High-precision QCD at hadron colliders: electroweak gauge boson rapidity distributions at NNLO

TL;DR

The paper addresses precise QCD predictions for Drell–Yan electroweak gauge boson rapidity distributions at hadron colliders by computing NNLO corrections. It introduces a novel rapidity-propagator technique to recast differential phase-space constraints into forward-scattering amplitudes, and uses IBP, Laporta reduction, master integrals, and differential equations to obtain analytic results. The study demonstrates that NNLO corrections yield sub-percent scale uncertainties for central rapidities and show PDF-driven differences (e.g., MRST vs Alekhin) at the few-percent level, enabling discrimination between PDF parameterizations at the LHC. The work provides a practical, highly accurate tool for PDF determination and luminosity monitoring, and suggests using NNLO K-factors to improve NLO Monte Carlo predictions for collider phenomenology.

Abstract

We compute the rapidity distributions of W and Z bosons produced at the Tevatron and the LHC through next-to-next-to leading order in QCD. Our results demonstrate remarkable stability with respect to variations of the factorization and renormalization scales for all values of rapidity accessible in current and future experiments. These processes are therefore ``gold-plated'': current theoretical knowledge yields QCD predictions accurate to better than one percent. These results strengthen the proposal to use W and Z production to determine parton-parton luminosities and constrain parton distribution functions at the LHC. For example, LHC data should easily be able to distinguish the central parton distribution fit obtained by MRST from that obtained by Alekhin.

Figures (17)

• Figure 1: Variables $(z,u)$ used to describe the kinematics of the vector boson rapidity distribution at parton level. The physical region is hatched. The point $u=z=1$ corresponds to no additional radiation, or Born-level kinematics. The left edge, $u=z$, corresponds to radiation of partons collinear with incoming parton 2. The right edge, $u=1/z$, corresponds to radiation collinear with parton 1. The arrows show flows relevant for the convolution integrals encountered in mass factorization (see Section \ref{['sec:collinear']}).
• Figure 2: Regions in the $(z,u)$ plane for which the hard functions have to be patched, because of singular behavior. Besides the soft limit $z \to 1$, and the left and right collinear edges, there are spurious singularities as $u\to1$, and as $z \to [2u/(1+u)]^2$ and $z \to [2/(1+u)]^2$.
• Figure 3: The CMS rapidity distribution of an on-shell $Z$ boson at the LHC. The LO, NLO, and NNLO results have been included. The bands indicate the variation of the renormalization and factorization scales in the range $M_Z/2 \leq \mu \leq 2M_Z$.
• Figure 4: More general variations of the renormalization and factorization scales, for production of an on-shell $Z$ boson at the LHC, at central rapidity $Y=0$. For each order in perturbation theory (LO, NLO, NNLO), three curves are shown. The solid curves depict common variation of the renormalization and factorization scales, $\mu_F = \mu_R = \mu$, as used in the rest of the paper, but extending the range of variation to $M/5 < \mu < 5M$. The dashed curves represent variation of the factorization scale alone, holding the renormalization scale fixed at $M$. The dotted curves result from varying the renormalization scale instead, holding the factorization scale fixed at $M$.
• Figure 5: The CMS rapidity distribution of an on-shell $Z$ boson at Run II of the Tevatron. The LO, NLO, and NNLO results have been included. The bands indicate the variation of the renormalization and factorization scales in the range $M_Z/2 \leq \mu \leq 2M_Z$.