Recoil and Threshold Corrections in Short-distance Cross Sections

TL;DR

The paper develops a unified joint resummation formalism that combines threshold and $Q_T$ resummations for short-distance QCD cross sections, while enforcing parton-energy conservation and avoiding double counting. It builds a refactorized framework with new perturbative building blocks (generalized parton distributions, eikonal/soft functions) and derives explicit NLL exponents for electroweak annihilation and prompt-photon production, including recoil effects. It also extends the formalism to include fragmentation and discusses nonperturbative power corrections, highlighting potential phenomenological implications for Drell–Yan, Higgs, and high-$p_T$ photon processes. Overall, the work provides a theoretically consistent, technically rich path to more accurate perturbative predictions across a broad class of hadronic processes, especially in regions with large soft-gluon effects.

Abstract

We identify and resum corrections associated with the kinematic recoil of the hard scattering against soft-gluon emission in single-particle inclusive cross sections. The method avoids double counting and conserves the flow of partonic energy. It reproduces threshold resummation for high-p_T single-particle cross sections, when recoil is neglected, and Q_T-resummation at low Q_T, when higher-order threshold logarithms are suppressed. We exhibit explicit resummed cross sections, accurate to next-to-leading logarithm, for electroweak annihilation and prompt photon inclusive cross sections.

Figures (6)

• Figure 1: Leading region for electroweak annihilation in cut diagram form. The vertical line represents the final state that includes an electroweak boson, labelled $Q$. The subdiagrams $J_a$, $J_b$, $U_{ab}$ and $H$ incorporate, respectively, on-shell lines with momenta collinear to $p_a$, lines with on-shell momenta parallel to $p_b$, lines with soft momenta, and lines off-shell by order $Q$.
• Figure 2: Leading region for prompt photon production near partonic threshold. The vertical line represents the final state, including the photon, $\gamma$, and the recoil jet, $J_c$.
• Figure 3: Diagrams that illustrate the cancellation of infrared divergences: (a) initial-state interactions, which require different diagrams, with different parton momenta ${\bf k}_a$ and ${\bf k}_b$. (b) initial-final-state interference, for which the cancellation proceeds through cuts of a single diagram, at fixed ${\bf k}_a$ and ${\bf k}_b$.
• Figure 4: (a) Diagrams which contribute to the soft anomalous dimension. The crosses on the gluon lines denote the modified propagator given in the text. The remainder of the $A^0=0$ gauge propagator cancels the real part of (b).
• Figure 5: Leading region for a single-particle inclusive cross section in cut diagram form. $c_I$ and $c_J$ represent color tensors colevol.