sin(2ϕ−ϕS) azimuthal asymmetry in the pion induced Drell-Yan process within TMD factorization

Abstract

We investigate the single transverse-spin asymmetry with a sin(2φ − φS) modulation in the pioninduced 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(2φ − φS) asymmetry in π − 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(2φ − φS) as functions of xp, xπ, xF and q ⊥ is qualitatively consistent with the recent COMPASS measurement in both sign and magnitude. I. INTRODUCTIONThe Boer-Mulders function, denoted by h ⊥ 1 , is one of the eight transverse momentum dependent (TMD) parton distribution functions (PDFs) describing the partonic structure of hadrons at leading-twist level. It represents the transversely polarization asymmetry of quarks inside an unpolarized hadron [1,2] arising from the correlation between the quark spin and the quark transverse momentum, thereby it manifests the novel structure of hadrons. However, the very existence of the Boer-Mulders function was not so obvious. Similar to its chiral-even partner-the Sivers function f ⊥ 1T [3], the Boer-Mulder function was initially thought to vanish under the constraint of (naive) time reversal invariance of QCD [4]. The situation was changed after explicit model calculations [5][6][7] incorporating gluon exchange between the struck quark and the spectator shows that the T-odd distributions can actually survive. The crucial ingredient in the argument is the Wilson lines (or the gauge links) appearing in the full gange-invariant definition of TMDs [8,9]. The presence of the Wilson lines also indicates that the T-odd distributions, such as Sivers function and the Boer-Mulders function are process dependent, i.e., they change sign [6][7][8] between the semi-inclusive deeply inelastic scattering and Drell-Yan process, a vital prediction which needs verification by future experimental measurement. In the last decades, the Boer-Mulders function of the proton as well as that of the pion has been studied intensively in literature [7, by models and phenomenological analysis.As the Boer-Mulders function is a chiral-odd distribution function, it has to be coupled with another chirlal-odd distribution/fragmentation function to survive in a high energy scattering process. A promising process for accessing the Boer-Mulders function is the unpolarized Drell-Yan process, which displays an azimuthal dependence of the finalstate dilepton with the cos 2φ modulation. As proposed by Boer [2], the coupling of two Boer-...

The Drell-Yan process with pions and polarized nucleons

“…For completeness we remark that the importance of TMD evolution for the description of pion-induced DY and the recent COMPASS data was also studied in refs. [73,[97][98][99][100][101].…”

Kotzinian-Mulders effect in semi-inclusive DIS within TMD factorization *

“…Measurements have also been conducted for the KM effect in SIDIS with a neutron target [3,34]. TMD factorization has been applied in many studies [35][36][37][38][39][40] focusing on various asymmetries in Drell-Yan and SIDIS processes. Beginning from the previous research by Collins-Soper-Sterman (CSS) [41,42], the so-called TMD evolution following from factorization theorems has been fully developed in recent years.…”

The Drell-Yan process with pions and polarized nucleons

“…TMD evolution has been studied for the COMPASS DY data and asymmetries also in Refs. [71,[73][74][75][76]. QCD evolution is particularly important when applying CQM results obtained at a low initial scale to the description of high-energy processes.…”