Revisiting supernova constraints on dark gauge bosons

We revisit the supernova constraints on three well-motivated light gauge bosons: the dark photon, the $U(1)_{B-L}$ gauge boson, and the $U(1)_{L_μ-L_τ}$ gauge boson. For the dark photon and the $U(1)_{B-L}$ gauge boson, we re-evaluate the nucleon bremsstrahlung process within the one-pion exchange approximation, retaining the full momentum and mass dependence. The geometrical dependence of the decay and absorption of these gauge bosons inside the supernova core is also taken into account. Updated bounds on these models are derived based on the cooling of SN1987A and energy deposition constraints from low-energy supernovae (LESNe). Taking the SFHo-18.8 $18.8\,M_\odot$ profile, the SN1987A cooling constraints reach masses of about $230$ MeV, $280$ MeV, and $300$ MeV for the dark photon, the $U(1)_{B-L}$ boson, and the $U(1)_{L_μ-L_τ}$ boson, while the corresponding LESN limits extend to about $450$ MeV, $440$ MeV, and $600$ MeV, respectively. The kinetic mixing parameter $ε$ for dark photon, the gauge coupling $g_{BL}$ in the $U(1)_{B-L}$ model, and the gauge coupling $g_{μτ}$ for the $U(1)_{L_μ-L_τ}$ model are constrained down to $5.8\times10^{-12}$, $2.9\times10^{-16}$, and $6.4\times10^{-12}$, respectively.