Electroweak higher-order effects and theoretical uncertainties in deep-inelastic neutrino scattering

TL;DR

This work extends electroweak corrections to deep-inelastic neutrino scattering by incorporating universal two-loop effects from $\Delta\alpha$ and $\Delta\rho$ and by including higher-order final-state photon radiation within a structure-function framework. It employs ${\cal O}(\alpha)$-improved MRST2004QED PDFs under a DIS-like factorization scheme and accounts for photon-induced real corrections, with careful phase-space methods described. Numerically, the study finds that remaining electroweak uncertainties are dominated by non-universal two-loop effects at about $3\times10^{-4}$ in $\sin^2\theta_W$, while ${\cal O}(\alpha)$ corrections implicit in the PDFs contribute roughly $4\times10^{-4}$. The results, including differential cross sections, have implications for precision extractions of $\sin^2\theta_W$ from NuTeV/NOMAD and guide Monte Carlo implementations via reweighting strategies.

Abstract

A previous calculation of electroweak O(alpha) corrections to deep-inelastic neutrino scattering, as e.g. measured by NuTeV and NOMAD, is supplemented by higher-order effects. In detail, we take into account universal two-loop effects from Δαand Δρas well as higher-order final-state photon radiation off muons in the structure function approach. Moreover, we make use of the recently released O(alpha)-improved parton distributions MRST2004QED and identify the relevant QED factorization scheme, which is DIS like. As a technical byproduct, we describe slicing and subtraction techniques for an efficient calculation of a new type of real corrections that are induced by the generated photon distribution. A numerical discussion of the higher-order effects suggests that the remaining theoretical uncertainty from unknown electroweak corrections is dominated by non-universal two-loop effects and is of the order 0.0003 when translated into a shift in sin^2θ_W=1-MW^2/MZ^2. The O(alpha) corrections implicitly included in the parton distributions lead to a shift of about 0.0004.

Figures (2)

• Figure 1: Lowest-order predictions for the distributions in $y$ (total) and individual contributions from different ranges in $x$ ($=x_{{\rm Bj}}$ in lowest order). The NC channel for $\nu$ scattering is shown on the l.h.s., the CC channel on the r.h.s.
• Figure 3: Relative electroweak corrections $\delta^\nu=\delta\sigma^\nu/\sigma^\nu_0$ (upper plots) and higher-order FSR (lower plots) to the distributions in $y$ (total) and to individual contributions from different ranges in $x$ (l.h.s.) and in $x_{{\rm Bj}}$ (r.h.s.).