Solving leptonic (g-2) anomalies with a single Z'

In light of independent verification of the muon (g-2) anomaly by Fermilab and hints of a similar anomaly in the electron sector emerging from the improved measurement of fine-structure constant, it is important to ask if both these anomalies could have a common origin. I will talk about one such attempt involving contributions from a single Z’ of a U(1)’ extension to the Standard Model (SM). I will first describe a model-independent analysis of various experimental constraints on the Z’ couplings to leptons and show that only a narrow region of parameter space with a MeV-scale Z’ can account for both the anomalies. Following this conclusion, I will show that any attempt to realize these couplings in a specific U(1)’ extension of the SM fails as a result of an additional constraint from the gauge structure, and the stringency of neutrino scattering bounds. This leads us to conclude that no single U(1)’ extension can resolve both the anomalies unless additional fields are introduced.