  Neutrinophilic mediators are well-motivated messenger particles that can
probe some of the least known sectors of fundamental physics involving
nonstandard interactions of neutrinos with themselves and potentially with dark
matter. In particular, light mediators coupling to the active neutrinos will
induce new decay modes of the Standard Model mesons (e.g., $\pi^\pm, K^\pm \to
\ell^\pm + \nu + \phi$), charged leptons (e.g., $\tau^\pm \to \pi^\pm + \nu +
\phi$), and gauge bosons (e.g., $Z \to \nu + \bar{\nu} + \phi$). A common lore
is that these decays suffer from infrared divergences in the limit of the
vanishing mediator mass, i.e., $m_\phi \to 0$. Here, we show for the first time
that including the 1-loop contributions of these mediators to the standard
2-body decays (e.g., $\pi^\pm,\,K^\pm \to \ell^\pm + \nu$, etc.), the infrared
divergence from the 3-body decay cancels out exactly by virtue of the
Kinoshita-Lee-Nauenberg theorem. Including these cancellation effects, we then
update the existing laboratory constraints on neutrinophilic scalar mediators,
thereby extending the limits far beyond the decaying parent particle mass and
excluding a wider range of parameter space. These new "physical" limits derived
here have significant implications for the future detection prospects of
nonstandard neutrino (self-)interactions.
