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

3. 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  PT 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. 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 more channels, next-to-leading order, Born terms beyond WT (s-channel, u- channel), fits including new data … 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.

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

5. HYP06, K- bound states?5 A moderate attraction of about -40 MeV at  0 is obtained A. Ramos, E. Oset, Nucl. Phys. A671, 481 (2000) L. Tolós, A. Ramos, E. Oset, Phys. Rev. C (2006) Akaishi and Yamazaki: Phenomenological KN-  potential: + many-body treatment (self-consistency ignored)  deep optical potential + shrinkage effect (  (0)~10  0 !) + extra tuning:  strongly bound kaonic states: B K = 169 MeV in ppn-K - (T=0) B K = 194 MeV in pnn-K - (T=1) 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) 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 !

6. HYP06, K- bound states?6 The KEK proton missing mass experiment: T. Suzuki et al., Phys. Lett. B597, 263 (2004) S 0 is a tribaryon with S = -1 and T = 1 If interpreted as a pnn-K - bound system…  B K = 197 MeV formation rate: 1% per absorbed K -

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

8. HYP06, K- bound states?8 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 6 Li) A study of the angular correlations (p and  - are emitted back-to-back) allow them to conclude that the reaction: in 6 Li is the most favorable one to explain their signal 6 Li 4 He

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

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

11. HYP06, K- bound states?11 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 Primary  and N emitted according to phase space: The K - is absorbed by two nucleons with momenta randomly chosen within the local Fermi sea: Further collisions of  and N as they cross the nucleus according to a probability per unit length  with   ~2  N /3 Finally, the invariant  p mass is reconstructed from the final events

12. HYP06, K- bound states?12

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

14. HYP06, K- bound states?14 First (narrow) peak: formation of the g.s. of the daughter nucleus How much strength? Formation probability (FP) x Survival probability (P S ) In light nuclei: FP ~ | 0.3 - 0.7 | 2 = 0.1 – 0.5 and P S ~ 0.6  6 - 30% (ex: 7 Li (pp) -1  5 H) In heavier nuclei: FP increases but P S decreases  also below 30% for the light nuclei  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  p masses

15. 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  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’), (  ’),… (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!

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

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

18. HYP06, K- bound states?18 Angular correlations

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

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

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

22. HYP06, K- bound states?22 Conclusions The  p invariant mass distribution of the FINUDA  p invariant mass experiment is naturally explained in terms of the reaction followed by further interactions of the  or the N in the daughter nucleus. 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) 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. In summary, present data can be interpreted without the need of invoking exotic mechanisms, like the formation of deeply bound K- nuclear states!

23. HYP06, K- bound states?23

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