Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Sudakov suppression in azimuthal spin asymmetries

Daniel Boer

TL;DR

The paper analyzes Sudakov suppression of transverse momentum dependent azimuthal spin asymmetries in the regime $q_T \ll Q$, using a TMD factorization framework with a Sudakov form factor and a nonperturbative component. It applies this framework to two Collins-effect–driven cases: a cos(2φ) asymmetry in $e^+e^-$ annihilation and the Collins single-spin asymmetry in SIDIS, demonstrating substantial suppression relative to tree-level expectations and a shift of the peak $q_T$ to higher values as $Q$ grows. The authors derive analytic asymptotic bounds for certain weight structures and show that larger transverse-momentum weights lead to stronger suppression, providing upper limits on the energy-dependence of these asymmetries. The work underscores the importance of including Sudakov effects—and accurately parameterizing $S_{NP}$—to reliably extract the Collins function and transversity from experimental data across $e^+e^-$ and SIDIS processes.

Abstract

It is shown that transverse momentum dependent azimuthal spin asymmetries suffer from suppression due to Sudakov factors, in the region where the transverse momentum is much smaller than the large energy scale Q^2. The size and Q^2 dependence of this suppression are studied numerically for two such asymmetries, both arising due to the Collins effect. General features are discussed of how the fall-off with Q^2 is affected by the nonperturbative Sudakov factor and by the transverse momentum weights and angular dependences that appear in different asymmetries. For a subset of asymmetries the asymptotic Q^2 behavior is calculated analytically, providing an upper bound for the decrease with energy of other asymmetries. The effect of Sudakov factors on the transverse momentum distributions is found to be very significant already at present-day collider energies. Therefore, it is essential to take into account Sudakov factors in transverse momentum dependent azimuthal spin asymmetries.

Sudakov suppression in azimuthal spin asymmetries

TL;DR

The paper analyzes Sudakov suppression of transverse momentum dependent azimuthal spin asymmetries in the regime , using a TMD factorization framework with a Sudakov form factor and a nonperturbative component. It applies this framework to two Collins-effect–driven cases: a cos(2φ) asymmetry in annihilation and the Collins single-spin asymmetry in SIDIS, demonstrating substantial suppression relative to tree-level expectations and a shift of the peak to higher values as grows. The authors derive analytic asymptotic bounds for certain weight structures and show that larger transverse-momentum weights lead to stronger suppression, providing upper limits on the energy-dependence of these asymmetries. The work underscores the importance of including Sudakov effects—and accurately parameterizing —to reliably extract the Collins function and transversity from experimental data across and SIDIS processes.

Abstract

It is shown that transverse momentum dependent azimuthal spin asymmetries suffer from suppression due to Sudakov factors, in the region where the transverse momentum is much smaller than the large energy scale Q^2. The size and Q^2 dependence of this suppression are studied numerically for two such asymmetries, both arising due to the Collins effect. General features are discussed of how the fall-off with Q^2 is affected by the nonperturbative Sudakov factor and by the transverse momentum weights and angular dependences that appear in different asymmetries. For a subset of asymmetries the asymptotic Q^2 behavior is calculated analytically, providing an upper bound for the decrease with energy of other asymmetries. The effect of Sudakov factors on the transverse momentum distributions is found to be very significant already at present-day collider energies. Therefore, it is essential to take into account Sudakov factors in transverse momentum dependent azimuthal spin asymmetries.

Paper Structure

This paper contains 6 sections, 56 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Factorization and transverse momentum
  3. Unpolarized asymmetry in electron-positron annihilation
  4. Collins asymmetry in SIDIS
  5. Asymptotic behavior
  6. Conclusions

Figures (6)

  • Figure 1: Kinematics of the annihilation process in the lepton center of mass frame for a back-to-back jet situation. $P_2$ is the momentum of a hadron in one jet, $P_1$ is the momentum of a hadron in the opposite jet.
  • Figure 2: The asymmetry factor ${\cal A}(Q_T)$ (in units of $M^2$) at $Q=30 \, \text{GeV}$ (upper curve), $Q = 60 \, \text{GeV}$ (middle curve) and at $Q = 90 \, \text{GeV}$.
  • Figure 3: The asymmetry factor ${\cal A}(Q_T)$ (in units of $M^2$) at $Q = 90 \, \text{GeV}$ with $S_{NP}(b) = 2.05 \, b^2$ (solid curve) and $S_{NP}(b) = 1.37 \, b^2$ (dashed curve).
  • Figure 4: The asymmetry factor ${\cal A}(Q_T)$ (in units of $M^2$) at $Q = 90 \, \text{GeV}$ multiplied by a factor 10 (solid curve) and the tree level quantity (in units of $M^2$) using $R_u^2=1 \, \text{GeV}^{-2}$ and $R^2/R_u^2 = 3/2$.
  • Figure 5: The asymmetry factor ${\cal A}(Q_T)$ (in units of $M_h$) at $Q=30 \, \text{GeV}$ (upper curve), $Q = 60 \, \text{GeV}$ (middle curve) and at $Q = 90 \, \text{GeV}$.
  • ...and 1 more figures