Linearly polarized small- x gluons in forward heavy-quark pair production

Abstract

We use the Color Glass Condensate (CGC) framework to study the production of forward heavy quark-antiquark pairs in unpolarized proton-nucleus or proton-proton collisions in the small-x regime. In the limit of nearly back-to-back jets, the CGC result simplifies into the transversemomentum dependent (TMD) factorization approach. For massless quarks, the TMD factorization formula involves three unpolarized gluon TMDs: the Weizsäcker-Williams gluon distribution, the adjoint-dipole gluon distribution, and an additional one. When quark masses are kept non-zero, three new gluon TMDs appear -each partnered to one of the aforementioned distributions -which describe the distribution of linearly-polarized gluons in the unpolarized small-x target. We show how these six gluon TMDs emerge from the CGC formulation and we determine their expressions in terms of Wilson line correlators. We calculate them analytically in the McLerran-Venugopalan model, and further evolve them towards smaller values of x using a numerical implementation of JIMWLK evolution.

Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

“…Indeed, the gauge links account for multiple scatterings from slow gluons, and the importance of such gauge links is that they can be used as a probe for multiple scattering effects. These effects have been investigated recently in [23,25]. They are expected to appear at small |k|, since all TMD distributions reduce to the unintegrated PDF in the large |k| limit regardless of their gauge link structure, as discussed earlier.…”

“…Transverse Momentum Dependent (TMD) distributions were first recovered in [15,16] via a so-called correlation expansion, which was extended in [17,18] for 3-particle final states and to infinite kinematic twist accuracy in [19]. The correspondance between low x and TMD observables is the subject of many recent studies [20][21][22][23][24][25]. For a review on TMD gluon distributions at small x, the reader is referred to [26].…”

Prompt photon-jet angular correlations at central rapidities in p+A collisions

“…[10] where a direct relationship to the distributions in the conventional transverse-momentum-dependent (TMD) formalism discussed in [8,9] was given. Reference [10] also established a set of linear relationships to the various dipole and Weizsäcker-Williams gluon distributions [10]; see also [22]. In addition, we provide explicit expressions in terms of the BK two-point function of A þ in Appendix B.…”

“…By partial integration we can turn powers of k i , ðk 2 − kÞ i and k i 2 into gradients of the correlator of four Wilson lines (22). For example,…”

Probing the linear polarization of photons in ultraperipheral heavy ion collisions

“…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.…”