Production cross sections of ${}_{\Lambda }^{3,4}$H bound states in ${}^{3,4}$He($K^{-}$, ${\pi }^0$) reactions at 1 GeV/$c$

Abstract

We investigate theoretically productions of ${}_{\Lambda }^{3,4}$H bound states in the exothermic ($K^{-}$, ${\pi }^0$) reactions on ${}^{3,4}$He targets at $p_{K^{-}}=$ 1.0 GeV/c in a distorted-wave impulse approximation with the optimal Fermi-averaging $K^{-}p\to {\pi }^0\Lambda$ $t$ matrix. We calculate angular distributions of the laboratory differential cross sections $d\sigma /d{\Omega }_{\mathrm{lab}}$ and the integrated cross sections ${\sigma }_{\mathrm{lab}}$ for a $J^P=0^{+}$ ground state and a $J^P=1^{+}$ excited state of ${}_{\Lambda }^4$H at ${\pi }^0$ forward-direction angles of ${\theta }_{\mathrm{lab}}=$ 0${}^{\circ }$-20${}^{\circ }$, and those for a $J^P=1/2^{+}$ ground state of ${}_{\Lambda }^3$H. The production of a $J^P=3/2^{+}$ excited state of ${}_{\Lambda }^3$H as a virtual state is also evaluated. The comparison in $d\sigma /d{\Omega }_{\mathrm{lab}}$ and ${\sigma }_{\mathrm{lab}}$ between ${}_{\Lambda }^4$H and ${}_{\Lambda }^3$H provides examining the mechanism of the production and structure of ${}_{\Lambda }^{3,4}$H, as well as in the endothermic (${\pi }^{-}$, $K^0$) reactions at $p_{{\pi }^{-}}=$ 1.05 GeV/c. This investigation confirms the feasibility of lifetime measurements of ${}_{\Lambda }^3$H at the J-PARC experiments.

Comments: 22 pages, 5 figures, 4 tables