AI 中文总结
本研究在Bethe-Salpeter框架下改进协变分析方法，研究$B_c^+$到$\u03c7_{c1}(nP)$的弱衰变，指出半轻衰变道更易探测$\u03c7_{c1}(3872)$，为LHCb实验和厘清其性质提供指导。
AI 中文摘要
我们在Bethe-Salpeter（贝特-萨尔佩特）形式框架下研究弱衰变 $B_c^+\to\beta_{c1}(nP)\u2113^+ \u03bd_{\u2113}$ 和 $B_c^+\to\beta_{c1}(nP)X$（n=1,2,3），将 $\u03c7_{c1}(3872)$ 视为常规的 $\u03c7_{c1}(2P)$ 粲偶素。我们改进了协变强子跃迁振幅，以在末态静止系中自洽地计算末态波函数，从而能够可靠描述高激发粲偶素相关的大反冲过程和显著的相对论修正。我们的结果为通过 $B_c$ 衰变探测 $\u03c7_{c1}(3872)$ 的内部结构提供了新平台。尽管LHCb对 $B_c^+\to\beta_{c1}(3872)\u03c0^+$ 的搜寻仅得到上限，但我们证明这主要是由于亮度不足，要得到确定性观测结果，所需的 $B_c$ 数据样本量约为当前的20倍。相比之下，我们发现半轻衰变模式 $B_c^+\to\beta_{c1}(3872)\u03bc^+\u03bd_\u03bc$ 是更具前景的衰变道，仅需现有数据集的两倍数据即可探测到。我们的预言为即将开展的LHCb分析提供了具体指导，并补充了当前为厘清 $\u03c7_{c1}(3872)$ 性质所做的努力。
英文摘要
We study the weak decays $B_c^+\toχ_{c1}(nP)\ell^+ ν_{\ell}$ and $B_c^+\toχ_{c1}(nP)X$ (n=1,2,3) within the Bethe-Salpeter formalism, treating $χ_{c1}(3872)$ as the conventional $χ_{c1}(2P)$ charmonium. We upgrade the covariant hadronic transition amplitude to consistently evaluate the final-state wave function in its rest frame, enabling a reliable description of large-recoil processes and sizable relativistic corrections pertinent to highly excited charmonium. Our results provide a novel platform to probe the internal structure of $χ_{c1}(3872)$ via $B_c$ decays. While the LHCb search for $B_c^+\toχ_{c1}(3872)π^+$ yielded only an upper limit, we demonstrate that this is primarily due to insufficient luminosity, approximately 20 times the current $B_c$ data sample would be required for a definitive observation. In contrast, we identify the semileptonic mode $B_c^+\toχ_{c1}(3872)μ^+ν_μ$ as a far more promising channel, which could become accessible with merely twice the existing data set. Our predictions offer concrete guidance for upcoming LHCb analyses and complement ongoing efforts to resolve the nature of $χ_{c1}(3872)$.
Comments24 pages, 6 figures
