QCD Factorized Drell-Yan Cross Section at Large Transverse Momentum

TL;DR

The paper introduces a factorization framework for Drell–Yan production at large $Q_T$ that resums all-orders $\ln(Q_T^2/Q^2)$ contributions into perturbatively calculable parton-to-virtual-photon fragmentation functions. It presents a two-track perturbative expansion: a direct term for non-logarithmic short-distance physics and a fragmentation term that encapsulates the logarithmic resummation, both defined at a single hard scale. The virtual-photon fragmentation functions obey inhomogeneous evolution equations and are free of collinear singularities, enabling reliable predictions even when $Q_T\gg Q$. Numerical results across Tevatron, LHC, and RHIC demonstrate improved perturbative stability and underline the sensitivity of the high-$Q_T$ spectrum to the gluon distribution, while maintaining agreement with conventional fixed-order results when $Q_T\sim Q$.

Abstract

We derive a new factorization formula in perturbative quantum chromodynamics for the Drell-Yan massive lepton-pair cross section as a function of the transverse momentum $Q_T$ of the pair. When $Q_T$ is much larger than the pair's invariant mass $Q$, this factorization formula systematically resums the logarithmic contributions of the type $α_s^m \ln^m(Q_T^2/Q^2)$ to all orders in the strong coupling $α_s$. When $Q_T\sim Q$, our formula yields the same Drell-Yan cross section as conventional fixed order QCD perturbation theory. We show that resummation is important when the collision energy $\sqrt{S}$ is large enough and $Q_T\gg Q$, and we argue that perturbative expansions are more stable and reliable in terms of the modified factorization formula.

Figures (16)

• Figure 1: Feynman diagrams for the LO contribution to the Drell-Yan cross section: (a) quark-antiquark annihilation $q+\bar{q}\rightarrow\gamma^*+g$, and (b) Compton $g+q\rightarrow\gamma^*+q$ subprocesses.
• Figure 2: Feynman diagrams that illustrate situations in which the photon can become collinear to a quark in (a) the initial-state and (b) the final-state.
• Figure 3: A generic diagram of the lowest order $2\rightarrow 3$ subprocess that contributes to the Drell-Yan cross section with large final-state logarithmic terms when $Q^2\ll Q_T^2$.
• Figure 4: Sketch of the fragmentation contribution to low mass Drell-Yan lepton-pair production at high $Q_T$.
• Figure 5: Scattering amplitudes that provide large logarithmic contributions to the Drell-Yan cross section via quark fragmentation.