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

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