Azimuthal asymmetry in unpolarized $πN$ Drell-Yan process

TL;DR

The paper addresses the origin of the large cos 2φ azimuthal asymmetry in unpolarized Drell–Yan by focusing on the Boer-Mulders function $h_1^\perp$ for the pion. It computes the pion's $h_{1\pi}^\perp$ within a quark-spectator-antiquark model incorporating final-state interactions via a Wilson line, using a dipole-form pion coupling to obtain finite, physically meaningful results. The cos 2φ asymmetry is predicted as the product $h_{1\pi}^\perp \times \bar h_1^\perp$ with a similarly treated nucleon distribution, and the authors compare their predictions to NA10 data. The results show good agreement when a dipole coupling is used, supporting the role of T-odd transverse momentum dependent distributions and final-state interactions in explaining the Drell–Yan azimuthal asymmetries and providing a consistent interpretation of historical measurements.

Abstract

Taking into account the effect of final state interaction, we calculate the non-zero (naïve) $T$-odd transverse momentum dependent distribution $h_1^{\perp}(x,\kp^2)$ of the pion in a quark-spectator-antiquark model with effective pion-quark-antiquark coupling as a dipole form factor. Using the model result we estimate the $\cos 2φ$ asymmetries in the unpolarized $π^- N$ Drell-Yan process which can be expressed as $h_1^{\perp}\times\bar{h}_1^{\perp}$. We find that the resulting $h_{1π}^\p(x,\kp^2)$ has the advantage to reproduce the asymmetry that agrees with the experimental data measured by NA10 Collaboration. We estimate the $\cos2φ$ asymmetries averaged over the kinematics of NA10 experiments for 140, 194 and 286 GeV $π^-$ beam and compare them with relevant experimental data.

Figures (4)

• Figure 1: Effective correlation function $\Phi$ in the antiquark spectator model with final-state interaction modelled by one gluon exchange.
• Figure 2: Angular definitions of the unpolarized Drell-Yan process in the lepton pair center of mass frame.
• Figure 3: The $\cos2\phi$ asymmetry (solid line) in the unpolarized $\pi^-N$ Drell-Yan process defined in the Collins-Soper frame at $\bar{x}=x=0.5$. The dashed line represents asymmetry given by the previous model result lm04b (with $h_{1\pi}^\perp$ calculated in case 1). The data are taken from Ref. na10 at 194 GeV.
• Figure 4: The $\cos2\phi$ asymmetries in the Collins-Soper frame for pion beam with different energy averaged over kinematics region: $\bar{x}<0.7$, $4.0\leq Q\leq 8.5~\textmd{GeV}$ ($4.05\leq Q\leq 8.5~\textmd{GeV}$ for the $194~\textmd{GeV}$ Data) and $Q \geq 11~\textmd{GeV}$. The data are taken from Ref. na10.