  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 B decay anomalies, and that in a model
framework the constraints from neutrino scattering can have implications for
these anomalies.
