We study the decay $D^0\to {\overline{K}}^{*0\mathrm{}}{\pi }^{-}{e}^{+}{\nu }_e$, using $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R$ chiral perturbation theory for heavy charmed mesons and vector mesons, in the kinematic regime where $\frac{p_M·p_{\pi }}{m_M}$ (here $M=D^0 or {\overline{K}}^{*0\mathrm{}}$) is much smaller than the chiral symmetry-breaking scale ${\Lambda }_{{\chi }^{\mathrm{SB}}}$ (${\Lambda }_{{\chi }^{\mathrm{SB}}}\sim 1$ GeV). We present the leading diagrams and amplitude, and calculate the rate, in the region where, to leading order in our calculations, the ${\overline{K}}^{*0\mathrm{}}$ is at zero recoil in the $D^0$ rest frame. The rate thus calculated is given in terms of a known form factor and depends on the $D{D}^{*}\pi$ coupling constant $g_D$ of the heavy (charmed) meson chiral perturbation theory Lagrangian. A measurement of the above decay, in the aforementioned kinematic regime, can result in the extraction of an experimental value for $g_D$, accurate at the level of our approximations, and gives us a measure of the validity of approaches based on chiral perturbation theory in studying similar processes.

Close

PrevNext

View figure in article