K(-)d -> pi Lambda N reaction for studying charge symmetry breaking in the Lambda N interaction

We propose to utilize the K(-)d -> pi(-) Lambda p and K- d -> pi(0) Lambda n reactions in order to investigate the difference between the low-energy Lambda p and Lambda n interactions. In these reactions, the Lambda p and Lambda n scatterings appear as final state interactions. We calculate the differential cross sections of these reactions with stopped kaons theoretically. We introduce isospin breaking by using the physical masses for the participating hadrons and through the chiral unitary amplitudes for K- N -> pi N and K- N -> (K) over barN. With stopped kaons, the Lambda N interaction takes place dominantly in the spin-triplet state thanks to the deuteron spin and s-wave dominance of the scattering amplitudes at low energy. We find that the ratio of the Lambda N invariant mass spectra of these reactions is useful for revealing qualitative properties of charge symmetry breaking in the low-energy Lambda N interaction. We also find that the contributions coming from the pi and Sigma exchange diagrams which have pi N final state interaction and Sigma N -> Lambda N conversion, respectively, are negligibly small around the Lambda N threshold, while the contributions from the impulse diagram without final state interactions and the (K) over bar exchange diagram containing the pi Lambda final state interaction are main sources of the background.