$K^- d\rightarrow πΛN$ reaction for studying charge symmetry breaking in the $ΛN$ interaction

Abstract

We discuss charge symmetry breaking in the ΛN interaction. In order to investigate the Λp and Λn interactions at low energies, we propose to utilize the K − d → π − Λp and K − d → π 0 Λn reactions. They are symmetric under the exchange of both the pion and nucleon isospin partners in the final states. This advantage allows us to study charge symmetry breaking in the ΛN interaction. We calculate the differential cross sections of these reactions with stopped kaons theoretically and discuss the possibility to extract the scattering length and effective range of the ΛN scattering. With stopped kaons, the ΛN interaction takes place dominantly in the spin-triplet state thanks to the deuteron spin and s-wave dominance of the scattering amplitudes at the low energy. We find that the ratio of the differential cross sections as a function of the ΛN invariant mass between the two reactions is useful for revealing how charge symmetry breaking, or isospin symmetry breaking appears in the low-energy ΛN scattering.