Exotic Atoms and Exotic 05,RIKEN 16 Feb. ’05 S. Hirenzaki (Nara Women’s Univ.)

@Chiral05,RIKEN, 16 Feb. ‘05  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 Objects Features ( cf Invariant Mass Methods) Interests

@Chiral05,RIKEN, 16 Feb. ‘05 Many Interesting Systems  …  …, Interior state  … in medium  … anomaly  …  … Penta - Hypernuclei K. Itahashi ‘s talk. J. Yamagata, H. Nagahiro, H. Nagahiro ‘s talk, R. S. Hayano ‘s talk H. Nagahiro ‘ s talk R. S. Hayano ‘ s talk, N. Muramatsu ‘ s talk H. Nagahiro, T. Hatsuda, T. Kunihiro. H. Nagahiro, D. Jido. Y. Okumura. M.J. Vicente Vacas ‘s talk H. Nagahiro, E. Oset, M.J. Vicente Vacas

@Chiral05,RIKEN, 16 Feb. ‘05 Basic Concepts N initial final look carefully !! In-Medium Dispersion Relation Zoom In meson Medium Effects Peaks!! : Missing Mass ( Invariant Mass)

@Chiral05,RIKEN, 16 Feb. ‘05  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? Formation Cross Section by ‘pick-up’ reactions, (d, 3 He), ( , N), etc. Experimental data or Theoretical model Experimental data or Theoretical model

@Chiral05,RIKEN, 16 Feb. ‘05 Pionic 1s states of Sn nuclei K. Suzuki et al. PRL (04) Umemoto, Hirenzaki, Kume, Toki PRC62(00)024606

@Chiral05,RIKEN, 16 Feb. ‘05 K. Suzukiet al  K. Suzuki et al., Phys. Rev. Lett. 92(2004) observation Kolomeitsev, Kaiser, Weise  Kolomeitsev, Kaiser, Weise (PRL90(2003)092501) in two-loop chiral perturbatio Energy dependent of Gauge coupling of Phenomenological pieces, (, p-wave terms) Garcia-Recio, Nieves, Oset  Discussion on rn (n>1) ? … (Garcia-Recio, Nieves, Oset) E. Friedman and A. Gal  E. Friedman and A. Gal G. Chanfray, M. Ericson, M. Oertel  G. Chanfray, M. Ericson, M. Oertel D. Jido, T. Hatsuda, T. Kunihiro  ‘Chiral Restoration in nonlinear realization’ D. Jido, T. Hatsuda, T. Kunihiro, PRD63(2000) U.-G. Meissner, J. Oller, A. Wirzba  U.-G. Meissner, J. Oller, A. Wirzba, … Ann. Phys. 297 (2002) 27 There are active discussions are important

@Chiral05,RIKEN, 16 Feb. ‘05  Many activities in these days.  What we consider Chiral Unitary K-Nucleus interaction (by Ramos, Oset) (K-,p) by Neff approach (Same as p atom) Both atom + Nucleus states systematically Yamagata Yamagata, Nagahiro, Hirenzaki (+Okumura) K-atom/K-nucleus K-K- K-K-

@Chiral05,RIKEN, 16 Feb. ‘05  KN reaction － (In-flight K,N) Reaction B.E. [MeV] 130, 90, 50 [T.Kishimoto, et al., Prog. Theor. Phys. Suppl. 149 (2003) 264] [ T.Kishimoto Phys. Rev. Lett. 83 (1999) 4701] － (Stopped K,N) [Y.Akaishi,T.Yamazaki, Phys. Rev. C 65 (2002) ] [M.Iwasaki, et al., nucl-ex/ ] [T.Suzuki, et al., Phys. Lett. B 597 (2004) 263] Kishimoto Group (Exp.) Iwasaki, Suzuki Group (Exp.) Akaishi, Yamazaki Group (Theor.)

