Scattering equations formalism for QCD and supersymmetric Yang-Mills theories

Scattering amplitudes are one of the most important observables in perturbative quantum field theory, because they allow for the calculation of cross-sections, which are central to collision experiments. In this thesis, we perform a thorough review of some of the modern method for the calculation of...

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Autores:
Vesga Simmons, Juan Pablo
Tipo de recurso:
Fecha de publicación:
2017
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/64025
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/64025
http://bdigital.unal.edu.co/64731/
Palabra clave:
5 Ciencias naturales y matemáticas / Science
53 Física / Physics
CHY formalism
Dispersion amplitudes
Theory of perturbative quantum fields
Formalismo CHY
Amplitudes de dispersión
Teoría de campos cuánticos perturbativa
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_9433247adcd91c72ffbc86d5704e6f91
oai_identifier_str oai:repositorio.unal.edu.co:unal/64025
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
title Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
spellingShingle Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
5 Ciencias naturales y matemáticas / Science
53 Física / Physics
CHY formalism
Dispersion amplitudes
Theory of perturbative quantum fields
Formalismo CHY
Amplitudes de dispersión
Teoría de campos cuánticos perturbativa
title_short Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
title_full Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
title_fullStr Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
title_full_unstemmed Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
title_sort Scattering equations formalism for QCD and supersymmetric Yang-Mills theories
dc.creator.fl_str_mv Vesga Simmons, Juan Pablo
dc.contributor.author.spa.fl_str_mv Vesga Simmons, Juan Pablo
dc.contributor.spa.fl_str_mv Fazio, Angelo Raffaele
dc.subject.ddc.spa.fl_str_mv 5 Ciencias naturales y matemáticas / Science
53 Física / Physics
topic 5 Ciencias naturales y matemáticas / Science
53 Física / Physics
CHY formalism
Dispersion amplitudes
Theory of perturbative quantum fields
Formalismo CHY
Amplitudes de dispersión
Teoría de campos cuánticos perturbativa
dc.subject.proposal.spa.fl_str_mv CHY formalism
Dispersion amplitudes
Theory of perturbative quantum fields
Formalismo CHY
Amplitudes de dispersión
Teoría de campos cuánticos perturbativa
description Scattering amplitudes are one of the most important observables in perturbative quantum field theory, because they allow for the calculation of cross-sections, which are central to collision experiments. In this thesis, we perform a thorough review of some of the modern method for the calculation of tree-level amplitudes, the leading order contributions to the perturbative expansion of scattering amplitudes, focusing on the gauge theories that make up the standard model of particle physics. We will study methods for their calculation that overcome the issues and inefficiencies of Feynman diagrams, focusing on the Cachazo-He-Yuan (CHY) formalism, which provides closed formulas for tree amplitudes in arbitrary dimension as integrals over n-punctured Riemann spheres localized on the solutions to a set of constraints that relate the punctures over the Riemann spheres to the kinematic invariants of the process, known as the scattering equations. We will introduce the CHY formalism for pure Yang-Mills amplitudes, as well as one of its supersymmetric generalizations, the so-called maximally supersymmetric or N = 4 super Yang-Mills theory (SYM). We will introduce the notion of basis amplitudes for Yang-Mills and Quantum Chromodynamics (QCD), which are based on the idea of color decomposition, the separation of color and kinematic degrees of freedom, and see how one can obtain CHY representations for QCD amplitudes. We will use one of these representations, given in terms of basis amplitudes, to derive soft theorems for the CHY integrand of QCD, which is a first step into obtaining constraints on its mathematical structure.
