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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, $ u e to u 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.
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Neutrino-nucleus elastic scattering provides a unique laboratory to study the quantum mechanical coherency effects in electroweak interactions, towards which several experimental programs are being actively pursued. We report results of our quantitative studies on the transitions towards decoherency. A parameter ($alpha$) is identified to describe the degree of coherency, and its variations with incoming neutrino energy, detector threshold and target nucleus are studied. The ranges of $alpha$ which can be probed with realistic neutrino experiments are derived, indicating complementarity between projects with different sources and targets. Uncertainties in nuclear physics and in $alpha$ would constrain sensitivities in probing physics beyond the standard model. The maximum neutrino energies corresponding to $alpha$>0.95 are derived.
We study the sensitivity of detectors with directional sensitivity to coherent elastic neutrino-nucleus scattering (CE$ u$NS), and how these detectors complement measurements of the nuclear recoil energy. We consider stopped pion and reactor neutrino sources, and use gaseous helium and fluorine as examples of detector material. We generate Standard Model predictions, and compare to scenarios that include new, light vector or scalar mediators. We show that directional detectors can provide valuable additional information in discerning new physics, and we identify prominent spectral features in both the angular and the recoil energy spectrum for light mediators, even for nuclear recoil energy thresholds as high as $sim 50$ keV. Combined with energy and timing information, directional information can play an important role in extracting new physics from CE$ u$NS experiments.
Neutrino oscillation experiments at accelerator energies aim to establish CP violation in the neutrino sector by measuring the energy-dependent rate of $ u_e$ appearance and $ u_mu$ disappearance in a $ u_mu$ beam. Extracting the correct oscillation rate demands control over QED radiative corrections at the percent level. Focusing on the critical charged-current neutrino-nucleon scattering process, we show that the cross section factorizes into two pieces. The first piece depends on hadron structure but is universal for $ u_e$ and $ u_mu$, and hence constrained by high-statistics $ u_mu$ data. The second piece is nonuniversal and suffers large logarithm enhancements, but is computed to high precision using renormalization group improved perturbation theory. Our results provide a missing ingredient for the robust interpretation of current NOvA and T2K experiments, and can be applied to future experiments such as DUNE and HyperK.
The presence of new neutrino-quark interactions can enhance, deplete or distort the coherent elastic neutrino-nucleus scattering (CEvNS) event rate. The new interactions may involve CP violating phases that can potentially affect these features. Assuming light vector mediators, we study the effects of CP violation on the CEvNS process in the COHERENT sodium-iodine, liquid argon and germanium detectors. We identify a region in parameter space for which the event rate always involves a dip and another one for which this is never the case. We show that the presence of a dip in the event rate spectrum can be used to constraint CP violating effects, in such a way that the larger the detector volume the tighter the constraints. Furthermore, it allows the reconstruction of the effective coupling responsible for the signal with an uncertainty determined by recoil energy resolution. In the region where no dip is present, we find that CP violating parameters can mimic the Standard Model CEvNS prediction or spectra induced by real parameters. We point out that the interpretation of CEvNS data in terms of a light vector mediator should take into account possible CP violating effects. Finally, we stress that our results are qualitatively applicable for CEvNS induced by solar or reactor neutrinos. Thus, the CP violating effects discussed here and their consequences should be taken into account as well in the analysis of data from multi-ton dark matter detectors or experiments such as CONUS, $ u$-cleus or CONNIE.
We calculate coherent elastic neutrino-nucleus scattering cross sections on spin-0 nuclei (e.g. $^{40}$Ar and $^{28}$Si) 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 nontrivial 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.
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