The Weizsäcker-Williams distribution of linearly polarized gluons (and its fluctuations) at small x

¹ Department of Natural Sciences, Baruch College, CUNY, 17 Lexington Avenue, New York, NY 10010, USA
² The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York, NY 10016, USA
³ Physics Department, Brookhaven National Lab, Upton, NY 11973, USA
⁴ RIKEN/BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA

^* e-mail: adrian.dumitru@baruch.cuny.edu
^** e-mail: vskokov@quark.phy.bnl.gov

Published online: 26 January 2018

Abstract

The conventional and linearly polarized Weizsäcker-Williams gluon distributions at small x are defined from the two-point function of the gluon field in light-cone gauge. They appear in the cross section for dijet production in deep inelastic scattering at high energy. We determine these functions in the small-x limit from solutions of the JIMWLK evolution equations and show that they exhibit approximate geometric scaling. Also, we discuss the functional distributions of these WW gluon distributions over the JIMWLK ensemble at rapidity Y ~ 1/α_s. These are determined by a 2d Liouville action for the logarithm of the covariant gauge function g²tr A⁺(q)A⁺(-q). For transverse momenta on the order of the saturation scale we observe large variations across configurations (evolution trajectories) of the linearly polarized distribution up to several times its average, and even to negative values.