Light-front quark model analysis of the exclusive rare $B_c\to D_{(s)}({\ell }^{+}{\ell }^{-},{\nu }_{\ell }{\bar{\nu }}_{\ell })$ decays

Abstract

We investigate the exclusive rare $B_c\to D_{(s)}{\nu }_{\ell }\overline{{\nu }_{\ell }}$ and $B\to D_{(s)}{\ell }^{+}{\ell }^{-}$ ($\ell =e,\mu ,\tau$) decays within the standard model and the light-front quark model constrained by the variational principle for the QCD motivated effective Hamiltonian. The form factors $f_{\pm }(q^2)$ and $f_T(q^2)$ are obtained from the analytic continuation method in the $q^{+}=0$ frame. While the form factors $f_{+}(q^2)$ and $f_T(q^2)$ are free from the zero-mode, the form factor $f_{-}(q^2)$ is not free from the zero-mode in the $q^{+}=0$ frame. We discuss the covariance(i.e. frame-independence) of our model calculation and quantify the zero-mode contributions to $f_{-}(q^2)$ for $B_c\to D_{(s)}$ decays. The branching ratios and the longitudinal lepton polarization asymmetries are calculated with and without the long-distance contributions. Our numerical results for the non-resonant branching ratios for $B_c\to D(D_s)\sum {\nu }_{\ell }\overline{{\nu }_{\ell }}$ and $B_c\to D(D_s){\ell }^{+}{\ell }^{-}$ are in the order of $10^{-8}(10^{-7})$ and $10^{-9}(10^{-8})$, respectively. The averaged values of the lepton polarization asymmetries obtained from the linear (harmonic oscillator) potential parameters are found to be $-0.99(-0.99)$ for $B_c\to D{\mu }^{+}{\mu }^{-}$ and $-0.16(-0.15)$ for $B_c\to D{\tau }^{+}{\tau }^{-}$, and $-0.98(-0.98)$ for $B_c\to D_s{\mu }^{+}{\mu }^{-}$ and $-0.14(-0.12)$ for $B_c\to D_s{\tau }^{+}{\tau }^{-}$, respectively.

Comments: 11 pages, 8figures, version to appear in Phys. Rev. D