in nuclei • Information on UA(1) anomaly in nuclear medium • the (g,p) reaction with the 12C 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 h’-nucleus optical potential • repulsive?? attractive?? • the relation with the h meson ? • effect of UA(1) anomaly?

19. d s u Effective quark interaction (KMT) u s d Phys. Rep. 247 (94) 221 by T. Hatsuda, T. Kunihiro Case II Case I : const T0=100 MeV

20. PRC63 (2001) 045203 by K. Fukushima, K. Ohnishi, K. Ohta 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

21. Momentum transfer (g,p) reactions (d,3He) reaction h’ h’ SPring-8 energy

22. 0.02 ~ 0.04 mb/sr Reaction parameters : h’(958) mesic nuclei • (g,p) reaction @ Eg = 3 GeV (around SPring-8 energy) • Target 12C • Forward (q~0 deg.) • Elementary cross section Data:SAPHIR collaboration PLB444(98)555-562 Fig: Chiang, Yang, PRC68(03)045202

23. Background in (g,p) reactions • We estimate the background roughly to be • 1.5 [mb/sr MeV]. • S/N = 1/15 – 1/20 . • Exact background of (g,p) still unknown…

24. Background in 12C(d,3He) reactions • calculatedSIGNAL ~ 1 [nb/sr MeV] • experimentalBACKGROUND ~ 10 [nb/sr MeV] (from test experiment at GSI) “real” experiment in this year ?

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

26. h-production threshold (s-wave) h-production threshold 18 MeV eta binding region quasi-free region 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]

27. Spectra of 12C target

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

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