Neutrino-Mass Limits fromK+→π+νν―Decay

The present limit on the mass of the tau neutrino ($m_{{\nu }_{\tau }}<143\mathrm{}$ MeV), obtained from tau decay, may be lowered significantly from a study of the pion spectrum in $K^{+}\to {\pi }^{+}\nu \bar{\nu }$. We show that if $m_{{\nu }_{\tau }}\gtrsim 50$ MeV then the pion spectrum differs significantly from its value when all neutrinos are massless. Our results are also applicable to any new massive neutrino with $50\lesssim m_{{\nu }_h}\lesssim 150$ MeV.