The K-d → πΣn reaction revisited

The appearance of some papers dealing with the K(-)d -> pi Sigma n reaction, with some discrepancies in the results and a proposal to measure the reaction at forward n angles at J-PARC justifies to retake the theoretical study of this reaction. We do this in the present paper showing results using the Watson approach and the truncated Faddeev approach. We argue that the Watson approach is more suitable to study the reaction because it takes into account the potential energy of the nucleons forming the deuteron, which is neglected in the truncated Faddeev approach. The paper shows the strength and limitations of both approaches and we perform calculations using four different approximations. Comparison of the results shows that the truncated Faddeev approach produces a strong asymmetry between the energy of the two nucleons of the deuteron, while in the Watson approach this energy is equally shared. From the experimental point of view the results are very valuable since they show that the different approximations share the feature that the peak of the pi Sigma mass distribution is drastically shifted in the presence of the Lambda(1405). Additionally, we also show that in the angle-integrated cross section the threshold cusp effects are basically washed away and all approximations show a clear shape of the Lambda(1405). In this sense, measurements of all these magnitudes in different K- energies are bound to bring new information that sheds new light on the properties and nature of the Lambda(1405) resonance.