K^-d → πΛN reaction with in-flight kaons for studying the ΛN interaction

We calculate the different cross sections of K^- d → π^-Λp and K^- d → π⁰Λn reactions in order to study the difference between low energy Λp and Λn interactions. The reactions contain scattering of Λp and Λn in the final-state interactions. We can detect low-energy behavior of the ΛN interaction when we focus on the different cross sections near the ΛN mass thresholds. The calculations have been performed for in-flight kaons with a momentum of 1000 Mev/c. We suppress the background processes using the angular restriction to forward imposed on the outgoing pions. This restriction also serves as the spin selection rule, where the spin triplet state of ΛN interaction becomes dominant. The amplitudes are constructed using the meson-baryon and baryon-baryon scattering amplitudes and deuteron wave function. We employ the chiral unitary amplitude obtained from partial wave analysis up to p-wave as the meson-baryon amplitude, and the effective-range expansion, taking into account the spin-flip term, as the baryon-baryon amplitude. To investigate the impact of the inequality in the low-energy behavior of Λp and Λn, we set two parameters: the ratio of the scattering length between Λn and Λp and the ratio of the effective range. We obtain the differential cross section ratio of π⁰Λn to π^-Λp as a function of the ΛN invariant mass when varying these parameters.