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

2. 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

3. 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

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

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

6. Cooler Synchrotron COSY

7. 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 )

8. Measurements of pp → ppK+K- reaction at threshold
COSY-11: C. Quentmeier et al., Phys.Lett. B 515 (2001)
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, (2001)
ANKE: Y.Maeda et al. Phys., Rev. C 77, (2008)

9. 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

10. 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

11. 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

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

13. 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:

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

15. 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

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

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

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

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

20. Thank you for attention