In medium dispersion relation effects in nuclear inclusive reactions at intermediate and low energies

Abstract

In a well-established many-body framework, successful in modeling a great variety of nuclear processes, we analyze the role of the spectral functions (SFs) accounting for the modifications of the dispersion relation of nucleons embedded in a nuclear medium. We concentrate in processes mostly governed by one-body mechanisms, and study possible approximations to evaluate the particle-hole propagator using SFs. We also investigate how to include together SFs and long-range RPA-correlation corrections in the evaluation of nuclear response functions, discussing the existing interplay between both type of nuclear effects. At low energy transfers (≤ 50 MeV), we compare our predictions for inclusive muon and radiative pion captures in nuclei, and charge-current (CC) neutrino-nucleus cross sections with experimental results. We also present an analysis of intermediate energy quasi-elastic neutrino scattering for various targets and both neutrino and antineutrino CC driven processes. In all cases, we pay special attention to estimate the uncertainties affecting the theoretical predictions. In particular, we show that errors on the σµ/σe ratio are much smaller than 5%, and also much smaller than the size of the SF+RPA nuclear corrections, which produce significant effects, not only in the individual cross sections, but also in their ratio for neutrino energies below 400 MeV. These latter nuclear corrections, beyond Pauli blocking, turn out to be thus essential to achieve a correct theoretical understanding of this ratio of cross sections of interest for appearance neutrino oscillation experiments. We also briefly compare our SF and RPA results to predictions obtained within other representative approaches.

Polarization of τ in quasielastic (anti)neutrino scattering: The role of spectral functions

“…The use of an effective mass for the nucleon is a simplified method to account for the effects due to the change of its dispersion relation inside of a nuclear medium. A proper description, however, is achieved by dressing the nucleon propagators and constructing realistic particle and hole spectral functions (SFs), which incorporate dynamical effects that depend on both the energy and momentum of the nucleons [6]. There was an attempt to include the SF formalism in the study of the polarization of the outgoing lepton produced in CC (anti-)neutrino-nucleus reactions [7].…”

“…In addition, one should bear in mind that RPA corrections take into account the absorption of the gauge boson, mediator of the interaction, by the nucleus as a whole instead of by an individual nucleon, and their importance decreases as the gauge boson wave-length becomes much shorter than the nuclear size. Thus, RPA effects on the polarization observables become little relevant, even for the total or partially integrated cross sections [6,25], for a great part of the phase-space accessible in the CC reaction [5,7]. This work is organized as follows.…”

Measurement of the muon antineutrino double-differential cross section for quasielastic-like scattering on hydrocarbon atEν∼3.5 GeV

“…Multiple RPA models are available within generators, including those of Nieves [54], Martini [48], Graczyk and Sobczyk [55], and Singh [56]. There is also discussion of the interplay between RPA with the Fermi gas and beyond-the-Fermi-gas models [57,58].…”

Semiphenomenological spectral functions in neutrino scattering

“…We introduce them into the model by summing the polarization diagrams which effectively amounts to a change of the strength of the interaction felt by the electroweak probe. With some caution (see the discussion in [2] Sec. II B), we will introduce the two effects together, bearing in mind that the RPA parameters were adjusted for the non interaction LFG system.…”

“…It is calculated with a semiphenomenological approach which takes as an input the nucleon-nucleon elastic cross section and introduces some in-medium modifications by summing up some polarization diagrams. The imaginary part of the Lindhard function and the hadron tensor can be expressed by means of the spectral functions [2]: The effect of the spectral functions on ImU(q 0 , q) is shown on Fig. 2.…”