The Decay $D^0\to \bar K^{*0} π^- e^+ ν_e$ in the Context of Chiral Perturbation Theory

We study the decay $D^0\rightarrow \bar K^{*0} \pi^- e^+ \nu_e$, using $SU(2)_L \otimes SU(2)_R$ chiral perturbation theory for heavy charmed mesons and vector mesons, in the kinematic regime where $p_M \cdot p_\pi/m_M$ (here $M = D^0$ or $\bar K^{*0}$) is much smaller than the chiral symmetry breaking scale, $\Lambda_{\chi SB}$ ( $\Lambda_{\chi 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 $\bar K^{*0}$ 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 $DD^* \pi$ 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 give us a measure of the validity of approaches based on chiral perturbation theory in studying similar processes.