We examine current constraints on and the future sensitivity to the strength of couplings between quarks and neutrinos in the presence of a form factor generated from loop effects of hidden sector particles that interact with quarks via new interactions. We consider models associated with either vector or scalar interactions of quarks and leptons generated by hidden sector dynamics. We study constraints on these models using data from coherent elastic neutrino-nucleus scattering and solar neutrino experiments and demonstrate how these new interactions may be discovered by utilizing the recoil spectra. We show that our framework can be naturally extended to explain the lepton universality violating neutral current
Bdecay anomalies, and that in a model framework the constraints from neutrino scattering can have implications for these anomalies.