Abstract
Transverse-momentum-dependent (TMD) gluon distributions have different operator definitions, depending on the process under consideration. We study that aspect of TMD factorization in the small-x limit, for the various unpolarized TMD gluon distributions encountered in the literature. To do this, we consider di-jet production in hadronic collisions, since this process allows to be exhaustive with respect to the possible operator definitions, and is suitable to be investigated at small x. Indeed, for forward and nearly back-to-back jets, one can apply both the TMD factorization and Color Glass Condensate (CGC) approaches to compute the di-jet cross-section, and compare the results. Doing so, we show that both descriptions coincide, and we show how to express the various TMD gluon distributions in terms of CGC correlators of Wilson lines, while keeping Nc finite. We then proceed to evaluate them by solving the JIMWLK equation numerically. We obtain that at large transverse momentum, the process dependence essentially disappears, while at small transverse momentum, non-linear saturation effects impact the various TMD gluon distributions in very different ways. We notice the presence of a geometric scaling regime for all the TMD gluon distributions studied: the "dipole" one, the Weizs\"acker-Williams one, and the six others involved in forward di-jet production.
Highlights
Gluon TMDs are affected by non-linear effects when kt becomes of the order of the saturation scale Qs(x), or below
We have studied the process dependence of unpolarized gluon TMDs at small-x, in the Color Glass Condensate (CGC) framework
We investigated what happens when the large gluon density of the target reaches the saturation regime, and how the various process-dependent gluon TMDs are affected by non-linear effects when the transverse momentum becomes of the order of the saturation scale Qs(x2), or below
Summary
We consider the process of inclusive di-jet production in the forward region, in collisions of dilute and dense systems p(pp) + A(pA) → j1(p1) + j2(p2) + X. The energy (or longitudinal momenta) fractions of the incoming parton (either a quark or gluon) from the projectile, x1, and the gluon from the target, x2, can be expressed in terms of the rapidities and transverse momenta of the produced jets as x1. The large-x partons of the dilute projectile are described in terms of the usual parton distribution functions of collinear factorization q(x1, μ2) and g(x1, μ2), with a scale dependence given by DGLAP evolution equations, while the small-x gluons of the dense target are described by several transverse-momentum-dependent (TMD) distributions, which evolve towards small values of x2 according to non-linear equations. Besides its longitudinal component k− = x2 s/2, the momentum of the incoming gluon from the target has in general a non-zero transverse component kt = p1t + p2t (2.5).
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