Precise hadron structure for low-energy tests in the electroweak sector

In view of apparent incompleteness of the Standard Model (SM), ongoing searches for new particles and interactions proceed at colliders, in astrophysics and at low energies. The latter avenue aims at extracting information on New Physics (NP) by confronting high-precision measurements of parameters of SM to equally precise theoretical calculations. Relative ~10^-4 measurements of the weak mixing angle in parity-violating electron scattering, and of CKM unitarity in the top row with beta-decays, are sensitive to light dark sector, as well as to heavy new particles at scales ~50 TeV, and represent a valuable complementarity to collider searches. This precision is warranted by a careful assessment of one-loop SM radiative corrections, most notably the electroweak box diagrams which include effects of the strong interaction
in the non-perturbative regime and represent the main source of the theoretical uncertainty.
I review the current status of the theoretical calculations and make connection to existing and upcoming electron and neutrino scattering data that allows for a controlled and largely model-independent assessment of the theoretical uncertainty.