Neutrino inclusive inelastic scattering off nuclei

TL;DR

The paper develops a comprehensive QCD-based framework for neutrino-nucleus inelastic scattering that integrates high-Q^2 LT physics with low-Q^2 PCAC behavior, explicitly accounting for nuclear effects such as shadowing, Fermi motion, binding, pion excess, and off-shell corrections. It extends a prior charged-lepton nuclear DIS model to neutrinos by incorporating axial-current nonconservation, C-parity/isospin decomposition, and a Glauber-Gribov description of coherent multiple scattering, constrained by Adler and GLS sum rules. The authors provide detailed formulations for incoherent and coherent nuclear corrections to all relevant structure functions (F_T, F_L, F_2, F_3) and test sum rules, showing cancellations between shadowing and off-shell effects in the nuclear Adler and GLS sums. Numerical results for multiple nuclear targets are compared with recent neutrino data, and PCAC-dominated behavior at low Q^2 is validated against experimental measurements, yielding practical cross-section predictions for current and future neutrino experiments.

Abstract

We present a detailed description of high-energy neutrino and antineutrino inelastic inclusive scattering off nuclei in terms of nuclear structure functions. In our approach we take into account a QCD description of the nucleon structure functions as well as a number of basic nuclear effects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and off-shell correction to bound nucleon structure functions. These effects prove to be important in the studies of charged-lepton deep-inelastic scattering. We discuss similarities and dissimilarities in the calculation of nuclear effects for charged-lepton and neutrino scattering caused by nonconserved axial current in neutrino scattering. We examine the Adler and the Gross-Llewellyn-Smith sum rules for nuclear structure functions and find a remarkable cancellation between nuclear shadowing and off-shell corrections in these sum rules. We present calculations of differential cross sections for inclusive neutrino and antineutrino scattering in comparison with recent data on different target materials.

Figures (5)

• Figure 1: The isovector nuclear effect $\langle F_2^{(\nu-\bar{\nu})p}\rangle_1/F_2^{(\nu-\bar{\nu})p}$ calculated for ${}^{207}$Pb at $Q^2=5\:\mathrm{GeV}^2$ with and without off-shell correction using the isovector nuclear spectral function of Ref.KP04. The labels on the curves correspond to effects due to Fermi motion and nuclear binding (FMB) and off-shell correction (OS), which was calculated using Eq.(\ref{['delf:fit']}).
• Figure 2: The ratio $\delta\mathcal{R}^{(I,C)}$ calculated for different isospin and $C$-parity scattering states for ${}^{207}$Pb at $Q^2=1\:\mathrm{GeV}^2$ using the parameters of the scattering amplitudes from Sec. \ref{['sec:aeff']}. The labels on the curves mark the values of the isospin $I$ and $C$-parity, $(I,C)$.
• Figure 3: The ratios $\delta\mathcal{R}^{(0,+)}$ and $\delta\mathcal{R}^{(0,-)}$ calculated for ${}^{207}$Pb at $Q^2=1\:\mathrm{GeV}^2$ using the scattering amplitudes from Sec. \ref{['sec:aeff']} and different values of the parameter $m_{\rm eff}$.
• Figure 4: Relative off-shell (OS), nuclear shadowing (NS) and total nuclear correction to the Adler sum rule calculated for iron (left panel). The right panel shows phenomenological cross section by Eq.(\ref{['xsec:ph']}) with the error band and effective cross section computed by requiring exact cancellation between OS and NS effects in nuclear Adler sum rule (1) and in the normalization of nuclear valence quark distribution (2) (see text for more details).
• Figure :