Loop effect with vector mediator in the coherent neutrino-nucleus scattering

The observation of the coherent elastic neutrino-nucleus scattering (CE$\nu$NS) provides us opportunities to explore a wide class of new physics. In the Standard Model (SM), the CE$\nu$NS process arises from the vector and axial-vector neutral currents through the exchange of $Z$ boson and the axial-vector current contribution turns out to be subdominant. It is thus natural to consider the extra contributions to CE$\nu$NS from more generic new physics beyond the SM with (axial-)vector interactions associated with a new vector mediator $Z'$. Besides the ordinary CE$\nu$NS, the active neutrinos can convert into a new exotic fermion $\chi$ through the process $\nu N\to \chi N$ mediated by $Z'$ without violating the coherence. It would be interesting to consider the implication of this conversion for the new fermion sector beyond the SM. We consider the framework of a simplified neutrino model in which a new Dirac fermion $\chi$ interacts with active neutrinos and a leptophobic vector mediator $Z'$. We evaluate both the tree-level and loop-level contributions to the CE$\nu$NS and in particular the loop diagrams produce active neutrino elastic scattering process $\nu N\to \nu N$ with the fermion $\chi$ inside the loops. When the interaction between $Z'$ and the SM quarks is vector type and axial-vector type, the CE$\nu$NS processes are respectively dominated by the tree-level and loop-level contributions. We investigate the constraints on the model parameters by fitting to the COHERENT data, assuming a wide range of $m_\chi$. The parameter space with $m_\chi$ larger than the maximal energy of incoming neutrinos can be constrained by including the loop-level contribution. More importantly, the inclusion of loop diagrams can place constraint on axial-vector interaction whose tree-level process is absent in the coherent neutrino-nucleus scattering.