Monte Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions: the fully polarized case

TL;DR

This work extends previous Monte Carlo studies by analyzing a fully polarized antiproton–proton Drell-Yan process to access nucleon transversity. Using Monte Carlo simulations at HESR-relevant kinematics, the authors model the leading-twist double-spin asymmetry $A_{TT}$ and its dependence on the transversity distribution $h_1(x)$ relative to the unpolarized $f_1(x)$ under the Soffer bound. They explore collider (s ≈ 200 GeV^2) and fixed-target (s ≈ 30 GeV^2) configurations and multiple functional forms for $h_1/f_1$, evaluating how many events are required to discern the transversity behavior. The results indicate that in collider mode a sample of about 17,000 good events can yield measurable asymmetries in the valence x range 0.1–0.3, supporting the feasibility of direct transversity extraction at HESR, while fixed-target kinematics are more challenging but still informative.

Abstract

In this paper, we extend the study of Drell-Yan processes with antiproton beams already presented in a previous work. We consider the fully polarized $\bar{p}^\uparrow p^\uparrow \to μ^+ μ^- X$ process, because this is the simplest scenario for extracting the transverse spin distribution of quarks, or transversity, which is the missing piece to complete the knowledge of the nucleon spin structure at leading twist. We perform Monte Carlo simulations for transversely polarized antiproton and proton beams colliding at a center-of-mass energy of interest for the future HESR at GSI. The goal is to possibly establish feasibility conditions for an unambiguous extraction of the transversity from data on double spin asymmetries.

Figures (10)

• Figure 1: The Collins-Soper frame.
• Figure 2: The leading-twist contribution to the Drell-Yan process.
• Figure 3: The sample of 17000 events for the $\bar{p}^\uparrow \, p^\uparrow \rightarrow \mu^+\, \mu^- \,X$ process where a transversely polarized antiproton beam with energy $E_{\bar{p}} = 15$ GeV collides on a transversely polarized proton beam with $E_p = 3.3$ GeV producing muon pairs of invariant mass $4 \leq M \leq 9$ GeV (for further details on the cutoffs, see text). a) $\langle h_1(x_p) \rangle / \langle f_1(x_p) \rangle = \sqrt{x_p}$ (brackets mean that each flavor contribution in the numerator is replaced by a common average term, similarly in the denominator; for further details, see text). b) $\langle h_1(x_p) \rangle / \langle f_1(x_p) \rangle = \sqrt{1-x_p}$. c) $\langle h_1(x_p) \rangle / \langle f_1(x_p) \rangle = 1$. d) $\langle h_1(x_p) \rangle / \langle f_1(x_p) \rangle = 0$. For each bin, the darker histogram corresponds to positive values of $\cos(2\phi - \phi_{_{S_{\bar{p}}}} - \phi_{_{S_p}})$ in Eq. (\ref{['eq:mcS']}), the superimposed lighter one to negative values.
• Figure 4: Asymmetry $(U-D)/(U+D)$ between cross sections in the previous figure corresponding to darker histograms ($U$) and superimposed lighter histograms ($D$), as bins in $x_p$. Full squares for the case when $\langle h_1(x_p) \rangle / \langle f_1(x_p) \rangle = \sqrt{x_p}$, upward triangles when it equals $\sqrt{1-x_p}$, downward triangles when it equals 1 and open squares when it equals 0. Continuous lines are drawn to guide the eye. Error bars due to statistical errors only, obtained by 20 independent repetitions of the simulation (see text for further details).
• Figure 5: Unintegrated asymmetry $(U-D)/(U+D)$ for the case $\langle h_1(x) \rangle / \langle f_1(x) \rangle = \sqrt{x}$ in the same conditions as the previous figure, but plotted in bins of $x_{\bar{p}}$ and $x_p$. Left panel: distribution of average values. Right panel: distribution of the variances, i.e. of half the statistical "error bars", obtained by 20 independent repetitions of the simulation (see text for further details).