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Drell-Yan Lepton Angular Distribution at Small Transverse Momentum

Daniel Boer, Werner Vogelsang

TL;DR

The paper analyzes how Drell-Yan lepton angular distributions depend on the lepton-pair transverse momentum by decomposing the cross section into structure functions W_T, W_L, W_Δ, and W_{ΔΔ} in two frames (Collins-Soper and Gottfried-Jackson). It derives the LO perturbative QCD results and their small-Q_T limits, showing that W_T carries the dominant logarithms resummed by CSS, while W_L and W_{ΔΔ} share similar leading logs in CS, with W_Δ lacking such logs in that frame; in GJ all functions carry leading logs with frame-dependent subleading pieces. The Lam-Tung relation remains exact and robust under resummation, but the impact of resummation on the angular coefficients is frame- and process-dependent, highlighting the need for extended resummation techniques beyond the standard CSS approach. The work underscores the importance of considering frame choice when predicting and interpreting angular observables and motivates development of a generalized resummation framework for angular structure functions beyond W_T.

Abstract

We investigate the dependence of the Drell-Yan cross section on lepton polar and azimuthal angles, as generated by the lowest-order QCD annihilation and Compton processes. We focus in particular on the azimuthal-angular distributions, which are of the form cos(phi) and cos(2phi). At small transverse momentum q_T of the lepton pair, q_T << Q, with Q the pair mass, these terms are known to be suppressed relative to the phi-independent part of the Drell-Yan cross section by one or two powers of the transverse momentum. Nonetheless, as we show, like the phi-independent part they are subject to large logarithmic corrections, whose precise form however depends on the reference frame chosen. These logarithmic contributions ultimately require resummation to all orders in the strong coupling. We discuss the potential effects of resummation on the various angular terms in the cross section and on the Lam-Tung relation.

Drell-Yan Lepton Angular Distribution at Small Transverse Momentum

TL;DR

The paper analyzes how Drell-Yan lepton angular distributions depend on the lepton-pair transverse momentum by decomposing the cross section into structure functions W_T, W_L, W_Δ, and W_{ΔΔ} in two frames (Collins-Soper and Gottfried-Jackson). It derives the LO perturbative QCD results and their small-Q_T limits, showing that W_T carries the dominant logarithms resummed by CSS, while W_L and W_{ΔΔ} share similar leading logs in CS, with W_Δ lacking such logs in that frame; in GJ all functions carry leading logs with frame-dependent subleading pieces. The Lam-Tung relation remains exact and robust under resummation, but the impact of resummation on the angular coefficients is frame- and process-dependent, highlighting the need for extended resummation techniques beyond the standard CSS approach. The work underscores the importance of considering frame choice when predicting and interpreting angular observables and motivates development of a generalized resummation framework for angular structure functions beyond W_T.

Abstract

We investigate the dependence of the Drell-Yan cross section on lepton polar and azimuthal angles, as generated by the lowest-order QCD annihilation and Compton processes. We focus in particular on the azimuthal-angular distributions, which are of the form cos(phi) and cos(2phi). At small transverse momentum q_T of the lepton pair, q_T << Q, with Q the pair mass, these terms are known to be suppressed relative to the phi-independent part of the Drell-Yan cross section by one or two powers of the transverse momentum. Nonetheless, as we show, like the phi-independent part they are subject to large logarithmic corrections, whose precise form however depends on the reference frame chosen. These logarithmic contributions ultimately require resummation to all orders in the strong coupling. We discuss the potential effects of resummation on the various angular terms in the cross section and on the Lam-Tung relation.

Paper Structure

This paper contains 6 sections, 41 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Azimuthal dependences in terms of structure functions
  3. Azimuthal asymmetries from LO perturbative QCD processes
  4. Small-$Q_T$ limit of the structure functions $W_T$, $W_L$, $W_\Delta$, $W_{\Delta\Delta}$ at LO
  5. Effects of resummation at small $Q_T$
  6. Summary

Figures (2)

  • Figure 1: The Collins-Soper frame.
  • Figure 2: The Gottfried-Jackson frame.