中間子ー原子核束縛系の物理 - A brief summary of current interests - 奈良女子大学比連崎 悟

Pionic Atom, Kaonic Atoms( 代表的・歴史的なも の ) Meson ( Yukawa Particle ) Large !!Small !! Electromagnetic Strong B.E. Radius Interactions A(Z,N) -- m  ~ 300 m e Strong Interacting Particle System!

Observation of Pionic Atom = Traditional Way : Slow Pion Trap = X-ray Detector X-ray Slow Nucleus Absorption to Nucleus by Strong Interaction

4 He 16 O 40 Ca

In-Medium Dispersion Relation Pion – Nucleus Optical Potential with Ericson-Ericson, Ann. Phys. 36 (66) 323 Seki-Masutani, Phys. Rev. C27(83)2799 Medium Effects Nucleus Densities Potential Parameters

Observed by X-ray Spectroscopy Toki, Hirenzaki, Yamazaki, Hayano (1989)

Toki, Hirenzaki, Yamazaki, Hayano (1989)

Energy and Width Information on pion-nucleus interactions Do you believe this ? の限界

Missing mass spectroscopy emitted particle Incident particle target meson -hole proton

Distortion effect distortion Factor reduction of the flux due to absorption [Eikonal approx.] These two reactions have different sensitivities to systems.

Missing mass spectroscopy Incident particle target meson -hole proton emitted particle

Deeply bound  - states in the 208 Pb(d,3He) reaction PRC62(00) K. Itahashi et al. Hirenzaki, Toki, Yamazaki PRC(1991)

PRL88(02) Deeply bound 1s and 2p Pionic States in the 206 Pb(d, 3 He) reaction Hirenzaki, Toki PRC55(97)2791

Pionic 1s states of Sn nuclei Umemoto, Hirenzaki, Kume, Toki PRC62(00) K. Suzuki et al. Phys. Rev. Lett. 92(2004) GOR relation + Tomozawa-Weinberg Relation

 New method – Observation of Meson-Nucleus states ( 数年間の試行錯誤があった )  Information on at finite  ~  0  Eigen state observation Invariant Mass Method  Quantum number fixed Selective information Umemoto et al., PRC62 (2000)

Further Progresses Exotic few body systems. (core, fermion, boson) 1. Exotic Many Body Physics 2. Hadron Physics at finite density Fundamental theory (QCD) Effective theory Hadron property at finite  有限系 無限系 観測量計算、 データ

Higgs mechanism U A (1) Anomaly Effect Meson Mass Spectrum  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)  P. Costa et al.,PLB560(03)171, hep-ph/ etc… : J p = 0 - Spontaneous Chiral Symmetry Breaking

 Junko Yamagata  Junko Yamagata (Nara Women ’ s Univ.) H. Nagahiro (RCNP, Osaka Univ.) S. Hirenzaki (Nara Women ’ s Univ.) In-Flight (K -,p) Reactions for the formation of Kaon-Nucleus bound systems * J. Yamagata, H. Nagahiro, Y. Okumura, S. Hirenzaki, Prog. Theor. Phys. 114 (2005) 301; Errata 114 (2005) 905 arXive:nucl-th/ * J. Yamagata, H. Nagahiro, S. Hirenzaki, arXive:nucl-th/

 Kaonic Nuclei K-Nucleus bound system  strong interaction 100 MeV Binding Energy : 10 – 100 MeV Formation Reaction Formation Reaction  (In-flight K,N) reaction – Kishimoto Group (Exp.)  (Stopped K,N) reaction – Iwasaki, Suzuki Group (Exp.) (K – light nuclei) system structure – Akaishi, Yamazaki, Dote (K – light nuclei) system structure – Akaishi, Yamazaki, Dote (Theor.) (Theor.) Critical analysis – E. Oset, H. Toki (Theor.) Introduction for kaon K Very deep!! We theoretically study the formation spectra of In-flight (K -,p) reactions. quasi-stable K-Nuclear State Ultra high density state Really Exist or not ? Cf. Kaonic Atoms

Introduction for kaon Kaonic Nuclei case large widths Green Function Method Cf. Effective Number Approach (previous work) Good for small width cases J. Yamagata et. al., Prog. Theor. Phys. 114(05)301  Our Study Structure of Kaonic Atoms and Kaonic Nuclei (two different K-Nucleus optical potentials) Formation spectra of In-flight (K -,p) reactions Green Function Method The energy dependence of the optical potential The Quasi-Free Kaon production processes

Formulation -- Structure  Klein-Gordon Equation Chiral Unitary Model Phenomenological Model [Batty, Friedman, Gal, Phys. Rep. 287(97)385] [A. Ramos, E. Oset, NPA671(00)481] [Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]

Phase Space Factor (for the phenomenological potential) threshold ・・・ Phase Space Factor

Formulation -- Structure  Klein-Gordon Equation Chiral Unitary Model Phenomenological Model [Batty, Friedman, Gal, Phys. Rep. 287(97)385] [A. Ramos, E. Oset, NPA671(00)481] [Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]

Energy level (examples by the potential at E=0) Atomic State Similar Nuclear State Different

Formulation – Reaction  Green Function Method O. Morimatsu, K. Yazaki NPA435 (85)727 O. Morimatsu, K. Yazaki NPA483 (88)493 : Green function for K interacting with the nucleus : Elementary cross section (Exp. data) Previous work: Effective Number Approach (J. Yamagata et. al., PTP114(05)301) 12 C is interesting !

