The study of light invisible particles in $B_c$ decays

In this paper, we study the light scalar and pseudoscalar invisible particles in the flavor changing neutral current processes of the $B_c$ meson. Effective operators are introduced to describe the couplings between quarks and light invisible particles. The Wilson coefficients are extracted from the experimental results of the $B$ and $D$ mesons, which are used to predict the upper limits of the branching fractions of the similar decay processes for the $B_c$ meson. The hadronic transition matrix element is calculated with the instantaneously approximated Bethe-Salpeter method. The upper limits of the branching fractions when $m_{\chi }$ taking different values are presented. It is found that at some region of $m_{\chi }$, the channel $B_c\to D_s^{(\ast)}\chi\chi$hasthelargestupperlimitwhichisoftheorderof$10^{-6}$,andfor$B_c\to D_s^\ast\chi\chi^\dagger$, the largest value of the upper limits can achieve the order of ${10}^{-5}$. Other decay modes, such as $B_c\to D^{(\ast )}\chi {\chi }^{(†)}$ and $B_c\to B^{(\ast )}\chi {\chi }^{(†)}$, are also considered.