A search for $B_{s0}^{*}$ and $B^{*}_{s1}$ through the $K^{-}p$ interaction

Abstract

Studying heavy-quark hadrons is crucial due to the nonperturbative nature of low-energy QCD, with Heavy-Quark Symmetry (HQS) serving as a key framework for understanding their spin and flavor symmetries. However, a key issue is that the theoretically expected $B^{(*)}\bar{K}$ molecular states have not yet been observed, although they are considered the bottom-quark counterparts of the observed $\bar{D}^{(*)}\bar{K}$ molecular states (corresponding to $D_{s0}(2317/2460)^{-}$), which challenges the universality of HQS. The main goal of this work is to search for the theoretically predicted $B\bar{K}$ and $B^{*}\bar{K}$ molecular states, namely $B_{s0}^{*}(5725)$ and $B_{s1}^{*}(5778)$, via the reactions $K^{-}p \to \Lambda_{b}^{0} B_{s0}^{*}$ and $K^{-}p \to \Lambda_{b}^{0} B_{s1}^{*}$. Within an effective Lagrangian framework, we compute the relevant cross sections, considering $t$-channel $B^{(*)}$ exchanges and $K^{-}p$ initial-state interactions (ISI). The results show that the production cross sections of $B_{s0}^{*}(5725)$ and $B_{s1}^{*}(5778)$ can reach the order of 0.01~nb, and we suggest that experiments searching for $B_{s0}^{*}(5725)$ are best performed at $P_{K^{-}} = 12.18~\mathrm{GeV}$, while higher energies are most favorable for producing $B_{s1}^{*}(5778)$. The ISI play a crucial role, as they not only significantly enhance the production cross sections of $B_{s0}^{*}(5725)$ and $B_{s1}^{*}(5778)$ (by roughly one order of magnitude) but also markedly affect the angular distributions of the produced particles. We also calculated the production cross sections of the conventional quark-antiquark states $B_{s0}^*(5700)$ and $B_{s1}^*(5720)$, which are found to be nearly the same as those of $B_{s0}^{*}(5725)$ and $B_{s1}^{*}(5778)$. Although their internal structures remain ambiguous, these results can inform future experimental searches at CERN and J-PARC.