Form factors for semileptonic $B_c$ decays into ${\eta }^{{(}^{\prime })}$ and Glueball

Abstract

We calculated the form factors of $B_c$ transitions into ${\eta }^{{(}^{\prime })}$ meson and pseudoscalar Glueball, where the $B_c$ meson is a bound state of two different heavy flavors and is treated as a nonrelativistic state, while the mesons ${\eta }^{{(}^{\prime })}$ and Glueball are treated as light-cone objects since their masses are smaller enough compared to the transition momentum scale. The mechanism of two gluon scattering into ${\eta }^{{(}^{\prime })}$ dominated the form factors of $B_c$ decays into ${\eta }^{{(}^{\prime })}$. We considered the $\eta -{\eta }^{\prime }-$Glueball mixing effect, and then obtained their influences on the form factors. The form factors of $B_c$ transitions into ${\eta }^{{(}^{\prime })}$ and pseudoscalar Glueball in the maximum momentum recoil point were obtained as follows: $f_{0,+}^{\eta }(q^2=0)=1.38_{-0.02}^{+0.00}\times 10^{-3}$,$f_{0,+}^{{\eta }^{\prime }}(q^2=0)=0.89_{-0.10}^{+0.11}\times 10^{-2}$ and $f_{0,+}^G(q^2=0)=0.44_{-0.05}^{+0.13}\times 10^{-2}$. Also phenomenological discussions for semileptonic $B_c\to {\eta }^{{(}^{\prime })}+\ell +{\bar{\nu }}_{\ell }$, $B_c\to G(0^{-+})+\ell +{\bar{\nu }}_{\ell }$ and $D_s\to \eta +\ell +{\bar{\nu }}_{\ell }$ decays are given.

Comments: 11 pages, 8 figures, and 5 tables