{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/164497"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/164497","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"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.","abstract_html":"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_has_math":false,"creators":["Gao, Anjie"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Limits of QCD"]}]}],"canonical_facts":{"dc:contributor.advisor":["Stewart, Iain W."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Physics"],"dc:creator":["Gao, Anjie"],"dc:date.accessioned":["2026-01-12T19:40:31Z"],"dc:date.available":["2026-01-12T19:40:31Z"],"dc:date.issued":["2025-09"],"dc:description.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."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/164497"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Limits of QCD"],"dc:type":["Thesis"],"thesis:degree_name":["Doctoral","Doctor of Philosophy"]},"updated_at":"2026-07-22T22:22:26Z"}