Nucleon decays are an excellent way to explore new physics beyond the standard model. In this talk, I would like to discuss the implications of the following two processes of neutron decays; 1. Invisible decays of neutrons, 2. Decay of a neutron to a kaon and a charged lepton. Since these are not the primary channels suggested by theories such as GUTs, they have not received much attention; however, they could offer interesting clues regarding new physics.
If time permits, I would also like to discuss a scenario that relaxes the stringent constraints on neutrino masses derived from recent cosmological observations (which is a topic unrelated to neutron decays though).