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The recent confirmation by FNAL of the $(g-2)_\mu$ muon anomaly gives strongevidence for the possible existence of new physics beyond the Standard Model inthe muon sector. Thus it is worthy to revisit the existing experimentalconstraints on models suggesting theoretically consistent explanations of theanomaly. In this work, we point out that accounting for the loss of coherencebetween the wave packets(mass states) of solar neutrinos is important forsetting limits on any model with new flavor-sensitive couplings in the neutrinosector. By taking into account this effect and considering more accurately theexperimental constraints from the BOREXINO measurement of the $^7$Be solarneutrino interaction rate we corrected the limits previously placed on thecoupling of the light $Z'$ to $L_\mu$-$L_\tau$ current in the parameter spacerelevant to the muon $(g-2)_\mu$.

Refining constraints from Borexino measurements on a light $Z'$-boson coupled to $L_\mu$-$L_\tau$ current