Formation of Meson-Nucleus Bound Systems by (g,p) reactions @Japan-US Workshop on Electromagnetic Meson Production and Chiral Dynamics 9 Apr. ’05 S. Hirenzaki (Nara Women’s Univ.)

Features ( cf Invariant Mass Methods) Objects Hadron – Nucleus bound systems. Coulomb + Strong … Exotic Atoms (Deeply Bound) atom, Kaonic atom, atom … Strong … Exotic Nuleus Mesic Nucleus, Hypernuclei, … Exotic Many Body Systems. In Medium Hadron Properties. Spectroscopic Methods ( Peak structure) Quasi-Static Systems around Interests Features ( cf Invariant Mass Methods)

Basic Concepts In-Medium Dispersion Relation look carefully !! initial : Missing Mass ( Invariant Mass) Bound States look carefully !! Peaks!! initial final N Zoom In meson Medium Effects In-Medium Dispersion Relation

Formation Cross Section by ‘pick-up’ reactions, (g, N), (d,3He), (K,N), … Effective Number approach Recoilless Substitutional States formation For large widths systems; Green function Method by O. Morimatsu, K. Yazaki, NPA 435, 727 (85), NPA 483, 493 (88) :smaller distortion, background large? Experimental data or Theoretical model

Pionic 1s states of Sn nuclei Umemoto, Hirenzaki, Kume, Toki PRC62(00)024606 K. Suzuki et al. PRL (04)

There are active discussions K. Suzuki et al., Phys. Rev. Lett. 92(2004)072302 observation Kolomeitsev, Kaiser, Weise (PRL90(2003)092501) in two-loop chiral perturbatio Energy dependent of Gauge coupling of Phenomenological pieces, ( , p-wave terms) Discussion on rn (n>1) ?… (Garcia-Recio, Nieves, Oset, PLB541(2002)64) E. Friedman and A. Gal, PLB578(2004)85 G. Chanfray, M. Ericson, M. Oertel, PLB563(2003)61 ‘Chiral Restoration in nonlinear realization’ D. Jido, T. Hatsuda, T. Kunihiro, PRD63(2000)011901 U.-G. Meissner, J. Oller, A. Wirzba, … Ann. Phys. 297 (2002) 27 are important

Kinematics of (g, N) at forward angles 500 400 q [MeV/c] 300 200 100 500 1500 2000 2500 3000 p atom w mesic Nuclei S. Hirenzaki, E. Oset E. Marco, W. Weise Phys. Lett. B527 (2002) 69 Phys. Lett. B502 (2001) 59

We consider here (g,p) – (K,N) – K nucleus (K,p) – nucleus D. Jido, H. Nagahiro, S. Hirenzaki : PRC66(02)045202 H. Nagahiro, D. Jido, S. Hirenzaki : PRC68(03)035205 H. Nagahiro, S. Hirenzaki : hep-ph/0412072 H. Nagahiro, D. Jido, S. Hirenzaki : in preparation J. Yamagata, H. Nagahiro, Y. Okumura, S. Hirenzaki : nucl-th/0503039 H. Nagahiro, S. Hirenzaki, E. Oset, M.J. Vicente-Vacas : nucl-th/0408002, v2

h -Nucleus system : Introduction works for eta-mesic nuclei D. Jido and H. Nagahiro * 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,3He) properties of eta meson eta meson system -No baryon contamination -Large coupling constant -no suppression at threshold (s-wave coupling) eta-N system Strong Coupling to N*(1535), eta-Nucleus system Doorway to N*(1535)

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

Chiral models for N and 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 * the N* is introduced as a resonance generated dynamically from meson-baryon scattering.

h -Nucleus optical potential associated with mass reduction

(g,p) Spectra of 12C target Bound state @Japan_US Workshop, 9 Arp. ‘05 enhanced It seems impossible to observe b.s. as a peak from the spectrum. (g,p) We can see the difference between two models clearly.

