S. Fajfer

1. S. Fajfer based on hep-ph/0308100, Phys. Rev. D 68 (2003) 094012 by

2. Motivation Hidden strangeness FSI • Framework • Comparison with the experimental data • Conclusions

3. Motivation a) The decay rate: PDG result It has been suggested by that this observation is a clean signature of the annihilation decay of . The factorization approximation gives zero for the decay amplitude due to the isospin and G parity . The knowledge of the annihilation contribution is very important for the hadronic decays!

4. We argue that the experimental value for the transition can be accommodated by considering ONLY color suppressed spectator decay with subsequent final state interactions (FSI). This leaves little room for unambiguous study of the annihilation effects from the decay mode. b) the decay rate PDG status: with

5. Previous theoretical results 0.26% 0.24% • the flavor topology approach is limited in usefulness to fit any reasonable pattern • for the amplitudes in these two decay modes;

6. Annihilation contribution A scan through PDG book reveals that there are no resonances with but with there are This indicates the enhancement of the annihilation contribution:

7. rate gives The PDG upper bound for the Usingthe factorization approximation for the weak vertex we obtain an estimate for the size of annihilation contribution:

8. Hidden strangeness final state interactions We resort following approximations:

12. For the matrix elements between Ds and light vector and pseudoscalar states we use standard decomposition

14. (lattice results) (experimental results)

16. The factorization approach results in the following predictions reasonabledescription does not satisfactorily reproduce experimental result We have checked that factorization approximation works well in the case

17. Note that the loop contributions coming from hidden strangeness states are finite!

18. The numerical results for the amplitudes:

19. This result contains the amplitudes for the transition calculated within factorization approach. If one uses experimental input to rescale the amplitudes, the prediction is

20. This contribution has almost the same size as annihilation contribution! Adding the FSI contribution with maximal annihilation contribution with alternating signs gives a fairly large interval:

21. If instead of double/single pole parametrization of the form factors, one uses standard single pole parametrization the loop integrals give logarithmic divergence. In this case the real part of amplitudes are cut – off dependent, while imaginary parts are not. By taking the cut-off parameter to be close to the charm meson mass scale we obtain that the amplitudes are very close to the ones obtained in the case of double/single pole parametrization. The numerical results are rather stable on the small variation of the cut-off.

22. FSI in FSI we are considering is not leading contribution. This decay can proceed through the spectator mechanism directly. The use of factorization approximation leads to in very good agreement with the experimental result . The inclusion of FSI reduces rate from 4% to 3.6%!

23. Conclusions: • hidden strangeness final state interactions are very important in understanding the decay mechanism; • the amplitude can be explained fully by this mechanism; • for the amplitude the predictions we obtain lie in fairly large range due to possible cancellation between FSI and single pole contribution; • the hidden strangeness FSI represents a second order effect, the inclusion of which • does not spoil the good agreement of factorization approximation obtained for • the Dalitz plot analysis by FOCUS (Phys. Lett. B 585 (2004) 200) in the case of shows that the S-wave component has dominant contribution;

24. Appendix: decay amplitudes