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S. Fajfer. based on hep-ph/0308100, Phys. Rev. D 68 (2003) 094012 by. Motivation. Hidden strangeness FSI. Framework. Comparison with the experimental data. Conclusions. Motivation. a ) The decay rate :. PDG result. It has been suggested by.

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S. Fajfer

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



Hidden strangeness FSI

  • Framework
  • Comparison with the experimental data
  • Conclusions


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!


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:



Previous theoretical results



  • the flavor topology approach is limited in usefulness to fit any reasonable pattern
  • for the amplitudes in these two decay modes;

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:


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:


Hidden strangeness final state interactions

We resort following approximations:


For the matrix elements between Ds and light vector and pseudoscalar states we

use standard decomposition


(lattice results)

(experimental results)


The factorization approach results in the following predictions


does not satisfactorily reproduce experimental result

We have checked that factorization approximation works well in the case


This result contains the amplitudes for the transition

calculated within factorization approach.

If one uses experimental input to rescale the amplitudes, the prediction is


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:


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


The numerical results are rather stable on the small variation of the cut-off.


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%!



  • 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