Abstract
We investigate the Sivers asymmetry in the pion-induced single polarized Drell-Yan process in the theoretical framework of the transverse momentum dependent factorization up to next-to-leading logarithmic order of QCD. Within the TMD evolution formalism of parton distribution functions, the recently extracted nonperturbative Sudakov form factor for the pion distribution functions as well as the one for the Sivers function of the proton are applied to numerically estimate the Sivers asymmetry in the $\pi^- p$ Drell-Yan at the kinematics of the COMPASS at CERN. In the low $b$ region, the Sivers function in $b$-space can be expressed as the convolution of the perturbatively calculable hard coefficients and the corresponding collinear correlation function, of which the Qiu-Sterman function is the most relevant one. The effect of the energy-scale dependence of the Qiu-Sterman function to the asymmetry is also studied. We find that our prediction on the Sivers asymmetries as functions of $x_p$, $x_\pi$, $x_F$ and $q_\perp$ is consistent with the recent COMPASS measurement.
Highlights
The Sivers function [1] is a transverse momentum dependent (TMD) parton distribution function (PDF), which describes the asymmetric distribution of unpolarized quarks inside a transversely polarized nucleon through the correlation between the quark transverse momentum and the nucleon transverse spin
Our analysis demonstrates that, combining the previous analysis of unpolarized pion TMD PDFs and that of the proton Sivers function within the TMD factorization and evolution, can lead to the Sivers asymmetry in π−N DrellYan which is consistent with the COMPASS measurement
We applied the formalism of the TMD factorization to study the Sivers asymmetry in the pion induced Drell-Yan process that is accessible at COMPASS
Summary
The Sivers function [1] is a transverse momentum dependent (TMD) parton distribution function (PDF), which describes the asymmetric distribution of unpolarized quarks inside a transversely polarized nucleon through the correlation between the quark transverse momentum and the nucleon transverse spin. The TMD framework of QCD predicts that the T-odd PDFs present generalized universality, i.e., the sign of the Sivers function measured in Drell-Yan process should be opposite to its sign measured in SIDIS [16,17,18]. The verification of this sign change [19,20,21,22,23,24] is one of the most fundamental. The COMPASS Collaboration has reported the first measurement of the Sivers asymmetry in the pion-induced Drell-Yan process, in which a π− beam was scattered off the transversely polarized NH3 target [25].
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