in collaboration with : V.K. Magas, E. Oset, R. Molina, L. Tolós, J. Yamagata-Sekihara, S. Hirenzaki A. Ramos University of Barcelona (JPS+SPHERE meeting, Vila Lanna, Prague 4-6 September, 2010) Strange mesons in nuclei S=-1 mesons: - K (J  =0 - ) - K* (J  =1 - )

Evidences of deeply bound K - nuclear states (B K ~ 100 MeV) from slow kaon reactions on nuclei has been claimed Pseudoscalar K mesons in nuclei Understanding the properties of Kbar mesons has been one of the major goals in strange nuclear physics.  How attractive is the Kbar-nucleus optical potential?  May kaon condensation occur in neutron star interiors? Phenomenological fits to kaonic atom data preferred U K (  0 ) ~ -200 MeV Self-consistent theoretical calculations that use realistic Kbar N interactions (KN data reproduced, chiral dynamics) obtain U K (  0 ) ~ -50 to -70 MeV OK X

The observed peaks in nuclear reactions using slow kaons: 1. (K - stop, p) (bump) 2. (K - stop,  p) 3. (K - stop,  d) can be explained in terms of conventional input that combines: a)an absorption mechanism K - NN   N (in 1. and 2.) K - NNN   d (in 3.) b)nuclear medium effects: Fermi motion/recoil (  direct reaction peaks broaden) FSI of the emitted particles (if daughter nucleus is big enough) (  secondary peaks/structures may appear) E. Oset, H. Toki, Phys. Rev. C74, (2006) M. Agnello et al. Phys. Lett. B654, 80 (2007) V.K. Magas, E. Oset, A. Ramos and H. Toki, Phys. Rev. 74 (2006) M. Agnello et al. Phys. Rev. Lett. 94, (2005) T. Suzuki et al., Mod. Phys. Lett. A23, 2520 (2008) V.K. Magas, E. Oset and A. Ramos, Phys. Rev C77, (2008) T. Suzuki al. Phys. Rev.C76, (2007) V.K. Magas, E. Oset, A. Ramos and H. Toki, Nucl.Phys. A804, 219 (2008)

Another “evidence” for a very deeply attractive K- nucleus potential: The (K -,p) reaction on 12 C at KEK T. Kishimoto et al., Prog. Theor. Phys. 118 (2007) 181 p K = 1 GeV/c  p < 4.1 o  forward nucleons (the most energetic)  in-flight kaons plus “coincidence requirement”: (at least one charged particle in decay counters surrounding the target) claimed not to affect the spectrum shape

J. Yamagata, H. Nagahiro and S. Hirenzaki, Phys.Rev. C74, (2006) shallow deep

Analysis of T. Kishimoto et al., Prog. Theor. Phys. 118 (2007) 181 Process: quasielastic scattering K - p  K - p in nuclei Green’s function method Normalization: fitted to experiment Background: fitted to experiment Re U K =−60 MeV Im U K =−60 MeV Re U K =−160 MeV Im U K =−50 MeV Re U K =−190 MeV Im U K =−40 MeV

The only mechanism for fast proton emission in the Green’s function method is the quasielastic process K - p  K - p where the low-energy kaon in the final state feels a nuclear optical potential and can occupy stable orbits (no width), unstable orbits, or be in the continuum (quasifree process) However, there are other mechanisms that can contribute: Taken from J. Yamagata and S. Hirenzaki, Eur. Phys. J. A 31, 255{262 (2007)  Multistep processes: K - and/or N undergo secondary collisions as they leave the nucleus  One-nucleon absorption: K - N  p  and K - N  p  followed by decay of  or  into  p  Two-body absorption: K - N N   N and K - N N   N followed by hyperon decays We implement these processes in a Monte Carlo simulation of K - absorption in nuclei

Monte Carlo simulation  Further collisions of the emitted particles as they cross the nucleus. We follow: the K- until it leaves the nucleus or gets absorbed all energetic p and n (until they leave the nucleus) all energetic  and  (until they leave the nucleus and decay into  N)  Finally, we represent the spectra of the emerging protons  The incoming K - will experience a certain process (quasielastic, one-nucleon or two-nucleon absorption) at a point r with a probability given by  qe   l,  1N   l o r  2N   l where  l is a typical step size.  The nucleus is described by a nuclear density profile  (r)  Once a process has been decided, we determine the local momenta of the emitted particles according to phase space (details in next talk by V. Magas)

Cross sections:  taken from the PDG Quasielastic scattering One-nucleon absorption (and all possible charge combinations)

Two-nucleon absorption (and all possible charge combinations) We assume: 1. A probability per unit length for two-body absorption given by: (2N-absorption is 20% of 1N-absorption) 2. Partial widths for the various channels according to a microscopic K-meson exchange picture P.A. Katz et al, Phys.Rev.D 1, 1267 (1970) P KNN = C abs  2 C abs ~ 6 fm 5

1N-absorption, rescattering Proton spectrum 2N absorption, rescattering No coincidence - V.K. Magas, J. Yamagata-Sekihara, S. Hirenzaki, E. Oset and A. Ramos, Phys. Rev. C81, (2010).

