Five-body $D\to V$ Semileptonic Decays

Abstract

Our main objective is to derive the decay rate for the semileptonic decays $D\to V{\ell }^{+}\hat{I}{½}_{\ell }(\ell =e,\hat{I}¼)$, where $V$ represents a vector particle. In these decays, the vector particle $V$ decays into three pseudo-scalar particles. To accomplish this, we evaluate the phase-space factor for the five-body decay with a set of eight independent variables which uniquely define a point in the phase space. We further conduct a detailed investigation of the $D\to \ddot{I}‰{\ell }^{+}\hat{I}{½}_{\ell }$, where $\ddot{I}‰$ subsequently decays into $\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$, within the Standard Model and in a general effective field theory description of the weak interactions at low energies. The outcomes of this study have potential applications in the measurement of $D\to \ddot{I}‰$ form factors. These measurements can be performed using data obtained from BESIII.