Electroweak physics in field theories of heavy composite particles

How do we incorporate non-perturbative structure (form factors etc.) into loop corrections? How do we respect sacrosanct principles like gauge invariance and locality? This is not an academic question but impacts many aspects of precision flavour physics that are butting up against experimental precision right now. 

In this talk I will overview some physical settings (from the few-GeV to the few-eV scale) where this question pops up, sketch different approaches and methods to attack this problem, and then focus specifically on weak scattering and decays of nuclei. Our goal in this most ambitious problem will be  to control radiative corrections to 100 ppm. I will explain how this problem requires a detailed understanding of how long- and short-distance approximations can be wedded together, and what lessons can be learned for the broader program of structure dependent QED corrections.