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

TL;DR

This paper theoretically investigates the production cross sections of $^{3,4}_ ext{Lambda}$H hypernuclei in ($K^-$, $ ext{pi}^0$) reactions on helium targets at 1 GeV/$c$, providing insights into their structure and production mechanisms.

Contribution

It introduces a detailed theoretical model for hypernuclei production in ($K^-$, $ ext{pi}^0$) reactions, including angular distributions and cross sections, aiding future experimental measurements.

Findings

Calculated angular distributions and cross sections for hypernuclei production.

Demonstrated the feasibility of lifetime measurements of $^3_ ext{Lambda}$H at J-PARC.

Provided insights into the production mechanisms and structure of hypernuclei.

Abstract

We investigate theoretically productions of $^{3,4}_\Lambda$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 $d\sigma/d\Omega_{\rm lab}$ and the integrated cross sections $\sigma_{\rm lab}$ for a $J^P= 0^+$ ground state and a $J^P=1^+$ excited state of $^4_\Lambda$H at $\pi^0$ forward-direction angles of $\theta_{\rm lab}=$ 0$^\circ$-20$^\circ$, and those for a $J^P= 1/2^+$ ground state of $^3_\Lambda$H. The production of a $J^P=3/2^+$ excited state of $^3_\Lambda$H as a virtual state is also evaluated. The comparison in $d\sigma/d\Omega_{\rm lab}$ and $\sigma_{\rm lab}$ between $^4_\Lambda$H and $^3_\Lambda$H provides examining the mechanism of the production and structure of $^{3,4}_\Lambda$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 $^3_\Lambda$H at the J-PARC experiments.