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oai:dspace.mit.edu:1721.1/1644972026-01-13T03:37:21Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022

Stewart, Iain W. Gao, Anjie Massachusetts Institute of Technology. Department of Physics 2026-01-12T19:40:31Z 2026-01-12T19:40:31Z 2025-09 2025-08-15T21:06:49.901Z https://hdl.handle.net/1721.1/164497 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. Ph.D. Massachusetts Institute of Technology In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ Limits of QCD Thesis application/pdf Doctoral Doctor of Philosophy Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="f1007c52-283b-4134-b0ab-2fdcfbba064f"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Title>Limits of QCD</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2025-09</PublicationDate> <Authors> <Author> <DisplayName>Gao, Anjie</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>https://rightsstatements.org/page/InC-EDU/1.0/</License> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>