Three-body analysis reveals the significant contribution of minor ${}^5$He $s$-wave component in ${}^6$Li$(p,2p{)}^5$He cross section

${}^6$Li is usually treated as an $\alpha +p+n$ three-body system, and the validity of this picture is important for understanding ${}^6$Li reactions. The ($p$,$2p$) reaction is a powerful method to study the structure of valence nucleons in ${}^6$Li. Recently, the new experimental data of the ${}^6$Li($p$,$2p$)${}^5$He reaction have been obtained and should be analyzed. We investigate the ${}^6$Li($p$,$2p$)${}^5$He reaction using the $\alpha +p+n$ three-body wave function of ${}^6$Li and study the validity of this model. We calculate the ${}^6$Li wave function by using Gaussian expansion method, and the function is used to obtain the relative wave function between $p$ and ${}^5$He. We combine the relative wave function with the distorted wave impulse approximation. Our results reproduce the experimental data of the triple differential cross section within about 10% difference in the absolute values, and contributions from both $p$- and $s$-wave states of ${}^5$He in ${}^6$Li are found to be important. We can qualitatively understand the ${}^6$Li($p$,$2p$)${}^5$He reaction by describing ${}^6$Li with the three-body model. Contribution from the $s$-wave component is important in reproducing the experimental data in the zero recoil-momentum region.