Photoproduction of three jets in the CGC: gluon TMDs and dilute limit

Abstract

We study the process $\gamma A\to q\bar{q}g+X$ in the Color Glass Condensate (CGC) effective theory. After obtaining the cross section, we consider two kinematic limits which are encompassed in our result. In the so-called correlation limit, the vector sum of the transverse momenta of the three outgoing particles is small with respect to the individual transverse momenta; the cross section then simplifies considerably and can be written in a factorized form, sensitive to both the unpolarized and linearly-polarized Weizsäcker-Williams transverse momentum dependent gluon distribution function (gluon TMD). The second limit of the CGC cross section that we consider is the dilute limit, which we obtain after performing a weak-field expansion; we recover a typical linear-regime expression, involving a single unintegrated gluon distribution function. Using numerical simulations of the small-$x$ QCD evolution of the TMDs, we investigate the rapidity dependence of the cross section in the correlation limit.

Comments: 49 pages, numerical results on dilute (HEF) limit added, minor error fixed in numerical computation of correlation (TMD) limit, section on the analytical relation between the TMD and HEF limits of the cross section added, typos fixed, conclusions unchanged. Matches the published version