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In this work we study the current bounds from the CE{\nu}NS process and mesoninvisible decays on generic neutrino interactions with sterile neutrinos ineffective field theories. The interactions between quarks and left-handed SMneutrinos and/or right-handed neutrinos are first described by the low-energyeffective field theory (LNEFT) between the electroweak scale and the chiralsymmetry breaking scale. We complete the independent operator basis for theLNEFT up to dimension-6 by including both the lepton-number-conserving (LNC)and lepton-number-violating (LNV) operators involving right-handed neutrinos.We translate the bounds on the LNEFT Wilson coefficients from the COHERENTobservation and calculate the branching fractions of light meson invisibledecays. The bounds on LNEFT are then mapped onto the SM effective field theorywith sterile neutrinos (SMNEFT) to constrain new physics above the electroweakscale. We find that the meson invisible decays can provide the only sensitiveprobe for {\tau} neutrino flavor component and s quark component in thequark-neutrino interactions involving two (one) active neutrinos and for theeffective operators without any active neutrino fields. The CE{\nu}NS processplaces the most stringent bound on all other Wilson coefficients. By assumingone dominant Wilson coefficient at a time in SMNEFT and negligible sterileneutrino mass, the most stringent limits on the new physics scale are 2.7 - 10TeV from corresponding dipole operator in LNEFT and 0.5 - 1.5 TeV fromneutrino-quark operator in LNEFT.

General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays