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Using $(10.087\pm0.044)\times10^{9}$ $J/\psi$ events collected with theBESIII detector at the BEPCII storage ring, the processes $\Lambdap\rightarrow\Lambda p$ and $\bar{\Lambda}p\rightarrow\bar{\Lambda}p$ arestudied, where the $\Lambda/\bar{\Lambda}$ baryons are produced in the process$J/\psi\rightarrow\Lambda\bar{\Lambda}$ and the protons are the hydrogen nucleiin the cooling oil of the beam pipe. Clear signals are observed for the tworeactions. The cross sections in$-0.9\leq\rm{cos}\theta_{\Lambda/\bar{\Lambda}}\leq0.9$ are measured to be$\sigma(\Lambda p\rightarrow\Lambdap)=(12.2\pm1.6_{\rm{stat}}\pm1.1_{\rm{sys}})$ mb and $\sigma(\bar{\Lambda}p\rightarrow\bar{\Lambda} p)=(17.5\pm2.1_{\rm{stat}}\pm1.6_{\rm{sys}})$ mb atthe $\Lambda/\bar{\Lambda}$ momentum of $1.074$ GeV/$c$ within a range of$\pm0.017$ GeV/$c$, where the $\theta_{\Lambda/\bar{\Lambda}}$ are thescattering angles of the $\Lambda/\bar{\Lambda}$ in the $\Lambdap/\bar{\Lambda}p$ rest frames. Furthermore, the differential cross sections ofthe two reactions are also measured, where there is a slight tendency offorward scattering for $\Lambda p\rightarrow\Lambda p$, and a strong forwardpeak for $\bar{\Lambda}p\rightarrow\bar{\Lambda}p$. We present an approach toextract the total cross sections by extrapolation. The study of$\bar{\Lambda}p\rightarrow\bar{\Lambda}p$ represents the first study ofantihyperon-nucleon scattering, and these new measurements will serve asimportant inputs for the theoretical understanding of the (anti)hyperon-nucleoninteraction.

First study of antihyperon-nucleon scattering  $\bar{\Lambda}p\rightarrow\bar{\Lambda}p$ and measurement of $\Lambda  p\rightarrow\Lambda p$ cross section