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K- bound states? A theoretical view

K- bound states? A theoretical view. V. Magas, A. Ramos (University of Barcelona) E. Oset (University of Valencia) H. Toki (RCNP,Osaka University). International Conference on Hypernuclear and Strange Particle Physics, HYP06 Mainz, September 10-14, 2006. K N scattering: a lively topic.

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K- bound states? A theoretical view

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  1. K- bound states? A theoretical view V. Magas, A. Ramos (University of Barcelona) E. Oset (University of Valencia) H. Toki (RCNP,Osaka University) International Conference on Hypernuclear and Strange Particle Physics, HYP06 Mainz, September 10-14, 2006

  2. K N scattering: a lively topic • K N scattering in the I=0 channel is dominated by the presence of the L(1405), located only 27 MeV below the K N threshold • In recent years, there has been a lot of activity in studying the interaction of antikaons with nucleons • Already in the late sixties, Dalitz, Wong and Rajasekaran [Phys. Rev. 153 (1967) 1617] obtained the L(1405) as a KN quasi-bound state in a potential model (Scrhoedinger equation). HYP06, K- bound states?

  3. The study of KN scattering has been revisited more recently from the modern view of chiral Lagrangians. The presence of a resonance makes cPT not applicable  non-perturbative techniques implementing unitarization in coupled channels are mandatory! • Since the pioneering work of Kaiser, Siegel and Weise [Nucl. Phys. A594 (1995) 325] many other chiral coupled channel models have been developed. more channels, next-to-leading order, Born terms beyond WT (s-channel, u-channel), fits including new data … E. Oset and A. Ramos, Nucl. Phys. A635 (1998) 99 J.A. Oller and U.G. Meissner, Phys. Lett. B500 (2001) 263 M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A700 (2002) 193 C.Garcia-Recio et al., Phys. Rev. D (2003) 07009 M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A700 (2002) 193 B.Borasoy, R. Nissler, and W. Weise, Phys. Rev. Lett. 94, 213401 (2005); Eur. Phys. J. A25, 79 (2005) J.A. Oller, J. Prades, and M. Verbeni, Phys. Rev. Lett. 95, 172502 (2005) J. A.Oller, arXiv:hep-ph/0603134. B. Borasoy, U. G. Meissner and R. Nissler, arXiv:hep-ph/0606108. HYP06, K- bound states?

  4. K in a nuclear medium: The presence of the L(1405) resonance makes the in-medium KN interaction to be very sensitive to the particular details of the many-body treatment. free (repulsive)  we’d better do a good job!(SELF-CONSISTENCY) medium (attractive) K K p Pauli blocking Weise, Koch K K p Self-consistent kaon dressing Lutz K K p pion and kaon dressing Ramos,Oset HYP06, K- bound states?

  5. A moderate attraction of about -40 MeV at r0 is obtained A. Ramos, E. Oset, Nucl. Phys. A671, 481 (2000) L. Tolós, A. Ramos, E. Oset, Phys. Rev. C (2006) Other shallow optical potentials: J. Schaffner-Bielich, V.Koch, M. Effenberber, Nucl. Phys. A669, 153 (2000) A.Cieply, E.Friedman, A.Gal, J.Mares, Nucl. Phys. A696, 173 (2001) Akaishi and Yamazaki: Phenomenological KN-pS potential: + many-body treatment (self-consistency ignored)  deep optical potential + shrinkage effect (r(0)~10r0!) + extra tuning:  strongly bound kaonic states: BK = 169 MeV in ppn-K- (T=0) BK = 194 MeV in pnn-K- (T=1) Y.Akaishi, T.Yamazaki, Phys.Rev.C65,044005 (2002) Y.Akaishi, A. Dote, T.Yamazaki, Phys.Lett.B613, 140 (2005) see, however: Shevchenko, Gal, Mares, nucl-th/0610022 ! HYP06, K- bound states?

  6. The KEK proton missing mass experiment: T. Suzuki et al., Phys. Lett. B597, 263 (2004) S0 is a tribaryon with S = -1 and T = 1 If interpreted as a pnn-K- bound system…  BK =197 MeV formation rate: 1% per absorbed K- HYP06, K- bound states?

  7. p • NO! This configuration (phase-space-like) would produce more broadening S- d Oset-Toki’s view: E. Oset, H. Toki, Phys. Rev. C74, 015207 (2006) K- absorption by two nucleons leaving the other nucleons as spectators do not absorbe energy nor momentum from the probe some Fermi motion broadening is possible,  it would explain the ~60 MeV/c peak spreading HYP06, K- bound states?

