Abstract
We study the transverse momentum dependent (TMD) parton distributions at small-x in a consistent framework that takes into account the TMD evolution and small-x evolution simultaneously. The small-x evolution effects are included by computing the TMDs at appropriate scales in terms of the dipole scattering amplitudes, which obey the relevant Balitsky–Kovchegov equation. Meanwhile, the TMD evolution is obtained by resumming the Collins–Soper type large logarithms emerged from the calculations in small-x formalism into Sudakov factors.
Highlights
Transverse momentum dependent (TMD) parton distributions are among the most important and interesting topics to be fully investigated at the current and future facilities, including JLab 12 GeV upgrade, RHIC, and the planed electron-ion collider (EIC), and have been subjects of intense studies from both theory and experiment sides in the last decade or so
From the theoretical point of view, it has been shown that the TMDs at small-x are unified with the un-integrated gluon distributions (UGDs), which are widely applied in heavy ion physics, in particular, as an important ingredient to describe the initial conditions for heavy ion collisions at high energies
The resulting hard parts contain two different type large logarithms which can be resummed by means of the Collins-Soper equation and the BK equation, respectively
Summary
Transverse momentum dependent (TMD) parton distributions are among the most important and interesting topics to be fully investigated at the current and future facilities, including JLab 12 GeV upgrade, RHIC, and the planed electron-ion collider (EIC), and have been subjects of intense studies from both theory and experiment sides in the last decade or so. The QCD evolution effects play important roles in describing the scale dependence of these gluon distributions This includes the small-x evolution, i.e., the BFKL/BK evolution [14, 15], and the so-called TMD evolution, i.e., the Collins-Soper evolution [3, 16]. The soft gluon radiation leads to the Collins-Soper evolution, whereas the collinear gluon contributes to the DGLAP resummation formulated in terms of the integrated parton distributions in the CSS resummation formalism In our case, these collinear gluon radiation contributions become the small-x evolution contributions, which are described by the associated BK/JIMWLK equations [14, 15, 26, 27].
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