Abstract
In recent years, the theoretical foundations of small-x physics have made significant advances in two frontiers: higher-order (NLO) corrections and power-suppressed (sub-eikonal) corrections. Among the former are the NLO calculations of the linear (BFKL) and nonlinear (BK-JIMWLK) evolution equations, as well as cross sections for various processes. Among the latter are corrections to the whole framework of high-energy QCD, including new contributions from quarks and spin asymmetries. One common element to both of these frontiers is the appearance of collinear logarithms beyond the leading-order framework. The proper treatment of these logarithms is a major challenge in obtaining physical cross sections at NLO, and they lead to a new double-logarithmic resummation parameter which governs spin at small x. In this paper, I will focus on the role of these collinear logarithms in both frontiers of small-x physics, as well as give a brief sample of other recent advances in its theoretical foundations.The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.
Highlights
Small-x Physics at Leading OrderIn the limit of high energies and fixed transverse momenta, QCD enters what is known as the “small-x regime,” with x ∼ p2T /s where pT is a particle’s transverse momentum and s is the center-of-mass energy squared of the collision.When x αs 1, one has the onset of “small-x kinematics” or “Regge kinematics.” In this regime, processes which can be higher order in αs but leading in x dominate
One example is the transition of Deep Inelastic Scattering from a “knockout” process, in which a virtual photon ejects a quark from the proton, to a dipole process in which the virtual photon fluctuates into a qqpair and scatters hadronically on the proton [2,3,4]
next-to-leading order (NLO) corrections are nominally suppressed by a factor of αs compared to the leading order
Summary
In the limit of high energies and fixed transverse momenta, QCD enters what is known as the “small-x regime,” with x ∼ p2T /s where pT is a particle’s transverse momentum and s is the center-of-mass energy squared of the collision (see [1] and references therein for a review). The linear small-x evolution leads to a power-law divergence of the F2 structure function as x → 0 which is irreconcilable with the unitarity of QCD. This contradiction is indicative of a third regime at even smaller x, when the saturation momentum Qs(x) induced by the small-x evolution has grown to become a semi-hard scale, Qs(x) ΛQCD. This high-energy, high-density regime of QCD is characterized by gluon. About the these descriptions beyond leading order
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