B.E. = 150 MeV B.E. = 100 MeV B.E. = 50 MeV B.E. = 0 MeV Kaon Binding Energy Momentum Transfer – =0°

Green vs. Effective (Energy Spectrum) Nuclear States Phenomenological potential At E=0 T K = 600 MeV Target : 12 C Quasi-free region Bound region

Green vs. Effective (Energy Spectrum) Nuclear States Phenomenological potential At E=0 T K = 600 MeV Target : 12 C Bound region

Energy Spectrum ( E=0 potential ) 12 C (K -,p) reactions – T K = 600 MeV Green Effective Number Atomic State 1s 2p 2s Atomic State 1s 2p 2s

Energy Spectrum ( Energy dependence ) 12 C (K -,p) reactions – T K = 600 MeV Smooth Structure?

Effect of Branching Ratio of Decay Channel  Phenomenological Potential 80%20% Phase Space Factor 80% 20% 90%10%

Energy Spectrum   ： Phenomenological Model (Energy Dependent) 80% 90% 20% 10%

Energy Spectrum   ： Energy Dependent PhenomenologyChiral Unitary Green Effective Number Green Effective Number J. Yamagata, H. Nagahiro, S. Hirenzaki, arXive:nucl-th/

Comparison with Kishimoto group ’ s data Energy Spectrum Energy dependent Green Effective Number Chiral Unitary Phenomenology Please ask Kishimoto san group.

Nuclear State : Just a tiny bump. *Exist!! *Exist!! But, it is very difficult to see. (large decay width) *Need more accurate experimental data. Summary for kaon ( not simple peaks ) Atomic State : *Exist as quasi-stable state.  We studied the formation spectra of In-flight (K -,p) reactions.  Target : 12 C, 16 O ; T K = 600 MeV  Green Function Method (cf. Effective number approach) Interesting spectrum shape. No peak structure is expected in spectra for all cases considered here.  Nuclear structure change was not considered.

Formation of  -mesic nuclei Formation of  -mesic nuclei › Optical potential ~ N*(1535) dominance model ~ » Chiral Doublet model » Chiral Unitary model › Numerical Results of (d, 3 He) & ( ,p) reactions Formation of  ’(958)-mesic nuclei Formation of  ’(958)-mesic nuclei › NJL model » U A (1) anomaly in finite density › Numerical Results of ( ,p) reactions Hideko Ngahiro, D.Jido and S.Hirenzaki, NPA761(05)92 Hideko Nagahiro, D.Jido and S.Hirenzaki, PRC68(03) D.Jido, Hideko Nagahiro and S.Hirenzaki, PRC66(02) Hideko Nagahiro, S. Hirenzaki, PRL94(05) Hideko Nagahiro, M.Takizawa and S. Hirenzaki, in preparation.

 ’ (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  Y. Kohyama, K.Kubodera and M.Takizawa, PLB208(1988)165  K.Fukushima, K.Onishi, K.Ohta, PRC63(01)  P. Costa et al.,PLB560(03)171, hep-ph/ etc… » 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 › U A (1) anomaly in medium from the viewpoint of “mesic nuclei” › the  ’ properties, especially mass shift, at finite density Hideko Nagahiro, S. H, Phys.Rev.Lett.94, (2005) Hideko Nagahiro, M.Takizawa and S. H, in preparation.

Model for  and  ’ meson in medium Nambu-Jona-Lasinio model with the KMT interaction › unified treatment of the  and  ’ meson d u s u d s One can reproduce the heavy  ’ mass Kunihiro, Hatsuda, PLB206(88)385, Fig.3 Anomaly effect in vacuum explicit breaking the U A (1) sym. Kobayashi, Maskawa Prog.Theor.Phys.44, 1422 (70) G. ’t Hooft, Phys.Rev.D14,3432 (76)

Masses in finite  with NJL ==…… quark-anti-quark scattering ++ Bethe-Salpeter equation == ++ condensate in finite  Fermi distribution function = + + Gap equations for quarks meson properties (mass) mesonmeson T. Kunihiro, PLB219(89)363, P. Costa et al.,PLB560(03)171. etc… flavor mixing terms partial restoration in medium [MeV] SU(2) sym. matter SU(3)