@Chiral05,RIKEN, 16 Feb. ‘05 Formulation -- Structure  Klein-Gordon equation  kaon-nucleus reduced mass : Coulomb Potential : Optical Potential  Optical Potential Chiral Unitary Model - Chiral Unitary Model [A.Ramos, E.Oset, Nucl. Phys. A671 (2000) 481] [Hirenzaki,Okumura,Toki,Oset,Ramos PRC 61 (2000) ] Phenomenology - Phenomenology [Batty,Friedman,Gal, Phys. Rep. 287 (1997) 385]

@Chiral05,RIKEN, 16 Feb. ‘05 Energy Levels of Kaonic States (Atomic and Nuclear) - Nuclear State - Atomic State

@Chiral05,RIKEN, 16 Feb. ‘05 Wave function Nuclear 1s Nuclear 2s Atomic 1s ←Nuclear radius of 39K 1s 2s 4s Phenomenology

@Chiral05,RIKEN, 16 Feb. ‘05 Energy Spectrum -- P K = 976 MeV/c (T K = 600 MeV ) bound region Almost ‘No structure’

@Chiral05,RIKEN, 16 Feb. ‘05 Phase Space factor threshold ・・・ B.E. ~ 240 MeV [J. Mares, E. Friedman, A. Gal, nucl-th/ ] threshold ・・・ B.E. ~ 100 MeV ① ②

@Chiral05,RIKEN, 16 Feb. ‘05 Energy Spectrum -- P K = 967MeV/c (T K = 600 MeV)  ++ f ( B.E. ) bound region Chiral Unitary – Almost No structure Phenomenology – Some structure ?

@Chiral05,RIKEN, 16 Feb. ‘05

Energy Spectrum (In-flight K,n) P K = 930 MeV/c bound region [ T.Kishimoto et al., Prog. Theor. Phys. Suppl. 149 (2003) 264 ] [ Fig. taken from the seminar by Dr.Hayakawa ] (In-flight K,p) P K = 976 MeV/c

@Chiral05,RIKEN, 16 Feb. ‘05  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 K

@Chiral05,RIKEN, 16 Feb. ‘05  H.C. Kim et al., [arXiv:hep-ph/ ]  the   self-energy in nucleus based on the decay too weak to make bound   in nuclei  D. Cabrera, Q.B. Li, W. Magas, E. Oset and M.J. Vicente Vacas two kinds of contributions  very small … consistent to the results by H.C.Kim et al..  ph (particle-hole) from the absorption of a virtual pion. large attractive potential of   large attractive potential of    X.H. Zhong et al., [arXiv:nucl-th/ ]  framework of relativistic mean field / quark meson coupling model  strong attractive interaction  strong attractive interaction for   -nucleus and   can be bound in nuclei.   Hypernuclei Studies of in-medium  + properties [arXiv:nucl-th/ ]

@Chiral05,RIKEN, 16 Feb. ‘05 Our motivation  Possible  + hypernuclei formation  Theoretical predictions …  + hypernuclei exist Can we observe ? New information New information about the Pentaquark  Information on bound state Information on  + itself S=+1 S=+1 hypernuclei  If it exists,  + hypernuclei will open a path for a research of new many-body systems with S=+1. S ? Z N

@Chiral05,RIKEN, 16 Feb. ‘05  Working Hypothesis  + SU(3) antidecuplet  + :, belongs to SU(3) antidecuplet SU(3) symmetric Lagrangian N*(1710) also belongs to antidecuplet N*(1710) also belongs to antidecuplet N*(1710) N  decay deta fix the coupling const. Interaction of the  + with the nuclear medium D. Cabrera, Q.B. Li, W. Magas, E. Oset and M.J. Vicente Vacas [arXiv:nucl-th/ ] : a vector current for two mesons where : antidecuplet states : octet of ½ + baryons : octet of 0 - mesons  attractive interaction diagram ++ ++ N  K In the nuclear medium, new channels are open.

