Sensitivity of the ${}^{3,4}$He($K^{-}$, ${\pi }^0$) production ratio to the $\Lambda$ binding energy of ${}_{\Lambda }^3$H

Abstract

We study the production of ${}_{\Lambda }^3$H and ${}_{\Lambda }^4$H in the ${}^{3,4}$He($K^{-}$,${\pi }^0$) reactions at $p_{K^{-}}=1.0$~GeV/$c$ within the distorted-wave impulse approximation, using the optimal Fermi-averaged $K^{-}p\to {\pi }^0\Lambda$ amplitude. Because the ${}_{\Lambda }^3$H ground state is extremely weakly bound, the $d$--$\Lambda$ wave function becomes spatially extended. We calculate the integrated cross sections ${\sigma }_{\mathrm{lab}}$ and their ratio $R_{34}={\sigma }_{\mathrm{lab}}{(}_{\Lambda }^3\mathrm{H})/{\sigma }_{\mathrm{lab}}{(}_{\Lambda }^4\mathrm{H})$ for forward angles ${\theta }_{\mathrm{lab}}=0^{\circ }$--$20^{\circ }$. The production strength of ${}_{\Lambda }^3$H and the ratio $R_{34}$ are strongly sensitive to the $\Lambda$ binding energy $B_{\Lambda }$, which is constrained to be approximately 0.05--0.15~MeV by comparison with experimental data from the J-PARC E73 experiment. This indicates that the ${}^3$He($K^{-}$,${\pi }^0$) reaction provides a sensitive probe of the weak binding of ${}_{\Lambda }^3$H.

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