Precision Measurement of the W-Boson Mass: Theoretical Contributions and Uncertainties

TL;DR

This work provides a comprehensive assessment of electroweak, QED, and mixed QCD-EW corrections relevant to precision $M_W$ measurements at hadron colliders. By employing Horace-3.1 and an enhanced Powheg-v2 two-rad framework, the authors quantify how radiative effects alter key observables and propagate into template-based $M_W$ extractions, detailing non-perturbative and perturbative uncertainties. The study finds QED FSR and light lepton-pair radiation as dominant EW sources, demonstrates that mixed ${ m O}( ext{alpha} ext{alpha}_s)$ corrections can shift $M_W$ by several tens of MeV depending on the observable and collider, and shows that the two-rad improvement significantly reduces these theoretical systematics, enabling MeV-level precision. Overall, the results provide concrete guidance for reducing theoretical uncertainties in $M_W$ determinations at the Tevatron and LHC and inform future high-precision electroweak tests of the Standard Model.

Abstract

We perform a comprehensive analysis of electroweak, QED and mixed QCD-electroweak corrections underlying the precise measurement of the W-boson mass M_W at hadron colliders. By applying a template fitting technique, we detail the impact on M_W of next-to-leading order electroweak and QCD corrections, multiple photon emission, lepton pair radiation and factorizable QCD-electroweak contributions. As a by-product, we provide an up-to-date estimate of the main theoretical uncertainties of perturbative nature. Our results can serve as a guideline for the assessment of the theoretical systematics at the Tevatron and LHC and allow a more robust precision measurement of the W-boson mass at hadron colliders.

Figures (10)

• Figure 1: Relative effect due to lepton-pair corrections on the $W$ transverse mass distribution, for $W \to \mu \nu$ (left plot) and $W \to e \nu$ (right plot) decays at the Tevatron ($\sqrt{s} =$ 1.96 TeV). The plots show the relative difference between the Horace-3.1 predictions for multiple FSR with and without pair emission.
• Figure 2: Relative difference, for the $\mu^+ \nu$ invariant mass distribution, normalized to the prediction of Powheg-v2 with NLO QCD corrections interfaced to the Pythia QCD PS, of two different implementations of EW corrections: predictions of Powheg-v2two-rad with NLO QCD+EW corrections (red dots), and of the old version of Powheg-v2 with NLO QCD+EW corrections (blue dots). Both codes are interfaced to the Pythia QCD PS and to Photos. For reference, the EW corrections normalized to the LO are reported in the insets.
• Figure 3: Same as in figure \ref{['fig:mixed-invm-lhc-mu']} for the lepton-pair transverse mass (left plot) and for the lepton transverse momentum (right plot).
• Figure 4: Fixed-order predictions for the transverse mass distribution, in the case of $W^+$ production with muons in the final state at LHC 14 TeV and acceptance cuts as in table \ref{['tab:parameters_comparison_with_fixed_order']}. We show different perturbative approximations, including only NLO QCD, only NLO EW and the sum of the two sets of corrections. In the left plot we show the shape of the distributions and in the right plot the relative effect of the radiative corrections, normalized to the LO prediction.
• Figure 5: Relative contribution of higher-order FSR and higher-order FSR plus pair radiation normalized to one-photon emission, for $W^+$ decay into muons (left) and into bare electrons (right). Predictions from Horace-3.1 at Tevatron energy, with the acceptance cuts of table \ref{['tab:parameters_qed']}.