# The $\sin (2\phi-\phi_S)$ azimuthal asymmetry in the pion induced Drell-Yan process within TMD factorization

## TL;DR

This paper predicts the $ ext{sin}(2 heta- heta_S)$ asymmetry in pion-induced Drell-Yan processes using TMD factorization, modeling distributions with light-cone wavefunctions and comparing results with COMPASS data.

## Contribution

It introduces a detailed TMD-based prediction of the single transverse-spin asymmetry in pion-induced Drell-Yan, incorporating nonperturbative evolution effects and model distributions.

## Key findings

- Prediction of asymmetry consistent with COMPASS data in sign and magnitude.
- Demonstration of the impact of TMD evolution on asymmetry estimates.
- Numerical estimates of asymmetry as functions of kinematic variables.

## Abstract

We investigate the single transverse-spin asymmetry with a $\sin (2\phi-\phi_S)$ modulation in the pion-induced Drell-Yan process within the theoretical framework of the transverse momentum dependent factorization. The asymmetry is contributed by the convolution of the Boer-Mulders function and the transversity. We adopt the model results for the distributions of the pion meson from the light-cone wavefunction approach and the available parametrization for the distributions of the proton to numerically estimate the $\sin (2\phi-\phi_S)$ asymmetry in $\pi^- p$ Drell-Yan at the kinematics of the COMPASS at CERN. To implement the TMD evolution formalism of parton distribution functions, we apply the recently extracted nonperturbative Sudakov form factor associated with the distribution functions of the proton and the pion. It is found that our prediction on the single transverse-spin dependent asymmetry ${\sin (2\phi-\phi_S)}$ as functions of $x_p$, $x_\pi$, $x_F$ and $q_\perp$ is qualitatively consistent with the recent COMPASS measurement in both sign and magnitude.