Comparison with KEK data:

“The experiment measures the proton PLUS at least one charged particle in the decay counters surrounding the target”  Our simulation should consider the coincidence requirement of KEK-PS E548 The simulation of such coincidence requirement is tremendously difficult, because it would imply keeping track of all charged particles coming out from all possible scatterings and decays. The best we can do is to eliminate processes that, for sure, cannot have a coincidence: quasi-elastic K - p  K - p events where neither the p nor the K - suffer secondary collisions. (In this type of processes the fast p moves forward and the K- escapes undetected through the back).  minimal coincidence requirement

The coincidence requirement removes a substantial fraction of events and changes the shape of the spectrum drastically Comparison with KEK data:

Supp. ~0.7 Comparison with KEK data: Low energy p – multiparticle final states  should be less supressed! Supp. ~ 1.0

- The results of the in-flight 12 C(K -,N) reaction at KEK (PS-E548) can probably be explained with a conventional kaon optical potential (U K (r 0 ) ~ -60 MeV) - We have seen that the coincidence requirement introduces a non-negligible distortion in the spectrum - This distortion is comparable in size (even bigger) than that produced by using a different kaon optical potential.

Vector K* mesons in nuclei  From (K -,K* - ) reaction in nuclei (see V. Magas’ talk) The study of vector meson properties in the nuclear medium has received a lot of attention, since they are tied to fundamental aspects of QCD ρ meson: KEK325, CLAS-g7, CERES, NA60 ω meson: NA60, CBELSA/TAPS ϕ meson: KEK325, LEPS, COSY-ANKE Less attention has been paid to the K* meson! (probably because it does not decay into dileptons).

K* N interaction in free space: (coupled-channels model) T ij = V ij + V il G l T lj = + transition potential channels: K*N ωΛ, ωΣ ρΛ, ρΣ ϕ Λ, ϕΣ K*Ξ  From local hidden gauge formalism Bando et al. Phys. Rev. Lett. 54, 1215 (85); Phys. Rep. 164, 217 (88) -Deals simultaneously with vector and pseudoscalar mesons - Implements chiral symmetry naturally - Leads to the same lowest order Lagrangian for pseudoscalar mesons -Reproduces all the empirically successful low-energy relations of the  meson (KSFR) relation, vector meson dominance,…) E. Oset, A. Ramos, Eur.Phys.J. A44 (2010) 431

VVV vertex  KSFR relation BBV vertex Bando et al, PRL 112 (1985) and Phys. Rep. 164 (1988) 217 Klingl, Kaiser, Weise, NPA 624 (1997) 527 transition potential VB->VB Loop function G incorporates mass distribution (width) of vector meson (same s-wave amplitude as in P B  P B S-wave scattering)

** ** 1783, Γ=9 1830, Γ=42 PDG: Λ(1690) 3/2- Λ(1800) 1/2- PDG: Σ(1750) 1/2- Our resonances are narrower than known PDG states because coupling to pseudoscalar-baryon channels is not included

K* self-energy in the medium a) K*  K  and medium modifications N N,  M K* free decay :  = -Im  /M K* = 50 MeV medium corrections (absorption) vertex corrections The K* width increases substantially (factor 2) due to pion self-energy in nuclear matter

T ij = V ij + V il G l T lj = + T ij (  ) = V ij + V il G l (  ) T lj (  ) = + Free space Medium Dressed K* meson: =+ Pauli blocking and baryon dressing meson dressing + b) K* N interaction in the medium: q.e. process K*N  K*N, and also new absorption processes: K*N   KN, K*NN  KNN

M K* K* self-energy in the medium Λ(1784)N -1 Σ(1830)N -1 free K* width at normal nuclear matter density (  0 ) is 5-6 times larger than in free space!! Can it be checked by some reaction in nuclei?? (V. Magas, next talk ) L. Tolos, R. Molina, E. Oset, and A. Ramos, arXiv: [nucl-th].

Thank you for your attention