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 smallx 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.

We propose to measure the linear polarization of the external electromagnetic fields of a relativistic heavy ion through azimuthal asymmetries in dilepton production in ultraperipheral collisions. The asymmetries estimated with the equivalent photon approximation are shown to be sizable.PACS numbers: I. INTRODUCTIONTransverse momentum dependent(TMD) parton distribution function [1] is one of the most powerful theoretical tools that are utilized to explore the three-dimensional imaging of nuleon/nuclei. Among many TMD parton distributions, the linearly polarized gluon distribution [2] has received growing attentions in recent years. It describes the correlation between gluon transverse momentum and its polarization vector inside an unpolarized nucleon or nucleus. It is of particular interest to study linearly polarized gluon distribution at small x [3, 4], as it is predicted to grow equally rapidly towards small x as compared to the unpolarized gluon distribution in the dilute limit. In the saturation limit, the dipole type linearly polarized gluon distribution and the dipole type unpolarized gluon distribution remain identical, whereas the linearly polarization of Weizsäcker-Williams gluons is suppressed. Though it has been found promising to probe the linearly polarized gluon distribution by measuring cos 2φ azimuthal asymmetry for two particle production in various high energy scattering processes at RHIC, LHC, or a future Electron-Ion Collider(EIC) [3][4][5][6][7][8][9][10][11][12][13], this gluon distribution so far has not yet been studied experimentally.In analogy to the QCD case, one also can define a linearly polarized photon distribution for an unpolarized nucleon or nuclei target, which can be accessed by measuring the azimuthal asymmetries in di-lepton production in hadronhadron collisions [8]. However, it is not very practical to extract the polarized photon distribution in hadronic reactions due to the di-lepton Drell-Yan production background. Instead, the cleaner and more promising way to probe the linearly polarization of photons would be the purely electromagnetic two photon reaction γγ → l + l − in heavy-ion ultra-peripheral collisions(UPCs) where the hadronic background is absent. Though photon-photon collisions in the UPC case has been extensively studied [14][15][16][17][18][19][20][21][22][23][24][25][26][27], to the best of our knowledge, the polarization dependent effects have not yet been addressed so far. Both the unpolarized photon distribution and the polarized one in the UPC case can be determined using the external classical field approximation [14,15]. It is not surprising to find that they are identical to each other in this approximation, just like the relation established between the dipole amplitude and the polarized gluon distributions [3,[28][29][30]. In the present paper, we propose to test this theoretical predication by measuring cos 2φ and cos 4φ asymmetries in di-lepton production induced by the linearly polarized photon distribution.Recently, the STAR collaboration at RH...

We investigate the impact parameter dependence of the cos 4φ azimuthal asymmetry for electromagnetic lepton pair production in heavy ion collisions. The asymmetry induced by linearly polarized coherent photons exhibits strong impact parameter dependence.