Low energy doubly-virtual Compton scattering from di-lepton electroproduction on a nucleon

We propose a new way to experimentally determine the subleading low-energy structure constant of doubly-virtual Compton scattering on a proton. Such empirical determination will reduce the theoretical model error in estimates of the hadronic correction to the muonic hydrogen Lamb shift. We demonstrate that the di-lepton forward-backward asymmetry in the $e^- p \to e^- p \, e^- e^+$ process, which can be accessed at electron scattering facilities, yields a large sensitivity to this so far unknown low-energy constant.