Abstract: We explore quantum corrections of electrically charged black holes subject to vacuum polarization effects of fermion fields in QED. Solving this problem exactly is challenging so we restrict to perturbative corrections that one can obtain using the heat kernel expansion in the one -loop effective action for electrons. Starting from the corrections originally computed by Drummond and Hathrell, we solve the full semiclassical Einstein -Maxwell system of coupled equations to leading order in Planck 's constant and find a new electrically charged, static black hole solution. To probe these quantum corrections, we study electromagnetic and gravitational (axial) perturbations on this background and derive the coupled system of Regge-Wheeler master equations that govern the propagation of these waves. In the classical limit, our results agree with previous findings in the literature. We finally compare these results with those that one can obtain by working out the Euler-Heisenberg effective action. We find again a new electrically charged static black hole spacetime and derive the coupled system of Regge-Wheeler equations governing the propagation of axial electromagnetic and gravitational perturbations. Results are qualitatively similar in both cases. We briefly discuss some challenges found in the numerical computation of the quasinormal mode frequency spectra when quantum corrections are included.

Abstract: In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus tau and its conjugate, (tau) over bar. We point out that certain combinations of observables depend only on tau , i.e. are meromorphic, and in some cases even holomorphic functions of tau. These functions, which we dub “invariants” in this Letter, are highly constrained, renormalization group invariant, and allow us to derive many of the models' features without the need for extensive parameter scans. We illustrate the robustness of these invariants in two existing models in the literature based on modular symmetries, Gamma(3) and Gamma(5). We find that, in some cases, the invariants give rise to robust relations among physical observables that are independent of tau. Furthermore, there are instances where additional symmetries exist among the invariants. These symmetries are relevant phenomenologically and may provide a dynamical way to realize symmetries of mass matrices.

Abstract: We report the first search for dark sectors performed at the NA64 experiment employing a high energy muon beam and a missing energy-momentum technique. Muons from the M2 beamline at the CERN Super Proton Synchrotron with a momentum of 160 GeV/c are directed to an active target. The signal signature consists of a single scattered muon with momentum < 80 GeV/c in the final state, accompanied by missing energy, i.e., no detectable activity in the downstream calorimeters. For a total dataset of (1.98 +/- 0.02) x 10(10) muons on target, no event is observed in the expected signal region. This allows us to set new limits on the remaining (m(Z)'; g(Z)') parameter space of a new Z' (L-mu – L-tau) vector boson which could explain the muon (g – 2)(mu) anomaly. Additionally, our study excludes part of the parameter space suggested by the thermal dark matter relic abundance. Our results pave the way to explore dark sectors and light dark matter with muon beams in a unique and complementary way to other experiments.