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

Abstract

We determine the four Fermi 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 $\mathcal{O}(\alpha {\alpha }_s)$ and quark coefficients accounting for all large logarithms through $\mathcal{O}(\alpha )$. 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.

arXiv comment18 pages, 1 figure. v2: journal version; minor corrections, references are added

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