https://doi.org/10.1140/epjc/s2004-01879-0
theoretical physics
The rare decay 
within the SM
1
INFN, Laboratori Nazionali di Frascati, 00044, Frascati, Italy
2
Institut für Theoretische Physik, Universität Bern, 3012, Bern, Switzerland
3
Institut für Theoretische Physik, Universität Wien, 1090, Wien, Austria
We present an updated analysis of the rare decay within the standard model. In particular, we present the first complete calculation of the two-photon CP-conserving amplitude within chiral perturbation theory, at the lowest non-trivial order. Our results confirm the previous findings that the CP-conserving contribution to the decay rate cannot be neglected. By means of an explicit two-loop calculation, we show that this contribution can be estimated with sufficient accuracy compared to the CP-violating terms. We predict 
, with approximately equal contributions from the CP-conserving component, the indirect-CP-violating term, and the interesting direct-CP-violating amplitude. The error of this prediction is mainly of parametric nature and could be substantially reduced with better data on the 
modes. The standard model predictions for various differential distributions and the sensitivity to possible new-physics effects are also briefly discussed.
© Springer-Verlag, 2004
