Study of $\Lambda p$ and $\bar{\Lambda} p$ scatterings via quasipotential Bethe-Salpeter equation

Abstract

Motivated by recent BESIII measurements of the $\Lambda p \to \Lambda p$ and $\bar{\Lambda} p \to \bar{\Lambda} p$ scattering processes, we investigate these reactions within the framework of the quasipotential Bethe-Salpeter equation using an effective Lagrangian approach. The interaction potentials are constructed via a one-boson-exchange model incorporating pseudoscalar, scalar, and vector meson exchanges, along with coupled-channel effects from the $\Sigma N$ and $\bar{\Sigma} N$ channels. For the $\Lambda p \to \Lambda p$ reaction, the total cross sections from threshold up to $\sqrt{s} = 2.5~\text{GeV}$ are well reproduced. A mild enhancement near the $\Sigma N$ threshold is attributed to coupled-channel dynamics. Using parameters constrained by the total cross section data, our model also predicts differential cross sections at $\sqrt{s} = 2.24~\text{GeV}$, which exhibit weak angular dependence, consistent with experimental observations. Partial-wave analysis indicates that the $1^+$ partial wave dominates over the entire energy range, while the $0^+$ wave plays a significant role near threshold. For the $\bar{\Lambda} p \to \bar{\Lambda} p$ reaction, our predicted total cross sections show good agreement with the BESIII data. The $1^-$ partial wave is found to dominate in most of the energy region. Notably, the calculated differential cross sections exhibit a strong forward peaking behavior, consistent with experimental findings and understood as resulting from constructive interference among various partial waves. This forward-peaked angular distribution persists across a range of energies, highlighting the distinct dynamics of the $\bar{\Lambda} p$ interaction.