Monte Carlo simulation of single spin asymmetries in pion-proton collisions

TL;DR

This study uses Monte Carlo simulations to explore how π± p↑ Drell–Yan events at COMPASS kinematics can illuminate transverse-momentum dependent parton distributions. By testing two Sivers parametrizations and exploring Boer–Mulders/transversity scenarios, the work assesses the feasibility of extracting the Sivers sign change between SIDIS and Drell–Yan and evaluates the sensitivity to h1 and h1⊥. The results show clear potential for validating the Sivers universality with realistic event samples, while Boer–Mulders and transversity remain challenging due to limited parametrizations and small asymmetries in the chosen kinematic range. Overall, the paper provides guidance for interpreting future COMPASS measurements in the context of nucleon spin structure and TMD phenomenology.

Abstract

We present Monte Carlo simulations of both the Sivers and the Boer-Mulders effects in the polarized Drell-Yan $π^\pm p^\uparrow \to μ^+ μ^- X$ process at the center-of-mass energy $\sqrt{s} \sim 14$ GeV reachable at COMPASS with pion beams of energy 100 GeV. For the Sivers effect, we adopt two different parametrizations for the Sivers function to explore the statistical accuracy required to extract unambiguous information on this parton density. In particular, we verify the possibility of checking its predicted sign change between Semi-Inclusive Deep-Inelastic Scattering (SIDIS) and Drell-Yan processes, a crucial test of nonperturbative QCD. For the Boer-Mulders effect, because of the lack of parametrizations we can make only guesses. The goal is to explore the possibility of extracting information on the transversity distribution, the missing piece necessary to complete the knowledge of the nucleon spin structure at leading twist, and the Boer-Mulders function, which is related to the long-standing problem of the violation of the Lam-Tung sum rule in the unpolarized Drell-Yan cross section.

Figures (7)

• Figure 1: The Collins-Soper frame.
• Figure 2: The samples of Drell-Yan events for the Sivers effect in the $\pi^\pm p^\uparrow \to \mu^+ \mu^- X$ reaction at $\sqrt{s}\sim 14$ GeV, $4<M<9$ GeV, and $0.5<q_{ T} <2.5$ GeV/$c$, using the parametrization of Eq. (\ref{['eq:pTanselm']}) (see text). a) left panel: $100\,000$ events with the $\pi^-$ beam; the darker histogram collects events with positive $\sin (\phi - \phi_{S_2})$, the superimposed lighter histogram collects the negative ones. b) right panel: the same for $25\,000$ events with the $\pi^+$ beam.
• Figure 3: The asymmetry $(U-D)/(U+D)$ corresponding to the histograms of Fig. \ref{['fig:pi+-anselm_histo']}, where $U$ identifies the darker histograms and $D$ the superimposed lighter ones (see text). Triangles for the parametrization of Eq. (\ref{['eq:pTanselm']}) using the $\pi^-$ beam and with $N_u>0$; squares for $N_u<0$. Open triangles using the $\pi^+$ beam and with $N_u>0$; open squares for $N_u<0$.
• Figure 4: The same situation with the same notations as in Fig. \ref{['fig:pi+-anselm_histo']}, but for the parametrization of Eq. (\ref{['eq:pTnoi']}) with $1<q_{ T} <3$ GeV/$c$ (see text).
• Figure 5: The same situation with the same notations as in Fig. \ref{['fig:pi+-anselm_as']}, but for the parametrization of Eq. (\ref{['eq:pTnoi']}) (see text).