Title: An improved perturbative QCD study of the decays $B_c^+ \to η_c L^+$ Show Chinese title

Title: 对衰变$B_c^+ \to η_c L^+$的改进微扰QCD研究

Abstract: We perform an improved perturbative QCD study of the decays $B_c^+ \to \eta_c L^+$ ($L$ denotes the light ground state pseudoscalar, vector mesons and the corresponding $p$-wave scalar, axial-vector, and tensor ones) and predict their branching ratios (BRs) associated with relative ratios at leading order in the strong coupling $\alpha_s$. Our results ${\rm BR}(B_c^+ \to \eta_c \pi^+) =(2.03^{+0.53}_{-0.41}) \times 10^{-3}$ and ${\rm BR}(B_c^+ \to \eta_c \pi^+)/{\rm BR}(B_c^+ \to J/\psi \pi^+) = 1.74^{+0.66}_{-0.50}$ are consistent with several available predictions in different approaches within uncertainties. Inputting the measured $\eta_c \to p\bar p$ and $\eta_c \to \pi^+\pi^- (\pi^+\pi^-, K^+ K^-, p\bar p)$ BRs with $p$ here being a proton, we derive the multibody $B_c^+ \to \eta_c (\pi, \rho)^+$ BRs through secondary decay chains via resonance $\eta_c$ under the narrow-width approximation, which might facilitate the (near) future tests of $B_c \to \eta_c$ decays. Under the $q\bar q$ assignment of light scalars, different to $B_c$ decaying into $J/\psi$ plus a scalar meson and other $B_c^+ \to \eta_c L^+$ modes, surprisingly small BRs around ${\cal O}(10^{-7}-10^{-9})$ of $\Delta S =0$ modes and highly large ratios near ${\cal O}(10^{2})$ between the BRs of $\Delta S=1$ and $\Delta S=0$ modes are found in the $B_c$ decays to $\eta_c$ plus light scalars. Many large BRs and interesting ratios presented in this work could be tested at the LHC experiments, which would help us to examine the reliability of this improved perturbative QCD formalism for $B_c$-meson decays and further understand the QCD dynamics in the considered decay modes, as well as in the related hadrons. Show Chinese abstract

Abstract: 我们对衰变$B_c^+ \to \eta_c L^+$（$L$表示轻的基态伪标量、矢量介子和相应的$p$波标量、轴矢量和张量介子）进行改进的微扰QCD研究，并预测其与强耦合常数$\alpha_s$的相对比值在主导阶次下的分支比（BRs）。 我们的结果${\rm BR}(B_c^+ \to \eta_c \pi^+) =(2.03^{+0.53}_{-0.41}) \times 10^{-3}$和${\rm BR}(B_c^+ \to \eta_c \pi^+)/{\rm BR}(B_c^+ \to J/\psi \pi^+) = 1.74^{+0.66}_{-0.50}$在不确定度范围内与不同方法中的几个可用预测一致。 输入测量的$\eta_c \to p\bar p$和$\eta_c \to \pi^+\pi^- (\pi^+\pi^-, K^+ K^-, p\bar p)$BRs，其中$p$是质子，我们通过共振$\eta_c$在窄宽度近似下通过二级衰变链推导出多体$B_c^+ \to \eta_c (\pi, \rho)^+$BRs，这可能有助于 (近) 未来对$B_c \to \eta_c$衰变的测试。 在光标量的$q\bar q$分配下，不同于$B_c$衰变为$J/\psi$加上一个标量介子和其他$B_c^+ \to \eta_c L^+$模式，发现在$B_c$衰变到$\eta_c$加上轻标量时，围绕${\cal O}(10^{-7}-10^{-9})$的$\Delta S =0$模式的 BRs 非常小，而$\Delta S=1$和$\Delta S=0$模式的 BRs 之间的比率接近${\cal O}(10^{2})$非常大。 许多大的BRs和有趣的比值在本工作中提出，可以在LHC实验中进行测试，这将有助于我们检验这种改进的微扰QCD形式在$B_c$-介子衰变中的可靠性，并进一步理解所考虑衰变模式以及相关强子中的QCD动力学。