h’(958)-Nucleus System : Introduction H. Nagahiro h’(958) meson Close relation to UA(1) anomaly heavy h’ mass due to the existence of anomaly term some theoretical works in vacuum / at finite temperature / at finite density T.Kunihiro, T.Hatsuda, PLB206(88)385 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 etc…

Models with NJL Lagrangian + KMT interaction Anomaly effect in vacuum KMT term T.Kunihiro, T.Hatsuda, PLB206(88)385, Fig.3 u d s Meson Mass u s d flavor mixing vertex  Large h and h’ mass due to anomaly

Anomaly effect @ finite T / r at finite Tempereture P. Costa, M. C. Ruivo, Yu. L.Kalinovsky PLB560(03)171, Fig.2 at finite density : const T.Kunihiro, PLB219(89)363, Figs.2, 3 : const T0=100 MeV Case I Case II

Our motivation & present work a poor experimental information on the UA(1) anomaly at finite density h’(958)-mesic Nucleus formation reaction UA(1) anomaly in medium h, h’ mass shift observation new information on the properties of UA(1) anomaly ? We consider … NJL Lagrangian + KMT term h’ spectra h and h’ in the same framework cf. chiral doublet, chiral unitary models. h and h’ mesic nuclei formation cross section

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

mass shifts of h and h’ mesons (1) Constant gD in medium P. Costa et al., PLB560(03)171, Fig.2  Dmh’ ~ -150 MeV @ r = r0 Dmh ~ +20 MeV @ r = r0 (2) Smaller gD in medium … no information …  An estimation from the fig. in T.Kunihiro, T.Hatsuda, PLB206(88)385, Fig.3  (Notice : This fig. shows the results in Vacuum.) Dmh’ ~ -150 MeV Dmh ~ -100 MeV @ r = r0

Reaction Parameters w-mesic nuclei (g,p) reaction @ Eg=2.7 GeV target … 12C Forward (q ~ 0 deg.) Elementary cross section for gp  h’p w-mesic nuclei mh ~ 547 MeV mw ~ 783 MeV mh’ ~ 958 MeV plan of experiment for the formation of w-mesic nuclei @ SPring-8, 2005 two different predictions for optical potentials 【Attractive】 V= - (156 + 29 i) r/r0 MeV [Klingl, Waas, Weise NPA650(99)299] 【Repulsive】V= - ( - 42.8 + 19.5i) r/r0 MeV [Lutz, Wolf, Friman NPA706(02)431] elementary cross section ~ 150 nb/sr event # [h] ~ [w] ~ [h’] @ test experiment at SPring-8 [N.Muramatsu, private communication] h-mesic nuclei Data:SAPHIR collaboration, PLB444(98)555-562 Chiang, Yang, PRC68(03)045202

Numerical results : 12C(g,p)11Bh,w,h’ quasi-free V0= - (150+5i) [MeV] V0= - (156+29i) [MeV] (Weise) V0 = - (100+40i) [MeV] mass  small

Numerical results : 12C(g,p)11Bh,w,h’ quasi-free h w h’ V0= - (150+20i) [MeV] V0= - (156+29i) [MeV] (Weise) V0 = - (100+40i) [MeV] mass  small

Numerical results : 12C(g,p)11Bh,w,h’ quasi-free h w h’ V0= - (150+20i) [MeV] V0= - (156+29i) [MeV] (Weise) V0 = - (-20+40i) [MeV] mass  large

Numerical results : 12C(g,p)11Bh,w,h’ quasi-free h w h’ V0= - (150+20i) [MeV] V0= - (- 42.8 + 19.5i) [MeV] (Lutz) V0 = - (-20+40i) [MeV] mass  large

Numerical results : 12C(g,p)11Bh,w,h’ quasi-free h w h’ V0= - (150+20i) [MeV] V0= - (- 42.8 + 19.5i) [MeV] (Lutz) V0 = - (100+40i) [MeV] mass  small

