Resonance Contributions to Radiative Corrections in Charged-Current (Anti)Neutrino-Nucleon Elastic Scattering at GeV Energies

TL;DR

The paper addresses precision radiative corrections in charged-current (anti)neutrino-nucleon elastic scattering at GeV energies by evaluating virtual resonance contributions from the $Δ(1232)$ resonance. It adopts a magnetic-dipole–based vector transition for $N \to Δ$ and analyzes both on-shell and hadronic-model vertex treatments within a one-loop framework, confirming expected infrared behavior and unitarity while ensuring gauge invariance. The main finding is that $Δ(1232)$-mediated corrections are at the permille level and exhibit no significant kinematic enhancement, with results that remain robust against off-shell variations and modeling choices. This work reinforces the reliability of previous radiative-correction estimates and provides a quantified, subleading but non-negligible component for precision neutrino scattering analyses relevant to oscillation experiments.

Abstract

We present the first evaluation of virtual resonance contributions to the charged-current (anti)neutrino-nucleon elastic scattering at GeV energies, focusing on the dominant $Δ(1232)$ resonance. We approximate the vector part of the $N \to Δ$ transition by the leading magnetic dipole term. Our results for the cross-section corrections at fixed neutrino energy indicate the permille-level contribution of resonance intermediate states to the elastic and radiative scattering cross sections. This calculation exhibits the expected infrared behavior of the invariant amplitudes and unpolarized cross sections. Our findings provide important insights into inelastic excitations in the charged-current (anti)neutrino-nucleon elastic scattering at GeV energies.

Figures (5)

• Figure 1: Contributions of the $\Delta$ resonance to the charged-current (anti)neutrino-nucleon elastic scattering are shown. The photon is exchanged between the charged lepton and $N \to \Delta$ transition vertex.
• Figure 2: Relative contribution of the $\Delta$ intermediate state to the unpolarized charged-current elastic scattering cross section on nucleons is shown as a function of the squared momentum transfer $Q^2$ for initial neutrino energies $E_\nu = 600~\mathrm{MeV}$ (upper left plot), $E_\nu = 1~\mathrm{GeV}$ (upper right plot), $E_\nu = 1.2~\mathrm{GeV}$ (lower left plot), and $E_\nu = 2~\mathrm{GeV}$ (lower right plot). Results for different model calculations, which are described in Section \ref{['sec:virtual_delta']}, are presented.
• Figure 3: Same as Figure \ref{['fig:muon_neutrino_virtual_delta']} but for the antineutrino scattering.
• Figure 4: Same as Figure \ref{['fig:muon_neutrino_virtual_delta']} but for the electron flavor.
• Figure 5: Same as Figure \ref{['fig:muon_antineutrino_virtual_delta']} but for the electron flavor.