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

TL;DR

This paper calculates the form factors for semileptonic $B_c$ decays into $\, ext{eta}^{(')}$ and pseudoscalar Glueball, considering mixing effects and providing numerical results relevant for decay predictions.

Contribution

It introduces a novel calculation of $B_c$ transition form factors into $\, ext{eta}^{(')}$ and Glueball, including mixing effects, using a light-cone approach and nonrelativistic $B_c$ modeling.

Findings

Form factors at maximum recoil are quantitatively estimated.

Mixing effects influence the form factors significantly.

Phenomenological implications for various semileptonic decays are discussed.

Abstract

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