  8. 6Li 4He The FINUDA proton missing mass experiment: M. Agnello et al, Nucl. Phys. A775, 35 (2006) This view is consistent with the observation by the FINUDA collaboration of a peak in the proton missing mass spectrum at ~ 500 MeV/c (from K- absorbed in 6Li) A study of the angular correlations (p and S- are emitted back-to-back) allow them to conclude that the reaction: in 6Li is the most favorable one to explain their signal HYP06, K- bound states?

  9. The FINUDA (Lp) invariant mass experiment M. Agnello et al. Phys. Rev. Lett. 94, 212303 (2005) Nuclei: • The same elementary reaction takes place: K- p p  L p • (select pL > 300 MeV/c to eliminate K- N  L p) • But here both emitted particles are detected! (not just the proton) •  the invariant mass of the Lp pair is measured, MLp • A peak for the transition to the g.s. of the daugther nucleus should be • observed at: HYP06, K- bound states?

  10. Interpreted by the FINUDA experiment as a (K-pp) bound state Our view: Final State Interactions (FSI) of the primary L and p (produced after K- absorption) in their way out of the daughter nucleus! Transition to the g.s. of daughter nucleus M. Agnello et al. Phys. Rev. Lett. 94, 212303 (2005) HYP06, K- bound states?

  11. The K- is absorbed by two nucleons with momenta randomly chosen • within the local Fermi sea: • Primary L and N emitted according to phase space: Our calculation Monte Carlo simulation of K- absorption by pp and pn pairs in nuclei • For each nucleus, the K- is absorbed mainly from the lowest atomic orbit • for which the energy shift has been measured • Further collisions of L and N as they cross the nucleus according to • a probability per unit length sr with sL~2sN/3 • Finally, the invariant Lp mass is reconstructed from the final events HYP06, K- bound states?

  12. HYP06, K- bound states?

  13. Nuclear density profile and overlap p L L p p L HYP06, K- bound states?

  14. First (narrow) peak:formation of the g.s. of the daughter nucleus for the light nuclei How much strength? Formation probability(FP)xSurvival probability (PS) In light nuclei: FP ~ | 0.3 - 0.7 |2 = 0.1 – 0.5 and PS ~ 0.6  6 - 30% (ex: 7Li (pp)-1  5H) In heavier nuclei: FP increases but PS decreases also below 30% • The largest part of the K- absorption events go into nuclear excitations, mostly to the continuum. Where is this strength located?Obviously at smaller invariant Lp masses HYP06, K- bound states?

  15. Second (wider) peak:Quasi-elastic peak (QEP) after K- absorption A peak is generated in our Monte Carlo simulations when the primary L and p (produced after K- absorption) undergo quasi-elastic collisions with the nucleus, exciting it to the continuum. This is the analogue of the quasi-elastic peak (QEP) observed in nuclear inclusive reactions using a variety of different probes: (e,e’), (p,p’), (p,p’),… (The QEP comes mostly from one collision of the particles exciting the nucleus to the continuum).  The QEP accounts for the second peak of the FINUDA experiment! HYP06, K- bound states?

  16. Invariant mass distribution (one-collision) HYP06, K- bound states?

  17. Allowing up to three collisions HYP06, K- bound states?

  18. Angular correlations HYP06, K- bound states?

  19. Mixture of the light targets HYP06, K- bound states?

  20. Peak does not move with size of nucleus  Cannot be a bound K- nuclear state! HYP06, K- bound states?

  21. Can the peak be due to other processes? A) followed by This peaks around 2170 MeV (where there is indeed a small third peak in the experiment) and has a smaller strength than B) followed by  located in the region of the QEP and all events back-to-back, but strength is small, ~ 10-30% of events HYP06, K- bound states?

  22. Conclusions The recent experiments of proton missing mass spectra (at KEK and FINUDA) can be explained in terms of K- absorption by two nucleons. The remaining residual system is left in a bound (ground) state. The Lp invariant mass distribution of the FINUDA Lp invariant mass experiment is naturally explained in terms of the reaction followed by further interactions of the L or the N in the daughter nucleus. In summary, present data can be interpreted without the need of invoking exotic mechanisms, like the formation of deeply bound K- nuclear states! E. Oset and H. Toki, Phys. Rev. C74, 015207 (2006) V. K. Magas, E. Oset, A. Ramos and H. Toki, Phys. Rev. C74, 025206 (2006) HYP06, K- bound states?

  23. HYP06, K- bound states?

  24. M. Agnello et al. Phys. Rev. Lett. 94, 212303 (2005) We give a conventional explanation: Final State Interactions (FSI) of the primary L and p (produced after K- absorption) as they cross the daughter nucleus! (Discarded in the experimental analysis on the basis of back-to-back correlations) HYP06, K- bound states?

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