Form factors for semileptonic $B_{c}$ decays into $η^{(')}$ and Glueball

Abstract

We calculated the form factors of $B_{c}$ transitions into $η^{(')}$ 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 $η^{(')}$ 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 $η^{(')}$ dominated the form factors of $B_{c}$ decays into $η^{(')}$. We considered the $η-η'-$Glueball mixing effect, and then obtained their influences on the form factors. The form factors of $B_{c}$ transitions into $η^{(')}$ and pseudoscalar Glueball in the maximum momentum recoil point were obtained as follows: $f^η_{0,+}(q^2=0)=1.38^{+0.00}_{-0.02}\times 10^{-3}$,$f^{η'}_{0,+}(q^2=0)=0.89^{+0.11}_{-0.10}\times 10^{-2}$ and $f^{G}_{0,+}(q^2=0)=0.44^{+0.13}_{-0.05}\times 10^{-2}$. Also phenomenological discussions for semileptonic $B_{c}\toη^{(')}+\ell+\barν_\ell$, $B_{c}\to G(0^{-+})+\ell+\barν_\ell$ and $D_{s}\to η+\ell+\barν_\ell$ decays are given.