@Chiral05,RIKEN, 16 Feb. ‘05 Bound states of  + potential depth:, » due to ambiguities of  + properties (D. Cabrera et al., [arXive:nucl-th/ , Phys. Lett. B, in print.]) width: two sources › energy dependent self-energies narrower widths for deeper bound states » narrower widths for deeper bound states We calculate the spectra for both cases.  + bound spectra  + bound spectra V  = -60  /  0 [MeV] V  = -120  /  0 [MeV] No LS splitting » Volume type potential only

@Chiral05,RIKEN, 16 Feb. ‘05 – Reported process in Prof. Nakano’s experiment » ( , K – )  + hypernuclei formation reaction »  + K +  – p K 0  0 p K 0  p K +  0 n K +  n K 0  + n ++ B MM  Possible process ++  K–K– n »  + K +  – p K 0  0 p K 0  p K +  0 n K +  n K 0  + n charged – theoretical vertices,  + into MMB, in the SU(3) Lagrangian D. Cabrera, Q.B. Li, W. Magas, E. Oset and M.J. Vicente Vacas, nucl-th/ ] [ D. Cabrera, Q.B. Li, W. Magas, E. Oset and M.J. Vicente Vacas, nucl-th/ ] » (K +,  + ) » (  –, K – ) Notice : (  -,K - ) could be very small (KEK exp.)

@Chiral05,RIKEN, 16 Feb. ‘05  + hypernuclei formation reaction  Which reaction is suitable ?  Recoilless condition momentum transfer q q [MeV/c] ( , K – ) (K +,  + ) (K +,  + ) (  –, K – ) (  –, K – ) Incident kinetic energy Ti [MeV] In Lab frame, the energy conservation in heavy target limit is, nucleon separation energy  binding energy masses kinetic energies

@Chiral05,RIKEN, 16 Feb. ‘05 Numerical results of formation cross sections,  list of parameters used in this calculation initial Kaon kinetic energy :  T K =300 MeV (p K ~620 MeV/c) (minimal momentum transfer)  + potential depth :  targets  12 C  forward reaction

@Chiral05,RIKEN, 16 Feb. ‘05 12 C target case : V  = -60  /  0 [MeV]  clear peak separated from each other  clear peak separated from each other.  Reasonable [micro b/sr MeV]  Reasonable cross section of the order of [micro b/sr MeV]  not too small free  + production threshold (s-state proton pick-up case) free  + production threshold quasi-free  + region T K =300MeV p K ~620MeV/c

@Chiral05,RIKEN, 16 Feb. ‘05 12 C target case : V  = -120  /  0 [MeV] clear  We can see clear peaks.  quite different spectrum  quite different spectrum from V=-60 / 0 MeV case.  more bound states for V=-120  /  0 MeV  narrower peaks due to the deeper bound states distinguish these two type potentials we may be able to distinguish these two type potentials by the spectrum, if we can see. T K =300MeV p K ~620MeV/c

@Chiral05,RIKEN, 16 Feb. ‘05 Summary on  + hypernuclei   + hypernuclei formation by (K +, + ) reaction  New frontier of S=+1 hypernuclei ? (or just a dream)  Many Unknowns … Let’s try !

@Chiral05,RIKEN, 16 Feb. ‘05  – Nucleus Bound Systems  – Nucleus Potential (in Unit of MeV) … R. S. Hayano, S. Hirenzaki, A. Gillitzer Eur. Phys. J. A6, 99 (1999) … F. Klingl, T. Waas, W. Weise, NPA 650, 299 (1999) … M. F. M. Lutz, G. Wolf, B. Friman, NPA 706, 431 (2002) : No bound states

@Chiral05,RIKEN, 16 Feb. ‘05 Kinematics ( , N) forward  mesic Nuclei E. Marco, W. Weise q [MeV/c] Phys. Lett. B502 (2001) 59  atom S. Hirenzaki, E. Oset Phys. Lett. B527 (2002) 69

@Chiral05,RIKEN, 16 Feb. ‘05 Potentials by : [Marco, Klingl, Waas, Weise] [Lutz, Wolf, Friman] ( MeV )

@Chiral05,RIKEN, 16 Feb. ‘05 Summary on  nucleus  Different theoretical Results exist.  Exp. Coming soon … N. Muramatsu  Let’s wait what we will see.