  Using the general connection between the upper limit on the neutrino mass and
the upper limits on certain types of non-Standard Model interaction that can
generate loop corrections to the neutrino mass, we derive constraints on some
non-Standard Model $d\to ue^-\bar{\nu}$ interactions. When cast into limits on
$n\to pe^-\bar{\nu}$ coupling constants, our results yield constraints on
scalar and tensor weak interactions improved by more than an order of magnitude
over the current experimental limits. When combined with the existing limits,
our results yield $|C_S/C_V|\alt 5\times 10^{-3}$, $|C'_S/C_V|\alt 5\times
10^{-3}$, $|C_T/C_A| \alt 1.2\times 10^{-2}$ and $|C'_T/C_A| \alt 1.2\times
10^{-2}$.
