Ratios of $W$ and $Z$ cross sections at large boson $p_T$ as a constraint on PDFs and background to new physics

TL;DR

This paper proposes measuring ratios of W and Z boson cross sections at high transverse momentum at the LHC to improve constraints on parton distribution functions and validate background estimates for new physics searches.

Contribution

It analyzes the sensitivity of W/Z ratios to PDFs and electroweak effects, highlighting their potential to refine theoretical models and background estimations.

Findings

W+/W- ratio constrains up/down quark PDFs at high x

W/Z ratio is stable against most theoretical uncertainties

Differential cross sections can inform gluon distribution with improved theory

Abstract

We motivate a measurement of various ratios of $W$ and $Z$ cross sections at the Large Hadron Collider (LHC) at large values of the boson transverse momentum ($p_T\gtrsim M_{W,Z}$). We study the dependence of predictions for these cross-section ratios on the multiplicity of associated jets, the boson $p_T$ and the LHC centre-of-mass energy. We present the flavour decomposition of the initial-state partons and an evaluation of the theoretical uncertainties. We show that the $W^+/W^-$ ratio is sensitive to the up-quark to down-quark ratio of parton distribution functions (PDFs), while other theoretical uncertainties are negligible, meaning that a precise measurement of the $W^+/W^-$ ratio at large boson $p_T$ values could constrain the PDFs at larger momentum fractions $x$ than the usual inclusive $W$ charge asymmetry. The $W^\pm/Z$ ratio is insensitive to PDFs and most other theoretical uncertainties, other than possibly electroweak corrections, and a precise measurement will therefore be useful in validating theoretical predictions needed in data-driven methods, such as using $W(\to\ell\nu)$+jets events to estimate the $Z(\to\nu\bar{\nu})$+jets background in searches for new physics at the LHC. The differential $W$ and $Z$ cross sections themselves, ${\rm d}\sigma/{\rm d}p_T$, have the potential to constrain the gluon distribution, provided that theoretical uncertainties from higher-order QCD and electroweak corrections are brought under control, such as by inclusion of anticipated next-to-next-to-leading order QCD corrections.