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$T$-Odd Effects in Unpolarized Drell-Yan Scattering

Leonard P. Gamberg, Gary R. Goldstein

TL;DR

The paper tackles the origin of the cos 2φ azimuthal asymmetry in unpolarized Drell–Yan scattering by proposing leading-twist T-odd transversity distributions, specifically h1^⊥, as the dominant mechanism. It develops a quark–diquark spectator model with final/initial-state interactions to compute h1^⊥ and then evaluates the double T-odd convolution that generates ν2, comparing it to a small T-even twist-4 contribution. Numerical results at s=50 GeV^2 show the T-odd piece can be sizable (up to ~30% in certain kinematic slices) while the T-even piece remains a few percent, with additional dependence on q_T, x, x_F, and q. The analysis supports using unpolarized Drell–Yan, particularly in pbar-p collisions at GSI, to access intrinsic transverse spin effects and transversity without polarized beams, though a full QCD treatment requires higher-order and Sudakov corrections.

Abstract

We consider the leading twist $T$-odd contributions as the dominant source of the $\cos 2φ$ azimuthal asymmetry in unpolarized $p\bar{p}\to μμ^+ X$ dilepton production in Drell-Yan Scattering. This asymmetry contains information on the distribution of quark transverse spin in an unpolarized proton. In a parton-spectator framework we estimate these asymmetries at $50 {\rm GeV}$ center of mass energy. This azimuthal asymmetry is interesting in light of proposed experiments at GSI, where an anti-proton beam is ideal for studying the transversity properties of quarks due to the dominance of {\em valence} quark effects.

$T$-Odd Effects in Unpolarized Drell-Yan Scattering

TL;DR

The paper tackles the origin of the cos 2φ azimuthal asymmetry in unpolarized Drell–Yan scattering by proposing leading-twist T-odd transversity distributions, specifically h1^⊥, as the dominant mechanism. It develops a quark–diquark spectator model with final/initial-state interactions to compute h1^⊥ and then evaluates the double T-odd convolution that generates ν2, comparing it to a small T-even twist-4 contribution. Numerical results at s=50 GeV^2 show the T-odd piece can be sizable (up to ~30% in certain kinematic slices) while the T-even piece remains a few percent, with additional dependence on q_T, x, x_F, and q. The analysis supports using unpolarized Drell–Yan, particularly in pbar-p collisions at GSI, to access intrinsic transverse spin effects and transversity without polarized beams, though a full QCD treatment requires higher-order and Sudakov corrections.

Abstract

We consider the leading twist -odd contributions as the dominant source of the azimuthal asymmetry in unpolarized dilepton production in Drell-Yan Scattering. This asymmetry contains information on the distribution of quark transverse spin in an unpolarized proton. In a parton-spectator framework we estimate these asymmetries at center of mass energy. This azimuthal asymmetry is interesting in light of proposed experiments at GSI, where an anti-proton beam is ideal for studying the transversity properties of quarks due to the dominance of {\em valence} quark effects.

Paper Structure

This paper contains 5 sections, 12 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Drell-Yan and $T$-Odd Correlations
  3. $T$-odd transversity distribution
  4. $T$-Even Contribution
  5. Conclusion

Figures (7)

  • Figure 1: Above: Feynman diagram representing final state interactions giving rise to $T$-odd contribution to Drell-Yan Scattering. Below: Quark-target scattering amplitude depicting the $T$-odd contribution to the quark distribution function in the eikonal approximation.
  • Figure 2: $\nu$ plotted as a function of $q_T$ for $s=50\ {\rm GeV}^2$, $x$ in the range $0.2-1.0$, and $q$ ranging from $3-6 \ {\rm GeV}/c$.
  • Figure 3: $\nu$ plotted as a function of $q=m_{\mu\mu}$ for $s=50\ {\rm GeV}^2$, $x$ in the range $0.2-1.0$, and $q_T$ ranging from $0-3 \ {\rm GeV}/c$.
  • Figure 4: Contours of constant $x$ as a function of $\zeta$ and $q$ which ranges from 0 to 3 GeV/c.
  • Figure 5: $\nu$ plotted as a function of $\zeta$ for $s=50\ {\rm GeV}^2$, $q_T$ ranging from $3$ to $6$ GeV/c and $q$ from 0 to 3 GeV/c.
  • ...and 2 more figures