Summary (g,p) spectra of both h and h’ with w meson h mesic nuclei in Chiral doublet (N*(1535) dominance) Chiral Unitary h and h’ in the same framework (NJL+KMT) Reasonably large cross sections observation S/N ~ 1/10 … N.Muramatsu, private communication the experiment for the formation of w-mesic nuclei @ SPring-8 (planned) (information on h & h’ as byproducts ?) in Future What the peak position means? more microscopic treatment for h and h’-nucleus interaction

Kaonic Bound States Formation by In-flight (K-,N) reaction J. Yamagata J. Yamagata H. Nagahiro Y. Okumura S. Hirenzaki nucl-th/0503039

Energy Spectrum – 16O(In-flight K-,p) Comparison Exp. vs Calculated results 16O(In-flight K,n) PK = 930 MeV/c 16O(In-flight K-,ｐ) PK = 976 MeV/c Bound region Data by Kishimoto group. (Osaka Univ.) ? [ T.Kishimoto et al., Prog. Theor. Phys. Suppl. 149 (2003)264 ] [ Fig. taken from the seminar slide @NWU by Dr. Hayakawa ]

Q Hyper Nuclei formation H. Nagahiro, S. Hirenzaki, E. Oset, M.J. Vicente-Vacas, nucl-th/0408002, v2 Interaction of the Q+ with the nuclear medium Working Hypothesis Q+ : , belongs to SU(3) antidecuplet SU(3) symmetric Lagrangian N*(1710) also belongs to antidecuplet N*(1710) Npp decay deta fix the coupling const. D. Cabrera et al., PLB 608(2005)231 A. Hosaka et al., hep-ph/0411311 PRC in print : antidecuplet states : octet of ½+ baryons : octet of 0- mesons H. Nagahiro S. Hirenzaki E. Oset M.J. Vicente-Vacas where : a vector current for two mesons attractive interaction diagram Q+ N p K In the nuclear medium, new channels are open.

Q+ hypernuclei formation reaction Possible process Reported process in Prof. Nakano’s experiment (g, K–) Q+ g K– n Proposal at J-Lab. --- reaction (R. J. Feuerbach(spokesperson)) theoretical vertices, Q+ into MMB, in the SU(3) Lagrangian [D. Cabrera et al., PLB 608(2005)231, A. Hosaka et al., hep-ph/0411311, PRC in print.] Q+ K+ p– p K0 p0 p K0 h p K+ p0 n K+ h n K0 p+ n charged Q+ K+ p– p K0 p0 p K0 h p K+ p0 n K+ h n K0 p+ n Q+ B M (K+,p+) (p–, K–) Notice : (p-,K-) could be very small (KEK exp.)

12C target case : VQ= -60 r/r0 [MeV] free Q+ production threshold (s-state proton pick-up case) free Q+ production threshold TK=300MeV pK~620MeV/c quasi-free Q+ region clear peak separated from each other. Reasonable cross section of the order of [micro b/sr MeV] not too small

12C target case : VQ= -120 r/r0 [MeV] TK=300MeV pK~620MeV/c We can see clear peaks. quite different spectrum from V=-60 r/r0 MeV case. more bound states for V=-120 r/r0 MeV narrower peaks due to the deeper bound states we may be able to distinguish these two type potentials by the spectrum, if we can see.

12C target case : energy dependence We also calculate TK=500MeV(pK=863MeV/c) case. momentum transfer q doesn’t change drastically.

Summary on Q+ hypernuclei Summary on K Narrow K-Nuclear state, Ultra high density matter, Really exists ?? In flight (K,p) reaction theoretical results Kishimoto exp. Need systematic comparison of theoretical results and exp. data Summary on Q+ hypernuclei Q+ hypernuclei formation by (K+,p+) reaction New frontier of S=+1 hypernuclei ? (or just a dream) Many Unknowns … Let’s try !