Can we improve theντmass limit from the decay τ→lν¯lντ?

Abstract

In this paper, we discuss the possibility of improving the present limits on the ${\nu }_{\tau }$ mass by studying the end point of the charged-lepton energy spectrum in the decay τ→lν${¯}_l$ ${\nu }_{\tau }$. We compute a general expression for the τ differential decay rate in the laboratory system, assuming that neither the ${\nu }_{\tau }$ nor the charged-lepton masses are zero. From this expression we extract the influence of the τ-neutrino mass on the $e^{\mathrm{-}}$ energy spectrum in the case τ→eν${¯}_e$ ${\nu }_{\tau }$. We show that this influence is only important near the very end point of the electron energy spectrum (i.e., for x>0.99 where x=2$E_e$/$m_{\tau }$) and consider what luminosity and experimental resolutions are needed to improve the current ${\nu }_{\tau }$ mass limit. We also consider the decay τ→μν${¯}_{\mu }$ ${\nu }_{\tau }$ and show that it is less suited for our purposes since the μ mass causes the influence of the ${\nu }_{\tau }$ mass to be less important. We conclude that, from the study of the decay τ→lν${¯}_l$ ${\nu }_{\tau }$, an upper bound for the ${\nu }_{\tau }$ mass of the order of 20–40 MeV can easily be achieved by proposed experiments while an upper bound of the order of 1 MeV would require a luminosity and detector resolution which are out of the reach of such experiments.