$B_c$-meson decays into $J/\psi$ plus a light meson in the improved perturbative QCD formalism

In the wake of measurements on $B_c^+ \to J/\psi K^+$, $B_c^+ \to J/\psi \pi^+\pi^-\pi^+$, and $B_c^+ \to J/\psi K^+ K^-\pi^+$ at Large Hadron Collider experiments, we propose to study the decays $B_c^+ \to J/\psi M^+$ comprehensively, with $M$ being the light charged pseudoscalar ($P$), vector ($V$), scalar ($S$), axial-vector ($A$), and tensor ($T$) mesons, within the improved perturbative QCD (iPQCD) formalism at leading order in the Standard Model. The theoretical predictions for experimental observables such as branching fractions, relative ratios, and longitudinal polarization fractions in the iPQCD formalism await near future examinations relying on the upgraded Large Hadron Collider, even the forthcoming Circular Electron-Positron Collider. We emphasize that the investigations on the factorizable-emission-suppressed or -forbidden decays like $B_c^+ \to J/\psi S^+$, $B_c^+ \to J/\psi A^+_{1^1\!P_1}$, and $B_c^+ \to J/\psi T^+$, should go definitely beyond naive factorization to explore the rich dynamics, which could, in turn, further help understand the QCD nature of $B_c$ meson, as well as that of related hadrons. The future confirmations on those predictions about the relative ratios between the branching fractions of $B_c^+ \to J/\psi b_1(1235)^+ (a_0(980)^+, a_0(1450)^+, a_2(1320)^+)$ and $B_c^+ \to J/\psi \pi^+$ could further examine the reliability of this iPQCD formalism. Because of containing only tree-level $\bar b \to \bar c$ transitions, the {\it CP} asymmetries in the $B_c^+ \to J/\psi M^+$ decays exhibit naturally zero.