Monte-Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions

TL;DR

This study uses Monte-Carlo simulations of unpolarized and single-polarized Drell–Yan processes with antiproton–proton collisions to evaluate the feasibility of extracting transversity h1 and the chiral-odd distribution h1⊥ at the GSI HESR facility. By modeling kinematics, QCD corrections, angular distributions in the Collins–Soper frame, and target dilution effects, the authors compare fixed-target and collider configurations across different dilepton masses and energies. They find that collider setups (e.g., s ≈ 200 GeV^2) yield larger azimuthal asymmetries and much better statistics, enabling clearer discrimination of h1(x) shapes for x_p ≲ 0.4 with relatively modest event samples, while unpolarized measurements of the cos 2φ asymmetry test h1⊥ through ν. The results support the feasibility of accessing both transversity and h1⊥ at HESR, guiding planning for spin-physics programs with antiproton beams.

Abstract

The complete knowledge of the nucleon spin structure at leading twist requires also addressing the transverse spin distribution of quarks, or transversity, which is yet unexplored because of its chiral-odd nature. Transversity can be best extracted from single-spin asymmetries in fully polarized Drell-Yan processes with antiprotons, where valence contributions are involved anyway. Alternatively, in single-polarized Drell-Yan the transversity happens convoluted with another chiral-odd function, which is likely to be responsible for the well known (and yet unexplained) violation of the Lam-Tung sum rule in the corresponding unpolarized cross section. We present Monte-Carlo simulations for the unpolarized and single-polarized Drell-Yan $\bar{p} p^{(\uparrow)} \to μ^+ μ^- X$ at different center-of-mass energies in both configurations where the antiproton beam hits a fixed proton target or it collides on another proton beam. The goal is to estimate the minimum number of events needed to extract the above chiral-odd distributions from future measurements at the HESR ring at GSI. It is important to study the feasibility of such experiments at HESR in order to demonstrate that interesting spin physics can be explored already using unpolarized antiprotons.

Figures (12)

• Figure 1: The leading-twist contribution to the Drell-Yan process.
• Figure 2: The Collins-Soper frame.
• Figure 3: The scatter plot for 48000 events of Drell-Yan muon pairs produced by the collision of a 40 GeV antiproton beam on a proton target in the kinematic conditions discussed in the text.
• Figure 4: The correlation between the polar angle of $\mu^+$ in the laboratory, $\theta_{\rm lab}$, and in the Collins-Soper frame, $\theta$, for the collision of antiprotons with 40 GeV energy and fixed proton targets.
• Figure 5: The sample of 40000 events for the $\bar{p} \, p^\uparrow \rightarrow \mu^+\, \mu^- \,X$ process on a fixed proton target with an antiproton beam energy $E_{\bar{p}} = 40$ GeV and with a muon pair of invariant mass $4 \leq M \leq 9$ GeV and transverse momentum $q_{_T} > 1$ GeV/$c$ (for further details on the cutoffs, see text). a) Left panel for the choice $\langle h_1(x_p) \rangle / \langle f_1(x_p) \rangle = 2 x_p$ (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) Right panel for $\langle h_1(x_p) \rangle / \langle f_1(x_p) \rangle = 2 (1-x_p)$. For each bin, the darker histogram corresponds to positive values of $\sin(\phi + \phi_{S_p})$ in Eqs. (\ref{['eq:mcS']}) and (\ref{['eq:mcS4']}), the superimposed lighter one to negative values.