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Register a new userThe Weizsacker-Williams distribution of linearly polarized gluons (and its fluctuations) at small x
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The conventional and linearly polarized Weizsacker-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 $Ysim 1/alpha_s$. These are determined by a 2d Liouville action for the logarithm of the covariant gauge function $g^2 mathrm{tr},A^+(q)A^+(-q)$. 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.
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The production of a hard dijet with small transverse momentum imbalance in semi-inclusive DIS probes the conventional and linearly polarized Weizsu007faecker-Williams (WW) Transverse Momentum Dependent (TMD) gluon distributions. The latter, in particular, gives rise to an azimuthal dependence of the dijet cross-section. In this paper we analyze the feasibility of a measurement of these TMDs through dijet production in DIS on a nucleus at an Electron-Ion Collider. We introduce the MCDijet Monte-Carlo generator to sample quark-antiquark dijet configurations based on leading order parton level cross-sections with WW gluon distributions that solve the non-linear small-x QCD evolution equations. These configurations are fragmented to hadrons using PYTHIA, and final state jets are reconstructed. We report on background studies and on the effect of kinematic cuts introduced to remove beam jet remnants. We estimate that with an integrated luminosity of 20 fb^{-1}/A one can determine the distribution of linearly polarized gluons with a statistical accuracy of approximately 5%.
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