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The super-weak force is a minimal, anomaly-free U(1) extension of thestandard model (SM), designed to explain the origin of (i) neutrino masses andmixing matrix elements, (ii) dark matter, (iii) cosmic inflation, (iv)stabilization of the electroweak vacuum and (v) leptogenesis. We discuss theneutrino sector of this model in detail and study the allowed parameter spaceof the neutrino Yukawa matrices and mixing matrix elements. The model generatesnonstandard neutrino interactions, whose allowed experimental limits are usedto constrain the parameter space of the model. We provide benchmark points inthe relevant parameter space that fall within the sensitivity region of theSHiP and MATHUSLA experiments.

Experimental constraints on the neutrino and gauge parameters of the super-weak U(1) extension of the standard model