Limits of QCD

Abstract

This thesis explores the fundamental kinematic limits of Quantum Chromodynamics (QCD), including the soft, collinear, and Regge limits, using soft-collinear effective theory (SCET). We begin by studying transverse momentum dependent (TMD) physics in semi-inclusive deep inelastic scattering (SIDIS), which probes the small transverse momentum regime arising from the soft and collinear limits of QCD. We derive all-order factorization theorems for azimuthal asymmetries in SIDIS at next-to-leading power (NLP). We also propose a new angular observable, q_∗, for probing TMD dynamics at the future Electron-Ion Collider (EIC), which enables an order-of-magnitude improvement in experimental resolution while retaining sensitivity to TMD distributions. Next, we apply the TMD formalism to a class of observables known as energy correlators. We study the transverse energy-energy correlator (TEEC) in the back-to-back limit, a dijet observable at hadron colliders, and the three-point energy correlator (EEEC) in the coplanar limit, a trijet observable at lepton colliders. For both observables, we derive allorder factorization theorems and resum large logarithms to next-to-next-to-next-to-leading logarithmic (N3LL) accuracy. Finally, we analyze the Regge limit of 2 → 2 QCD amplitudes. By factorizing these amplitudes into collinear jet and soft functions and studying their rapidity evolution, we define Regge-like anomalous dimensions in a gauge-invariant manner. At the level of the exchange of two Glauber gluons in the t-channel, we recover the BFKL equation from a purely collinear perspective. Extending to three-Glauber exchange, we derive the first closed-form renormalization group equations for Regge cut contributions in several nontrivial t-channel color representations, providing a systematic method for organizing non-planar QCD amplitudes at high energy.