$c\to u\gamma$ in Cabibbo suppressed D meson radiative weak decays

Abstract

We investigate Cabibbo suppressed $D^0$, $D^{+}$ and $D_s^{+}$ radiative weak decays in order to find the best mode to test $c\to u\gamma$ decay. Combining heavy quark effective theory and the chiral Lagrangian approach we determine the decay widths. We calculate $\Gamma (D^0\to {\rho }^0/\omega \gamma )/\Gamma (D^0\to {\bar{K}}^{\ast 0}\gamma )$ previously proposed to search for possible New Physics. However, we notice that there are large, unknown, corrections within the Standard Model. We propose a better alternative, the ratio $\Gamma (D_s^{+}\to K^{\ast +}\gamma )/\Gamma (D_s^{+}\to {\rho }^{+}\gamma )$, and show that it is less sensitive to the Standard Model.

Comments: 14 pages, latex, 2 uuencoded Postscript figures in a separate file