Cosmological constraints on R-parity violation from neutrino decay

If the neutrino mass is non-zero, as hinted by several experiments, then R-parity-violating supersymmetric Yukawa couplings can drive a heavy neutrino decay into lighter states. The heavy neutrino may either decay radiatively into a lighter neutrino, or it may decay into three light neutrinos through a Z-mediated penguin. For a given mass of the decaying neutrino, we calculate its lifetime for the various modes, each mode requiring certain pairs of R-parity-violating couplings be non-zero. We then check whether the calculated lifetimes fall in zones allowed or excluded by cosmological requirements. For the latter case, we derive stringent new constraints on the corresponding products of R-parity-violating couplings for given values of the decaying neutrino mass.