TMD factorization for dijets + photon production from the dilute-dense CGC framework

Abstract

We calculate the production of a photon and two jets at forward rapidity in proton-nucleus collisions, within the hybrid dilute-dense framework in the Color Glass Condensate (CGC) formalism. After obtaining the cross section for both the quark-and gluon-initiated channels, we consider the correlation limit, in which the vector sum of the transverse momenta of the three outgoing particles is small with respect to the individual transverse momenta. In this limit, the cross section simplifies considerably and can be written in a factorized form, sensitive to various unpolarized and linearly-polarized transverse-momentum-dependent gluon distribution functions (gluon TMDs). Thus, we demonstrate for the first time that the emergence of a TMD factorization formula in the correlation limit, from CGC expressions, holds beyond the previously-considered simpler 2 → 2 processes.In the case of collinear factorization, there is a single hard scale, and the PDFs and FFs are only a function of this scale and of the longitudinal momentum fraction x of the parton. However, in less inclusive processes that depend on a second, smaller scale, these distributions need to be generalized to include the dependence on the transverse momentum of the parton, yielding the so-called transverse-momentum-dependent (TMD) PDFs and FFs. These TMD PDFs/FFs are of great interest since their measurement offers insight in the three-dimensional structure of the proton in terms of the QCD degrees of freedom. However, in contrast to their collinear counterparts, which are believed to be universal, they depend on the hard process under consideration and are therefore more complicated.The radiative corrections that are considered in collinear factorization involve logarithms ln Q 2 /µ 2 in the scale, and can be resummed with the help of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) [1] evolution equations. In the TMD factorization framework [2], additional logarithms of the form ln Q 2 /k 2 t need to be resummed, where k t is the small transverse momentum scale in the problem.At very high energies, however, soft logarithms in the center-of-mass energy ln s are expected to be dominant, necessitating a resummation and subsequently an evolution equation in rapidity instead of the scale, provided by the (linear) Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation [3]. BFKL involves a universal unintegrated gluon PDF, which just like the TMDs depends on transverse momentum. One of the most fascinating aspects of QCD at high energy or small x, is the phenomenon of saturation [4]: the damping of the steep rise of the gluon density predicted by BFKL, caused by gluon recombinations which become important due to the high density. The low-x evolution of the gluon density in the presence of these nonlinear interactions is described by an effective theory known as the Color Glass Condensate (CGC), which leads to the nonlinear BK-JIMWLK evolution equations [5][6][7][8].Within the CGC framework, the hybrid formalism [9] is used to study single inclusive particle produ...

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

“…For several processes and in several kinematic regimes, a matching between the low x Wilson line operators and some standard moderate x distributions have been found. 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].…”

Interplay of the CGC and TMD frameworks to all orders in kinematic twist

“…As a natural extension of this study, we plan to perform a similar analysis for more complex observables where not only the unpolarized TMD distributions but their linearly polarized partners appear. The two immediate observables that we are planning to study are the heavy quark production [46] and three-particle production such as dijet+photon production [47].…”

“…A matching of these schemes in the overlapping regime where |k| /Q and Q/s are both small was proven in [39,40]. Since then, gluon TMDs in the CGC have been at stake in many recent studies (see for example [41,[46][47][48] ). Indeed the measurement of TMD parton distributions offers great insight in the 3D structure of hadrons, yet these distributions are not fully universal and thus they require case-by-case studies.…”

ITMD factorization and broadening effects inproduction of forward di-jets

“…Steps in further extension of the formalism to three and more jets were undertaken in Ref. [14] and in [15] in the correlation limit. For some of phenomenological application of the formalizm see [16,17,18].…”