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We consider the hadroproduction of W gauge bosons in their leptonic decaymode. Starting from the leading-order expressions, we show that by defining asuitable scaling variable the centre-of-mass dependence of the cross sectionsat the LHC energies can be essentially described by a simple power law. Thescaling exponent is directly linked to the small-$x$ behaviour of partondistribution functions (PDF) which, at the high virtualities involved in Wproduction, is largely dictated by QCD evolution equations. This entails aparticularly simple scaling law for the lepton charge asymmetry and alsopredicts that measurements in different collision systems (p-p, p-$\bar{\rmp}$, p-Pb Pb-Pb) are straightforwardly related. The expectations are comparedwith the existing data and a very good overall agreement is observed. It isshown that the PDF uncertainty in certain cross-section ratios between nearbycentre-of-mass energies can be significantly reduced by taking the ratios atfixed value of scaling variable instead of fixed rapidity.

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