In this paper we consider the parametrizations of gluon transverse momentum dependent (TMD) correlators in terms of TMD parton distribution functions (PDFs). These functions, referred to as TMDs, are defined as the Fourier transforms of hadronic matrix elements of nonlocal combinations of gluon fields. The nonlocality is bridged by gauge links, which have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. For gluons, the specific correlator with one future and one past pointing gauge link is, in the limit of small x, related to a correlator of a single Wilson loop. We present the parametrization of Wilson loop correlators in terms of Wilson loop TMDs and discuss the relation between these functions and the small-x ‘dipole’ gluon TMDs. This analysis shows which gluon TMDs are leading or suppressed in the small-x limit. We discuss hadronic targets that are unpolarized, vector polarized (relevant for spin-1/2 and spin-1 hadrons), and tensor polarized (relevant for spin-1 hadrons). The latter are of interest for studies with a future Electron-Ion Collider with polarized deuterons.
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A.V. Belitsky, X. Ji and F. Yuan, Final state interactions and gauge invariant parton distributions, Nucl. Phys.B 656 (2003) 165 [hep-ph/0208038] [INSPIRE].
D. Boer, P.J. Mulders and F. Pijlman, Universality of T odd effects in single spin and azimuthal asymmetries, Nucl. Phys.B 667 (2003) 201 [hep-ph/0303034] [INSPIRE].
A.V. Efremov and A.V. Radyushkin, Field theoretic treatment of high momentum transfer processes. 1. Deep inelastic scattering, Theor. Math. Phys.44 (1980) 573 [Teor. Mat. Fiz.44 (1980) 17] [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Factorization for one loop corrections in the Drell-Yan process, Nucl. Phys.B 223 (1983) 381 [INSPIRE].ADSCrossRefGoogle Scholar
D. Boer and P.J. Mulders, Color gauge invariance in the Drell-Yan process, Nucl. Phys.B 569 (2000) 505 [hep-ph/9906223] [INSPIRE].
J.C. Collins, Leading twist single transverse-spin asymmetries: Drell-Yan and deep inelastic scattering, Phys. Lett.B 536 (2002) 43 [hep-ph/0204004] [INSPIRE].
P.J. Mulders and J. Rodrigues, Transverse momentum dependence in gluon distribution and fragmentation functions, Phys. Rev.D 63 (2001) 094021 [hep-ph/0009343] [INSPIRE].
S.J. Brodsky, D.S. Hwang and I. Schmidt, Final state interactions and single spin asymmetries in semiinclusive deep inelastic scattering, Phys. Lett.B 530 (2002) 99 [hep-ph/0201296] [INSPIRE].
A. Bacchetta, C.J. Bomhof, P.J. Mulders and F. Pijlman, Single spin asymmetries in hadron-hadron collisions, Phys. Rev.D 72 (2005) 034030 [hep-ph/0505268] [INSPIRE].
D. Boer and P.J. Mulders, Time reversal odd distribution functions in leptoproduction, Phys. Rev.D 57 (1998) 5780 [hep-ph/9711485] [INSPIRE].
D. Boer and W. Vogelsang, Asymmetric jet correlations in pp uparrow scattering, Phys. Rev.D 69 (2004) 094025 [hep-ph/0312320] [INSPIRE].
P.J. Mulders and R.D. Tangerman, The complete tree level result up to order 1/Q for polarized deep inelastic leptoproduction, Nucl. Phys.B 461 (1996) 197 [Erratum ibid.B 484 (1997) 538] [hep-ph/9510301] [INSPIRE].
J.P. Ralston and D.E. Soper, Production of dimuons from high-energy polarized proton proton collisions, Nucl. Phys.B 152 (1979) 109 [INSPIRE].ADSCrossRefGoogle Scholar
D.W. Sivers, Single spin production asymmetries from the hard scattering of point-like constituents, Phys. Rev.D 41 (1990) 83 [INSPIRE].ADSGoogle Scholar
J.C. Collins, Fragmentation of transversely polarized quarks probed in transverse momentum distributions, Nucl. Phys.B 396 (1993) 161 [hep-ph/9208213] [INSPIRE].
A. Kotzinian, New quark distributions and semiinclusive electroproduction on the polarized nucleons, Nucl. Phys.B 441 (1995) 234 [hep-ph/9412283] [INSPIRE].
R.D. Tangerman and P.J. Mulders, Intrinsic transverse momentum and the polarized Drell-Yan process, Phys. Rev.D 51 (1995) 3357 [hep-ph/9403227] [INSPIRE].
A. Bacchetta and P.J. Mulders, Deep inelastic leptoproduction of spin-one hadrons, Phys. Rev.D 62 (2000) 114004 [hep-ph/0007120] [INSPIRE].
I.O. Cherednikov, T. Mertens and F.F. Van der Veken, Evolution of cusped light-like Wilson loops and geometry of the loop space, Phys. Rev.D 86 (2012) 085035 [arXiv:1208.1631] [INSPIRE].ADSGoogle Scholar
W.J. den Dunnen, J.P. Lansberg, C. Pisano and M. Schlegel, Accessing the transverse dynamics and polarization of gluons inside the proton at the LHC, Phys. Rev. Lett.112 (2014) 212001 [arXiv:1401.7611] [INSPIRE].ADSCrossRefGoogle Scholar
A. Dumitru, T. Lappi and V. Skokov, Distribution of linearly polarized gluons and elliptic azimuthal anisotropy in deep inelastic scattering dijet production at high energy, Phys. Rev. Lett.115 (2015) 252301 [arXiv:1508.04438] [INSPIRE].ADSCrossRefGoogle Scholar
A. Bacchetta, C. Bomhof, U. D’Alesio, P.J. Mulders and F. Murgia, The Sivers single-spin asymmetry in photon-jet production, Phys. Rev. Lett.99 (2007) 212002 [hep-ph/0703153] [INSPIRE].