We introduce a model for Non-Standard neutral current Interaction (NSI)
between neutrinos and the matter fields, with an arbitrary coupling to the up
and down quarks. The model is based on a new U(1) gauge symmetry with a light
gauge boson that mixes with the photon. We show that the couplings to the u
and d quarks can have a ratio such that the contribution from NSI to the
Coherent Elastic Neutrino-Nucleus Scattering (CEνNS) amplitude vanishes,
relaxing the bound on the NSI from the CEνNS experiments. Additionally, the
deviation of the measured value of the anomalous magnetic dipole moment of the
muon from the standard-model prediction can be fitted. The most limiting
constraints on our model come from the search for the decay of the new gauge
boson to e−e+ and invisible particles, carried out by NA48/2 and NA64,
respectively. We show that these bounds can be relaxed by opening up the decay
of the new gauge boson to new light scalars that eventually decay into the e−e+ pairs. We show that there are ranges that can lead to both a solution to
the (g−2)μ anomaly and values of ϵμμ=ϵττ large enough to be probed by future solar neutrino experiments.Comment: 13+4 pages, 4 figures. V2 matches the published version in PR