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We study the impact of non-standard neutrino interactions in the context of anew gauge boson $Z'$ in neutral-current deep-inelastic scattering performed inForwArd Search ExpeRiment-$\nu$ (FASER$\nu$) and in monojet production at theLarge Hadron Collider (LHC). We simulate the neutral-current deep-inelasticneutrino-nucleon scattering $\nu N \rightarrow \nu N$ at FASER$\nu$ in thepresence of an additional $Z'$ boson, and estimate the anticipatedsensitivities to the gauge coupling in a wide range of $Z'$ mass. At the LHC,we study the effect of $Z'$ on monojet production, which can be enhanced inregions with large missing transverse momenta. We then use the recent resultsfrom ATLAS with an integrated luminosity of 139 fb$^{-1}$ to improve the limitson the gauge coupling of $Z'$. We interpret such limits on $Z'$ gauge couplingsas bounds on effective non-standard neutrino interactions. We show that theFASER$\rm \nu$ and the LHC results cover the medium and high energy scales,respectively, and complement one another.

Non-standard Neutrino and $Z'$ Interactions at the FASER$\nu$ and the LHC