S. Fajfer

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

Hidden strangeness FSI

• Framework

• Comparison with the experimental data

• Conclusions

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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!
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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
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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

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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
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rate gives
The PDG upper bound for the
Using the factorization approximation for the
weak vertex we obtain an estimate for the size
of annihilation contribution
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Hidden strangeness final state interactions
We resort following approximations
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For the matrix elements between Ds and light
vector and pseudoscalar states we use standard
decomposition
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(lattice results)
(experimental results)
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The factorization approach results in the
following predictions
reasonable description
does not satisfactorily reproduce experimental
result
We have checked that factorization approximation
works well in the case
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Note that the loop contributions coming from
hidden strangeness states are finite!
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The numerical results for the amplitudes
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This result contains the amplitudes for the

transition calculated within factorization
approach.
If one uses experimental input to rescale the
amplitudes, the prediction is
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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
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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.
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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!
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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
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Appendix decay amplitudes
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