Title: How to rule out $(g-2)_μ$ in $U(1)_{L_μ-L_τ}$ with White Dwarf Cooling

Abstract: In recent years, the gauge group $U(1)_{L_\mu-L_\tau}$ has received a lot of attention since it can, in principle, account for the observed excess in the anomalous muon magnetic moment $(g-2)_\mu$, as well as the Hubble tension. Due to unavoidable, loop-induced kinetic mixing with the SM photon and $Z$, the $U(1)_{L_\mu-L_\tau}$ gauge boson $A'$ can contribute to stellar cooling via decays into neutrinos. In this work, we perform for the first time an \textit{ab initio} computation of the neutrino emissivities of white dwarf stars due to plasmon decay in a model of gauged $U(1)_{L_\mu-L_\tau}$. Our central finding is that an observation of the early-stage white dwarf neutrino luminosity at the 30% level could exclude (or partially exclude) the remaining allowed parameter space for explaining $(g-2)_\mu$. In this work, we present the relevant white dwarf sensitivities over the entire $A'$ mass range. In particular, we have performed a rigorous computation of the luminosities in the resonant regime, where the $A'$ mass is comparable to the white dwarf plasma frequencies.