Non-zero transversity distribution of the pion in a quark-spectator-antiquark model

TL;DR

The paper addresses the origin of cos2phi azimuthal asymmetries in unpolarized Drell-Yan processes by computing the pion's naive-T-odd transversity distribution h1_pi_perp in a quark-spectator-antiquark model with final-state interactions modeled by one-gluon exchange. The main finding is that h1_pi_perp shares the same transverse-momentum dependence as the proton's h1_perp in a quark-scalar-diquark model, though their x-dependences differ, suggesting a common underlying mechanism for cos2phi across different hadrons. Using this result, the authors estimate an unsuppressed cos2phi asymmetry in pi^- p Drell-Yan with a magnitude around 10%, and the asymmetry's shape mirrors that found in pbar-p Drell-Yan. These results imply a connected framework for TMDs and azimuthal asymmetries in hadronic collisions, with concrete predictions for pion-induced Drell-Yan experiments.

Abstract

We calculate the non-zero (naïve) T-odd transverse momentum dependent transversity distribution $h_1^{\perp}(x,\kp^2)$ of the pion in a quark-spectator-antiquark model. The final-state interaction is modelled by the approximation of one gluon exchange between the quark and the antiquark spectator. Using our model result we estimate the unsuppressed cos2$φ$ azimuthal asymmetry in unpolarized $π^-p$ Drell-Yan process. We find that the transverse momentum dependence of $h_1^{\perp}(x,\kp^2)$ of the pion is the same as that of $h_1^{\perp}(x,\kp^2)$ of the proton calculated from the quark-scalar-diquark model, although the $x$ dependencies of them are different from each other. This suggests a connection between cos2$φ$ asymmetries in Drell-Yan processes with different initial hadrons.

Figures (5)

• Figure 1: Diagram which gives $\Phi$ of the pion in the quark-spectator-antiquark model in lowest order.
• Figure 2: Diagram which yields $\Phi$ with final-state interaction modelled by one gluon exchange.
• Figure 3: Model prediction of $|\mathbf{k}_\perp h_{1\pi}^\perp(x,\mathbf{k}_\perp^2)|/[M_\pi f_{1\pi}(x,\mathbf{k}_\perp^2)]$ as a function of $x$ and $|\mathbf{k}_\perp|$.
• Figure 4: Angular definitions of unpolarized Drell-Yan process in the lepton pair center of mass frame.
• Figure 5: Numerical result for the cos2$\phi$ asymmetry in $\pi^-p$ unpolarized Drell-Yan (solid line), using $M_\pi=0.137$ GeV, m=0.1 GeV, and $x=\bar{x}=0.2$. The dashed line corresponds to the same asymmetry in $\bar{p}p$ Drell-Yan process estimated in the quark-scalar-diquark model (see Ref. bbh03).