Probing new neutral gauge bosons with CEvNS and neutrino-electron scattering

The potential for probing extra neutral gauge boson mediators ($Z^\prime$) from low-energy measurements is comprehensively explored. Our study mainly focuses on $Z^\prime$ mediators present in string-inspired $E_6$ models and left-right symmetry. We estimate the sensitivities of coherent-elastic neutrino-nucleus scattering (CE$\nu$NS) and neutrino-electron scattering experiments. Our results indicate that such low-energy high-intensity measurements can provide a valuable probe, complementary to high-energy collider searches and electroweak precision measurements.