2023 Impact factor 4.2
Particles and Fields
Eur. Phys. J. C 27, 201-218 (2003)
DOI: 10.1140/epjc/s2002-01090-5

The radiative leptonic decays $D^0 \to e^+ e^-\gamma,\mu^+\mu^-\gamma $ in the standard model and beyond

S. Fajfer1, 2, P. Singer3 and J. Zupan1

1  J. Stefan Institute, Jamova 39, P.O. Box 3000, 1001 Ljubljana, Slovenia
2  Department of Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
3  Department of Physics, Technion - Israel Institute of Technology, Haifa 32000, Israel

(Received: 25 October 2002 / Published online: 24 January 2003 )

We present a calculation of the rare decay modes $ D^0 \to e^+ e^- \gamma $ and $ D^0 \to \mu^+\mu^- \gamma $ in the framework of the standard model. For the short distance part we have derived QCD corrections to the Wilson coefficients involved, including C9. The latter is found to be strongly suppressed by the corrections, leading to diminished values for the $c\to u l^+l^-$ branching ratios in the 10-10 range. Within SM the exclusive decays are dominated by long distance effects. Non-resonant contributions are estimated using heavy quark and chiral symmetries to be at the level of $10\%$, compared to the contributions arising from $D^0\to V
\gamma\to l^+l^-
\gamma$ , with $V=\rho, \omega, \phi$. The total SM branching ratio is predicted to be in the range (1- $3)\times 10^{-9}$. We also consider contributions coming from MSSM with and without R parity conservation. The effects from MSSM are significant only for the R parity violating case. Such contributions enhance the branching ratio $ D^0 \to \mu^+\mu^- \gamma $ to $\lesssim0.5
\times 10^{-7}$ , based on appropriately allowed values for C9 and C10. This selects $ D^0 \to \mu^+\mu^- \gamma $ as a possible probe of new physics.

© Società Italiana di Fisica, Springer-Verlag 2003