Gearing up for the next generation of LFV experiments, via on-shell methods

Standard Model has lepton flavor conservation as an accidental symmetry. Lepton flavor violating (LFV) processes at low energies can provide us a window into new physics beyond the scales reached by accelerators. In the light of upcoming experiments in searches for muon-to-electron decays, I will try to explain the implications of upcoming bounds on the new physics above electroweak scale from an effective field theory perspective. The upgrades in precision are so high that it sometimes requires a two-loop level renormalization group analysis of dimension-six LFV operators. I will give a picture of how they mix into each other with the running scale, and demonstrate how you can calculate the needed anomalous dimensions effortlessly (!) using tree-level on-shell scattering amplitudes. Then I will conclude by discussing how this analysis connects with a simple BSM theory involving vector-like fermions. Based on arXiv:2112.12131.