SU(2) symmetric matter we consider the SU(2) sym. matter as the sym. nuclear matter. ’’’’    m  ’ ~ -150  0  m  ’ ~ -150  0  m  ~ +20  0  m  ~ +20  0  and  ’ mass  0 P. Rehberg, et al., PRC53(96)410. parameters (in vacuum) parameters (in vacuum)  = [MeV] g S  2 = 3.67 g D  5 = m u,d = 5.5 [MeV] m s = [MeV] M u,d = [MeV] M s = [MeV] 〈 uu 〉 1/3 = [MeV] 〈 ss 〉 1/3 = [MeV] m  ’ = 958 [MeV] m  = 514 [MeV] m  = 135 [MeV] We can see the large medium effect even at normal nuclear density. anomaly term effect

anomaly effect in the finite density We simulate an extreme case. ’’’’   g D : constant  m  ’ ~ -150  0  m  ’ ~ -150  0  m  ~ +20  0  m  ~ +20  0 ’’’’    m  ’ ~ -250  0  m  ’ ~ -250  0  m  ~ -100  0  m  ~ -100  0 g D = g D (  ) ?? g D = g D (  =0) exp(-(  /  0 ) 2 )

 - &  ’ -Nucleus optical potential Real Part V 0 › evaluated by possible  ’ mass shift at  0 ~ potential description g D : constant V  ’ (r) V  (r)  : repulsive  ’ : attractive g D = g D (  =0) e -(  /  0) 2 V  ’ (r) V  (r)  : attractive  ’ : attractive

 - &  ’ -Nucleus optical potential Real Part V 0 › evaluated by possible  ’ mass shift at  0 Imaginary Part W 0 for  ’ › estimated from AIP Conf.Proc.717 (04)837(A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth) analysis of  p  ’ p data fix a coupling g NN*(1535) ’’g (only one resonance included) › in analogy with  -hole model for the  -nucleus system ’ ’ ~ phenomenological estimation Imaginary Part for  W 0 = - 40 MeV D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202, H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205, ~ potential description

( ,p) reaction : Parameters ( ,p) E  =2.7 GeV target … 12 C Forward (  ~ 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 SPring-8, 2005 › two different predictions for optical potentials » 【 attractive 】 V= - ( i)  /  0 MeV [Klingl, Waas, Weise NPA650(99)299] » 【 repulsive 】 V= - ( i)  /  0 MeV [Lutz, Wolf, Friman NPA706(02)431] › elementary cross section ~ 150 nb/sr » event # [  ] ~ [  ] ~ [  ’ ] test experiment at SPring-8 [N.Muramatsu, private communication]  -mesic nuclei › elementary cross section ~ 150 nb/sr Data:SAPHIR collaboration, PLB444(98) Chiang, Yang, PRC68(03)045202

Numerical results : 12 C( ,p) 11 B , ,  ’ quasi-freequasi-free  ’’’’ We only observe the quasi-free  ’ peak no medium effect

Numerical results : 12 C( ,p) 11 B , ,  ’ quasi-freequasi-free  ’’’’ V 0 = - ( i) [MeV] (NPA706(02)431) quasi-free no medium effect 

quasi-freequasi-free  ’’’’ Numerical results : 12 C( ,p) 11 B , ,  ’  no medium effect quasi-free V 0 = - (156+29i) [MeV] (NPA650(99)299)

Numerical results : 12 C( ,p) 11 B , ,  ’ quasi-freequasi-free  ’’’’quasi-free V 0 = - (156+29i) [MeV] (NPA650(99)299) g D = /  5

Numerical results : 12 C( ,p) 11 B , ,  ’ quasi-freequasi-free  ’’’’quasi-free V 0 = - (156+29i) [MeV] (NPA650(99)299) mass reduction due to the medium effect through anomaly term g D = /  5

quasi-freequasi-free  ’’’’ Numerical results : 12 C( ,p) 11 B , ,  ’ g D = /  5 quasi-free V 0 = - ( i) [MeV] (NPA706(02)431) Quasi-free  overlap with bound  ’ 

Numerical results : 12 C( ,p) 11 B , ,  ’ quasi-free quasi-free  ’’’’  and  ’ mass reductions quasi-free V 0 = - ( i) [MeV] (NPA706(02)431) density dependent g D 

Numerical results : 12 C( ,p) 11 B , ,  ’ quasi-free V 0 = - (156+29i) [MeV] (NPA650(99)299) density dependent g D quasi-free quasi-free  ’’’’

Summary for  and  ’ : mesic nuclei … hadron properties in finite   -mesic nuclei by (d, 3 He) and ( ,p) reactions » Chiral doublet model » Chiral unitary model  Different pictures for the N*(1535) in medium  ’ -mesic nuclei by ( ,p) reactions » NJL model  U A (1) anomaly in finite density Future works ›  -mesic nuclei » (d, 3 He) experiment for  -mesic nuclei GSI ›  ’ -mesic nuclei » ( ,p) experiment for  -mesic SPring-8  Coming soon ? » What is the density dependence of g D ?? » Other treatment ? » relation with other models for  &  ’  chiral doublet model & chiral unitary approach for the  -mesic nuclei

Summary  Mesic Atoms and Mesic Nuclei  A finite density Laboratory  観測量の物理的意味をキッチリ抑えたい 微視的な理解から実際のハドロン反応の計算まで、統 一的にやりたい   by (d, 3 He) Hayano (Tokyo   ( ,  ’) by ( ,p) Muramatsu (LEPS  k by In-Flight (K,p) Kishimoto (Osaka group) +Many Others  いろいろな事が、まだまだ不十分でわからない 関連する実験