We calculate coherent elastic neutrino-nucleus scattering cross sections on spin-0 nuclei (e.g. ⁴⁰Ar and ²⁸Si) at energies below 100 MeV within the Standard Model and account for all effects of permille size. We provide a complete error budget including uncertainties at nuclear, nucleon, hadronic, and quark levels separately as well as perturbative error. Our calculation starts from the four-fermion effective field theory to explicitly separate heavy-particle mediated corrections (which are absorbed by Wilson coefficients) from light-particle contributions. Electrons and muons running in loops introduce a non- trivial dependence on the momentum transfer due to their relatively light masses. These same loops, and those mediated by tau leptons, break the flavor universality because of mass-dependent electromagnetic radiative corrections. Nuclear physics uncertainties significantly cancel in flavor asymmetries resulting in subpercent relative errors. We find that for low neutrino energies, the cross section can be predicted with a relative precision that is competitive with neutrino-electron scattering. We highlight potentially useful applications of such a precise cross section prediction ranging from precision tests of the Standard Model, to searches for new physics and to the monitoring of nuclear reactors.

We present the proton and neutron vector form factors in a convenient parametric form that is optimized for momentum transfers $\lesssim \mathrm{few}{\mathrm{GeV}}^2$. The form factors are determined from a global fit to electron scattering data and precise charge radius measurements. A new treatment of radiative corrections is applied. This parametric representation of the form factors, uncertainties, and correlations provides an efficient means to evaluate many derived observables. We consider two classes of illustrative examples: neutrino-nucleon scattering cross sections at GeV energies for neutrino oscillation experiments and nucleon structure corrections for atomic spectroscopy. The neutrino-nucleon charged current quasielastic cross section differs by 3%–5% compared to commonly used form factor models when the vector form factors are constrained by recent high-statistics electron-proton scattering data from the A1 Collaboration. Nucleon structure parameter determinations include: the magnetic and Zemach radii of the proton and neutron, $[r_M^p,r_M^n]=[0.739(41)(23),0.776(53)(28)]$ fm and $[r_Z^p,r_Z^n]=[1.0227(94)(51),-0.0445(14)(3)]$ fm; the Friar radius of nucleons, $[(r_F^p{)}^3,(r_F^n{)}^3]=[2.246(58)(2),0.0093(6)(1)]{\text{fm}}^3$; the electric curvatures, $[⟨r^4{⟩}_E^p,⟨r^4{⟩}_E^n]=[1.08(28)(5),-0.33(24)(3)]{\text{fm}}^4$; and bounds on the magnetic curvatures, $[⟨r^4{⟩}_M^p,⟨r^4{⟩}_M^n]=[-2.0(1.7)(0.8),-2.3(2.1)(1.1)]{\text{fm}}^4$. The first and dominant uncertainty is propagated from the experimental data and radiative corrections, and the second error is due to the fitting procedure.

Theoretical predictions for elastic neutrino-electron scattering have no hadronic or nuclear uncertainties at leading order making this process an important tool for normalizing neutrino flux. However, the process is subject to large radiative corrections that differ according to experimental conditions. In this paper, we collect new and existing results for total and differential cross sections accompanied by radiation of one photon, $\nu e\to \nu e(\gamma )$. We perform calculations within the Fermi effective theory and provide analytic expressions for the electron energy spectrum and for the total electromagnetic energy spectrum as well as for double- and triple-differential cross sections with respect to electron energy, electron angle, photon energy, and photon angle. We discuss illustrative applications to accelerator-based neutrino experiments and provide the most precise up-to-date values of neutrino-electron scattering cross sections. We present an analysis of theoretical error, which is dominated by the $\sim 0.2\%–0.4\%$ uncertainty of the hadronic correction. We also discuss how searches for new physics can be affected by radiative corrections.

We study radiative corrections to low-energy charged-current processes involving nucleons, such as neutron beta decay and (anti)neutrino-nucleon scattering within a top-down effective-field-theory approach. We first match the Standard Model to the low-energy effective theory valid below the weak scale and, using renormalization group equations with anomalous dimensions of $\mathcal{O}(\alpha ,\alpha {\alpha }_s,{\alpha }^2)$, evolve the resulting effective coupling down to the hadronic scale. Here, we first match to heavy-baryon chiral perturbation theory and subsequently, below the pion-mass scale, to a pionless effective theory, evolving the effective vector coupling with anomalous dimensions of $\mathcal{O}(\alpha ,{\alpha }^2)$ all the way down to the scale of the electron mass, relevant for beta decays. We thus provide a new evaluation of the “inner” radiative corrections to the vector coupling constant and to the neutron decay rate, discussing differences with the previous literature. Using our new result for the radiative corrections, we update the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ud}$ from the neutron decay.

We evaluate the two-photon exchange corrections to the Lamb shift and hyperfine splitting of S states in electronic hydrogen relying on modern experimental data and present the two-photon exchange on...