An accurate evaluation of electron (anti-)neutrino scattering on nucleons

Abstract

We discuss as accurately as possible the cross section of quasi-elastic scattering of electron (anti-) neutrinos on nucleons, also known as inverse beta decay in the case of antineutrinos. We focus on the moderate energy range from a few MeV up to hundreds of MeV, and which includes neutrinos from reactors and supernovae. We assess the uncertainty on the cross section, which is relevant to experimental advances and increasingly large statistical samples. We estimate the effects of second-class currents, showing that they are small and negligible for current applications. INTRODUCTIONThe cross section of the process νe + p → e + + n (IBD, from inverse beta decay), which enabled the first direct observation of (anti-)neutrinos [1], is still essential today at relatively low energies for detectors that are based on water or hydrocarbons, i.e., the most commonly used detectors such as scintillators or Cherenkov light detectors.The most accurate estimates available today were described about 20 years ago by Beacom and Vogel [2] and by Strumia and Vissani [3]. In this paper, we aim to update the discussion, in consideration of some general facts: 1) the importance of the reaction itself, 2) the experimental progress of neutrino detectors, 3) the progress relating to the parameters that determine the reaction itself, 4) to quantify the role of second-class currents (SCCs) [4], previously omitted, but which has been the subject of a recent debate [5][6][7].Furthermore, there is a specific quantitative point that deserves to be highlighted: it is important to update not only the value, but also the estimate of the uncertainty on the cross section of the IBD process. Indeed, the conservative estimate of the uncertainty at low energies on this IBD cross section, obtained in [3] is 0.4 %. This corresponds to a statistical error over 60,000 events and therefore it is potentially relevant in cases where the statistical sample is quite large. There are at least two cases of this type, which concern reactor antineutrinos (with typical energies of 3 MeV and up to 10 MeV) and those from supernovae (with typical energies of 20 MeV and perhaps up to 60-70 MeV). We discuss them below:• Reactor neutrino experiment Daya Bay [8] has collected 3.5 million events already. Similar considerations apply to the other reactor experiments with very high statistics. But also the future detector JUNO [9] designed to study events from distant reactors, with a very large fiducial volume, about 20 kiloton of scintillator liquid, expects to collect 83 events/day and therefore in 6 years will amount to a total of 180000 events.• As for the future galactic supernova, Super-Kamiokande (SK) will collect more than 5000 IBD events with a mass of 32.4 kiloton and for a typical galactic distance of 10kpc (see e.g. [10]), a number that scales with the