On the effective theory of neutrino-electron and neutrino-quark interactions

We determine the four-fermion effective theory of neutrino interactions within the Standard Model including one-loop electroweak radiative corrections, in combination with the measured muon lifetime and precision electroweak data. Including two-loop matching and three-loop running corrections, we determine lepton coefficients accounting for all large logarithms through relative order O(αα_s) and quark coefficients accounting for all large logarithms through O(α). We present four-fermion coefficients valid in n_f=3 and n_f=4 flavor quark theories, as well as in the extreme low-energy limit. We relate the coefficients in this limit to neutrino charge radii governing matter effects via forward neutrino scattering on charged particles.