Neutrino Self-interaction and Weak Mixing Angle Measurements

Neutrino self-interaction with a larger ``Fermi constant'' is often resorted to for understanding various puzzles of our universe. We point out that a light, neutrinophilic scalar particle $\phi$ through radiative correction leads to an energy-scale dependence in the neutrino-$Z$-boson gauge coupling. The driver behind this phenomenon is a large separation between the mass scales of $\phi$ and additional heavy particles needed for gauge invariance. This is a generic effect insensitive to details of the UV completion. We show that the running can change the $Z\nu\bar\nu$ coupling by several percent and affect the measurement of weak mixing angle through neutrino neutral-current processes. We discuss the interplay between the running of the $Z\nu\bar\nu$ coupling and $\sin^2\theta_W$ in various experimental observables. It is possible to disentangle the two effects with more than one precise measurement.