Parton Distributions and QCD at LHCb

TL;DR

The paper addresses the precision of parton distribution functions (PDFs) at small and large $x$ and the associated QCD uncertainties by exploiting LHCb's forward rapidity coverage. It argues that measurements of $W$, $Z$, and Drell-Yan processes can be related to PDFs through explicit formulas, enabling early data to constrain quark and gluon distributions and to test the perturbative expansion. The authors highlight potential signs of missing small-$x$ dynamics, such as resummation or saturation, if data diverge from fixed-order predictions. The work emphasizes LHCb's unique reach in refining global PDF determinations and improving QCD predictions across forward kinematics.

Abstract

We consider the impact that can be made on our understanding of parton distributions (PDFs) and QCD from early measurements at the LHCb experiment. The high rapidity values make the experiment uniquely suited to a detailed study of small-x parton distributions and hence will make a significant contribution towards the clarification of both experimental and theoretical uncertainties on PDFs and their applications.

Figures (5)

• Figure 1: The kinematic range of $x$ and $Q^2$ which is probed at the LHC.
• Figure 2: The uncertainties on cross-section ratios and total cross-sections at the LHC.
• Figure 3: The result of fitting to hypothetical $d\sigma_Z/dy$ data.
• Figure 4: The improved constraint on $d_V(x,Q^2)$ from fitting to $(d\sigma_{W^-}/dy)/(d\sigma_{W^+}/dy)$ data (left) and on $g(x,Q^2)$ from fitting to $(d\sigma_{\gamma^{\star}}/dy)$ for $M_{\gamma^{\star}} = 14\,{\rm GeV}$ (right).
• Figure 5: The Drell-Yan cross-section as a function of rapidity in various mass bins.