The Decay $D^0\to {\bar{K}}^{\ast 0}{\pi }^{-}{e}^{+}{\nu }_e$ in the Context of Chiral Perturbation Theory

Abstract

We study the decay $D^0\to {\bar{K}}^{\ast 0}{\pi }^{-}{e}^{+}{\nu }_e$, 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 ${\bar{K}}^{\ast 0}$) 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 ${\bar{K}}^{\ast 0}$ 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 $D{D}^{\ast }\pi$ 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.

Comments: 17 pages, Latex, 2 embedded postscript figures