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The $\sin2ϕ$ azimuthal asymmetry in single longitudinally polarized $πN$ Drell-Yan process

We study the $\sin2ϕ$ azimuthal asymmetry in the $πN$ Drell-Yan process, when the nucleon is longitudinally polarized. The asymmetry is contributed by the combination of the Boer-Mulders function and the longitudinal transversity distribution function. We consider the Drell-Yan processes by $π^\pm$ beams colliding on the proton and deuteron targets, respectively. We calculate the $\sin2ϕ$ azimuthal asymmetries in these processes using the Boer-Mulders function and the longitudinal transversity from spectator models. We show that the study on single polarized $πN$ Drell-Yan processes can not only give the information on the new 3-dimensional parton distribution functions in momentum space, but also shed light on the chiral-odd structure of the longitudinally polarized nucleon.