  The appearance of some papers dealing with the $K^- d \to \pi \Sigma n$
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 with high precision to make accurate predictions for the experiment and
extract from there the relevant physical information. 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.
Predictions for the experiment are done as well as spectra with the integrated
neutron angle.
