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The cross section for coherent elastic neutrino-nucleus scattering(CE$\nu$NS) depends on the response of the target nucleus to the externalcurrent, in the Standard Model (SM) mediated by the exchange of a $Z$ boson.This is typically subsumed into an object called the weak form factor of thenucleus. Here, we provide results for this form factor calculated using thelarge-scale nuclear shell model for a wide range of nuclei of relevance forcurrent CE$\nu$NS experiments, including cesium, iodine, argon, fluorine,sodium, germanium, and xenon. In addition, we provide the responses needed tocapture the axial-vector part of the cross section, which does not scalecoherently with the number of neutrons, but may become relevant for the SMprediction of CE$\nu$NS on target nuclei with nonzero spin. We then generalizethe formalism allowing for contributions beyond the SM. In particular, westress that in this case, even for vector and axial-vector operators, thestandard weak form factor does not apply anymore, but needs to be replaced bythe appropriate combination of the underlying nuclear structure factors. Weprovide the corresponding expressions for vector, axial-vector, but also(pseudo-)scalar, tensor, and dipole effective operators, includingtwo-body-current effects as predicted from chiral effective field theory.Finally, we update the spin-dependent structure factors for dark matterscattering off nuclei according to our improved treatment of the axial-vectorresponses.

Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses