Scaling properties of inclusive W$^\pm$ production at hadron colliders

TL;DR

This paper demonstrates that the production cross sections of W bosons at hadron colliders follow a simple power-law scaling with center-of-mass energy when expressed in terms of a specific variable, linking the behavior to parton distribution functions and QCD evolution.

Contribution

It introduces a new scaling variable for W production cross sections, simplifying the energy dependence and reducing PDF uncertainties in cross-section ratios across different collider systems.

Findings

Scaling law accurately describes LHC W production data.

Ratios at fixed scaling variable reduce PDF uncertainties.

Predictions relate measurements across different collision systems.

Abstract

We consider the hadroproduction of W gauge bosons in their leptonic decay mode. Starting from the leading-order expressions, we show that by defining a suitable scaling variable the centre-of-mass dependence of the cross sections at the LHC energies can be essentially described by a simple power law. The scaling exponent is directly linked to the small-$x$ behaviour of parton distribution functions (PDF) which, at the high virtualities involved in W production, is largely dictated by QCD evolution equations. This entails a particularly simple scaling law for the lepton charge asymmetry and also predicts that measurements in different collision systems (p-p, p-$\bar{\rm p}$, p-Pb Pb-Pb) are straightforwardly related. The expectations are compared with the existing data and a very good overall agreement is observed. It is shown that the PDF uncertainty in certain cross-section ratios between nearby centre-of-mass energies can be significantly reduced by taking the ratios at fixed value of scaling variable instead of fixed rapidity.