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We present the constraints on the parameters of several light boson mediatormodels obtained from the analysis of the current data of the COHERENT CE$\nu$NSexperiment. We consider a variety of vector boson mediator models: theso-called universal, the $B-L$ and other anomaly-free $U(1)'$ gauge models withdirect couplings of the new vector boson with neutrinos and quarks, and theanomaly-free $L_e-L_\mu$, $L_e-L_\tau$, and $L_\mu-L_\tau$ gauge models wherethe coupling of the new vector boson with the quarks is generated by kineticmixing with the photon at the one-loop level. We consider also a model with anew light scalar boson mediator that is assumed, for simplicity, to haveuniversal coupling with quarks and leptons. Since the COHERENT CE$\nu$NS dataare well-fitted with the cross section predicted by the Standard Model, theanalysis of the data yields constraints for the mass and coupling of the newboson mediator that depend on the charges of quarks and neutrinos in each modelunder consideration. We compare these constraints with the limits obtained inother experiments and with the values that can explain the muon $g-2$ anomalyin the models where the muon couples to the new boson mediator.

Probing light mediators and $(g-2)_{\mu}$ through detection of coherent elastic neutrino nucleus scattering at COHERENT