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 $m_χ$ taking different values are presented. It is found that at some region of $m_χ$, the channel $B_c\to D_s^{(\ast)}χχ$ has the largest upper limit which is of the order of $10^{-6}$, and for $B_c\to D_s^\astχχ^\dagger$, the largest value of the upper limits can achieve the order of $10^{-5}$. Other decay modes, such as $B_c\to D^{(*)}χχ^{(\dagger)}$ and $B_c\to B^{(*)}χχ^{(\dagger)}$, are also considered.