[Paper Review] Angular coefficients in W+j production at the LHC with high precision

Mathieu Pellen, René Poncelet+2 more|arXiv (Cornell University)|Apr 26, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents the first next-to-next-to-leading order (NNLO) QCD and next-to-leading order (NLO) electroweak (EW) calculations of angular coefficients in W+j production at the LHC with finite transverse momentum. The results reduce theoretical uncertainties significantly and show corrections up to 10% in certain phase space regions, providing essential high-precision input for future W-boson mass measurements.

ABSTRACT

The extraction of the W-boson mass, a fundamental parameter of the Standard Model, from hadron-hadron collision requires precise theory predictions. In this regard, angular coefficients are crucial to model the dynamics of W-boson production. In this work, we provide, for the first time, angular coefficients at NNLO QCD + NLO EW accuracy for finite transverse momentum W-boson at the LHC. The corrections can reach up to 10% in certain regions of phase space. They are accompanied by a significant reduction of the scale uncertainty. This work should, besides providing reference values for theory-data comparison, provide state-of-the-art theory input for W-boson mass measurements.

Motivation & Objective

• To provide high-precision theoretical predictions for angular coefficients in W+j production at the LHC, addressing a key source of theoretical uncertainty in W-boson mass measurements.
• To eliminate reliance on Z-boson extrapolations for angular coefficients by computing them directly for W-boson production with finite transverse momentum.
• To reduce scale uncertainties in Monte Carlo predictions by including higher-order QCD and electroweak corrections.
• To validate the use of angular coefficient decomposition for NLO electroweak corrections, ensuring consistency with full off-shell computations.
• To deliver state-of-the-art theoretical input for future high-precision experiments at the LHC, particularly in the context of high-luminosity phase physics.

Proposed method

• Perform fixed-order computations at NNLO QCD and NLO EW accuracy for the process pp → W± → ℓ±νℓ + j, including finite transverse momentum of the W-boson.
• Use the angular coefficient decomposition defined in Eq. (3) to describe the W-boson decay angular distribution, with coefficients A2, A4, etc., computed at high perturbative order.
• Apply reweighting techniques to test the validity of the angular coefficient formalism by comparing reweighted on-shell W-boson events with full off-shell or narrow-width approximation (NWA) results.
• Use fine binning of angular coefficients to minimize binning-induced discrepancies in reweighting, and apply correction factors to account for residual binning effects.
• Validate the method by comparing differential distributions (e.g., lepton transverse momentum) between original and reweighted events at LO, NLO QCD, and NLO EW levels.
• Ensure infrared safety and consistency of the observable by including all relevant contributions in the perturbative expansion as defined in Eq. (2), focusing on dominant terms.

Experimental results

Research questions

• RQ1 To what extent do NNLO QCD and NLO EW corrections alter the angular coefficients in W+j production compared to lower-order predictions?
• RQ2 Can the angular coefficient decomposition accurately describe electroweak corrections when the W-boson is not on-shell, particularly in the presence of final-state photon radiation?
• RQ3 How significant are the differences between Z-boson and W-boson angular coefficients at NLO QCD and NLO EW, and why is direct extrapolation from Z to W problematic?
• RQ4 What is the residual uncertainty in using the angular coefficient formalism for NLO EW corrections, and how can it be minimized through binning and correction strategies?
• RQ5 To what extent do the computed angular coefficients reduce scale uncertainties in W-boson mass measurements at the LHC?

Key findings

• The NNLO QCD + NLO EW corrections to angular coefficients in W+j production reach up to 10% in certain regions of phase space, indicating a significant impact on theoretical predictions.
• The inclusion of higher-order corrections leads to a substantial reduction in scale uncertainties, improving the reliability of theoretical templates for W-boson mass measurements.
• The reweighting procedure using angular coefficients reproduces the full off-shell W-boson distributions with agreement at the few percent level, validating the formalism for NLO EW corrections.
• Residual discrepancies in reweighting are attributed to binning effects, and applying correction factors based on LO comparisons reduces these fluctuations to the level of 1% or less.
• The method is robust at NLO QCD and NLO EW, with corrected results showing improved agreement with full computations, especially in the low transverse-momentum region.
• The study demonstrates that the use of angular coefficients for NLO EW corrections is justified for practical purposes, provided fine binning and correction factors are employed.