In search of K+K- molecule Michał Silarski Jagiellonian University Frascati Spring School May 12 – 16, 2008

Kaon pairs production in nucleon – nucleon collisions Physical motivation Kaon pairs production in nucleon – nucleon collisions Measurements of the pp→ppK+K- reaction with COSY-11 Study of the K+K- final state interaction Generalizations of the Dalitz Plot: Chodrow and Goldhaber approach Present status of analysis

Physical motivation a0 and f0 mesons as a K+K- molecules Nature of (1405) – K-p bound state (?) Physics of heavy ion collisions Physics of neutron stars: kaon condensates

Kaon pair production in nucleons collisions Production of a non-strange meson which decays into K+K-: ( DISTO, ANKE ) Associated production :

Kaon pair production in nucleons collisions Proton-proton collisions close to K+K- threshold ( COSY-11, ANKE ):

Cooler Synchrotron COSY

COSY-11 apparatus positively charged particles detection: Drift chambers: momentum reconstruction scintilators S1 and S3: velocity determination K- detection: - Silicon pad detector: position of negatively charged particle (background reduction )

Measurements of pp → ppK+K- reaction at threshold COSY-11: C. Quentmeier et al., Phys.Lett. B 515 (2001) 276-282 COSY-11: P. Winter et al., Phys. Lett. B 635 (2006) 23-29 COSY-11: M. Wolke, PhD thesis DISTO: F. Balestra et al.., Phys. Rev. C 63, 024004 (2001) ANKE: Y.Maeda et al. Phys., Rev. C 77, 01524 (2008)

Measurements of pp → ppK+K- reaction at threshold Significant discrepancy between experimental data and pure phase space calculations Inclusion of the pp – fsi does not fully account for the difference Introduction of the fsi in the K-p system still underestimates data very close to threshold Possible influence of K+K- final state interaction

Study of the K+K- final state interaction General idea: analysis of the differential cross-sections for the reaction pp → ppK+K- In the investigation we will use data obtained from two measurements at COSY: Q = 10 MeV ( 27 events ) Q = 28 MeV ( 30 events ) The experimental data are compared to the results of Monte Carlo simulations generated with various parameters of the K+K- interaction

Dalitz plot - convenient method of analysis for three particles in final state Homogeneous event density on entire plot Area of the plot proportional to phase space volume Boundary of the physically allowed region: well defined smooth closed curve Interaction effects show up as a modification of event density on Dalitz plot

Generalization of the Dalitz Plot There are several extensions of Dalitz plot for four particles Two very convenient : ● Chodrow plot ● Goldhaber plot

Generalization of the Dalitz Plot Probability of reaction yielding a state with the i-th particle in momentum range dpi : Chodrow approach ( Nuvo Cim. 50 (1967) 647 ) Assuming that f depends only on energies, when particles 1 and 2 are identical and E2 >E1 one gets:

Chodrow plot Resonances may be directly read off event distribution in FE2-plane Event density on Chodrow plot is not homogeneous( but well defined)

Goldhaber plot Goldhaber approach (Goldhaber et al. Phys. Rev. Lettes 9 (1962 ) 330) Assumption: f depends only on invariant masses of the particles: Projection of the physical region on (M12 ,M34 )–plane gives heterogenous event distribution

Goldhaber plot Lorentz - invariant distribution The physical region: interior of the right isosceles triangle bounded by:

Present status of analysis Q=10 MeV Q=28 MeV

Present status of analysis Q=10 MeV Q=28 MeV Experiment Monte Carlo (pp-FSI only)

In the near future Quantitative comparsion with Monte Carlo results Conclusions,……

Thank you for attention