Monte Carlo simulation of the Sivers effect in high-energy proton-proton collisions

TL;DR

This study uses Monte Carlo simulations to examine the Sivers effect in polarized proton-proton Drell-Yan at √s = 200 GeV, testing the universality prediction of a sign change between SIDIS and Drell-Yan and assessing experimental feasibility at RHIC II. By implementing two distinct Sivers parametrizations (one SIDIS-based and one high-energy, RHIC-constrained), the authors quantify how the single-spin asymmetry depends on x and q_T, and they estimate cross sections and event rates under realistic luminosities. The results show that the sign-change test is feasible in favorable kinematic regions, especially with ample statistics and careful q_T cuts, and that the low-x region, where sea-quark contributions dominate, provides rich sensitivity to the Sivers mechanism. Overall, the work demonstrates how Drell-Yan SSA measurements at RHIC could illuminate the x-dependence of f_{1T}^⊥ and test fundamental QCD predictions about TMD universality.

Abstract

We present Monte Carlo simulations of the Sivers effect in the polarized Drell-Yan $pp^\uparrow \to μ^+ μ^- X$ process at the center-of-mass energy $\sqrt{s}=200$ GeV reachable at the Relativistic Heavy-Ion Collider (RHIC) of BNL. We use two different parametrizations for the Sivers function, one deduced from the analysis of Semi-Inclusive Deep-Inelastic Scattering (SIDIS) data at much lower energies, and another one constrained by the RHIC data for the $pp^\uparrow \to πX$ process at the same energy. For a given luminosity of $10^{32}$ cm$^{-2}$ sec$^{-1}$, we explore the necessary conditions to reach a statistical accuracy that allows to extract unambiguous information on the structure of the Sivers function. In particular, we consider the feasibility of the test on its predicted universality property of changing sign when switching from SIDIS to Drell-Yan processes.

Figures (7)

• Figure 1: The Collins-Soper frame.
• Figure 2: The scatter plot for $120\,000$ events of Drell-Yan muon pairs produced by proton-proton collisions at $\sqrt{s}=200$ GeV. The two bands in which data are grouped, correspond to two different ranges in the muon invariant mass: $4<M<9$ GeV for the lower band, $12<M<40$ GeV for the upper one.
• Figure 3: The sample of $20\,000$ Drell-Yan events for the $pp^\uparrow \to \mu^+ \mu^- X$ reaction at $\sqrt{s}=200$ GeV, $12<M<40$ GeV, and $1<q_{ T} <3$ GeV/$c$, using the parametrization of Eq. (\ref{['eq:pTnoi']}) (see text). Upper panel: for each bin in the parton momentum $x_2$ inside $p^\uparrow$, the darker histogram collects events with positive $\sin (\phi - \phi_{S_2})$$(U)$, the superimposed lighter histogram collects the negative ones $(D)$. Lower panel: the asymmetry $(U-D)/(U+D)$; upward triangles for $N_u>0$ in Eq. (\ref{['eq:pTnoi']}) corresponds to a sign change in the Sivers function from SIDIS to Drell-Yan processes; squares for $N_u<0$. Statistical error bars from 10 independent repetitions of the simulation. Continuous lines are drawn to guide the eye.
• Figure 4: Same as in Fig. \ref{['fig:noi12']} but considering $100\,000$ events using the parametrization of Eq. (\ref{['eq:pTanselm']}) and $0.1<q_{ T} <2$ GeV/$c$ (see text). Lower panel: upward triangles for $N_u>0$ in Eq. (\ref{['eq:c4mc-anselm']}), squares for $N_u<0$.
• Figure 5: The sample of $100\,000$ Drell-Yan events for the same reaction in the same conditions and notations as in Fig. \ref{['fig:noi12']} but for $4<M<9$ GeV. Left panel: parametrization of Eq. (\ref{['eq:pTnoi']}); right panel: parametrization of Eq. (\ref{['eq:pTanselm']}) (see text).