How to rule out $(g-2{)}_{\mu }$ in $U(1{)}_{L_{\mu }-L_{\tau }}$ 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 $A^{\prime }$ 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 $U(1{)}_{L_{\mu }-L_{\tau }}$. A key result is that current observations of the early-stage white dwarf neutrino luminosity at the 30\% level exclude previously allowed regions of the parameter space favoured by a simultaneous explanation of the $(g-2{)}_{\mu }$ and $H_0$ anomalies. In this work, we present the relevant white dwarf cooling limits over the entire $A^{\prime }$ mass range. In particular, we have performed a rigorous computation of the luminosities in the resonant regime, where the $A^{\prime }$ mass is comparable to the white dwarf plasma frequencies.

Comments: 17 pages, 6 figures, 2 data files; v2: improved discussion of the cooling limit, matches journal version to appear in JHEP