How to rule out (g-2)_μ in U(1)L_μ-L_τ with White Dwarf Cooling

In recent years, the gauge group U(1)L_μ-L_τ has received a lot of attention since it can, in principle, account for the observed excess in the anomalous muon magnetic moment (g-2)_μ, as well as the Hubble tension. Due to unavoidable, loop-induced kinetic mixing with the SM photon and Z, the U(1)L_μ-L_τ gauge boson $A'$ can contribute to stellar cooling via decays into neutrinos. In this work, we perform for the first time an ab initio computation of the neutrino emissivities of white dwarf stars due to plasmon decay in a model of gauged U(1)L_μ-L_τ. 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)_μ. 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.