publishDate 2017
dc.date.issued.spa.fl_str_mv 2017-11-24
dc.date.accessioned.spa.fl_str_mv 2019-07-02T22:24:28Z
dc.date.available.spa.fl_str_mv 2019-07-02T22:24:28Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
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status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/64025
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/64731/
url https://repositorio.unal.edu.co/handle/unal/64025
http://bdigital.unal.edu.co/64731/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Física
Departamento de Física
dc.relation.references.spa.fl_str_mv Vesga Simmons, Juan Pablo (2017) Scattering equations formalism for QCD and supersymmetric Yang-Mills theories. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/64025/1/MsThesis.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Fazio, Angelo RaffaeleVesga Simmons, Juan Pablo5a7132e7-dd9f-4322-9ab4-383c231bf1e93002019-07-02T22:24:28Z2019-07-02T22:24:28Z2017-11-24https://repositorio.unal.edu.co/handle/unal/64025http://bdigital.unal.edu.co/64731/Scattering amplitudes are one of the most important observables in perturbative quantum field theory, because they allow for the calculation of cross-sections, which are central to collision experiments. In this thesis, we perform a thorough review of some of the modern method for the calculation of tree-level amplitudes, the leading order contributions to the perturbative expansion of scattering amplitudes, focusing on the gauge theories that make up the standard model of particle physics. We will study methods for their calculation that overcome the issues and inefficiencies of Feynman diagrams, focusing on the Cachazo-He-Yuan (CHY) formalism, which provides closed formulas for tree amplitudes in arbitrary dimension as integrals over n-punctured Riemann spheres localized on the solutions to a set of constraints that relate the punctures over the Riemann spheres to the kinematic invariants of the process, known as the scattering equations. We will introduce the CHY formalism for pure Yang-Mills amplitudes, as well as one of its supersymmetric generalizations, the so-called maximally supersymmetric or N = 4 super Yang-Mills theory (SYM). We will introduce the notion of basis amplitudes for Yang-Mills and Quantum Chromodynamics (QCD), which are based on the idea of color decomposition, the separation of color and kinematic degrees of freedom, and see how one can obtain CHY representations for QCD amplitudes. We will use one of these representations, given in terms of basis amplitudes, to derive soft theorems for the CHY integrand of QCD, which is a first step into obtaining constraints on its mathematical structure.Las amplitudes de dispersion representan algunos de los observables más imporantes de la teoría cuántica de campos perturbativa, puesto que estos permiten el cálculo de las secciones eficaces, las cuales son centrales para los experimentos de colisión. En esta tesis presentamos una revisión de algunos de los métodos modernos para el cálculo de amplitudes a nivel árbol, las cuales constituyen la primera contribución a la expansión perturbativa de las amplitudes, haciendo énfasis en el caso de las teorías de gauge a partir de las cuales el modelo estandar de la física de partículas está construido. Estudiaremos métodos que evitan los problemas e ineficiencias de los diagramas de Feynman, enfocándonos en el formalismo Cachazo-He-Yuan (CHY), el cual provee fórmulas cerradas para las amplitudes a nivel árbol en dimensión arbitraria como integrales sobre esferas de Riemann con n punturas, localizadas en la solución de un conjunto de ecuaciones que relacionan dichas punturas con el espacio de invariantes cinemáticos asociados al proceso, las cuales son conocidas como las ecuaciones de scattering. Haremos una introducción al formalismo CHY para amplitudes en teorías de Yang-Mills, así como una de sus generalizaciones supersimétricas, conocida como supersimetría maximal o símplemente teoría de super Yang-Mills N = 4. Discutiremos la noción de las amplitudes base en Yang-Mills y Cromodinámica Cuántica (QCD), la cual está basada en la idea de la descomposición de color. Esta representa una forma de separar los grados de libertad cinemáticos de los grados de libertad de color, y veremos distintas alternativas para obtener representaciones CHY para las amplitudes de QCD. Usaremos una de estas representaciones, la cual estará dada en términos de amplitudes base, para obtener teoremas de emisión infraroja sobre el integrando CHY de la QCD, lo cual representa un primer paso en la obtención de restricciones sobre su estructura matemática.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de FísicaDepartamento de FísicaVesga Simmons, Juan Pablo (2017) Scattering equations formalism for QCD and supersymmetric Yang-Mills theories. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá.5 Ciencias naturales y matemáticas / Science53 Física / PhysicsCHY formalismDispersion amplitudesTheory of perturbative quantum fieldsFormalismo CHYAmplitudes de dispersiónTeoría de campos cuánticos perturbativaScattering equations formalism for QCD and supersymmetric Yang-Mills theoriesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINALMsThesis.pdfapplication/pdf1061204https://repositorio.unal.edu.co/bitstream/unal/64025/1/MsThesis.pdf8c0545f6d9134153d2b6af545cc418fbMD51THUMBNAILMsThesis.pdf.jpgMsThesis.pdf.jpgGenerated Thumbnailimage/jpeg3738https://repositorio.unal.edu.co/bitstream/unal/64025/2/MsThesis.pdf.jpgb6374bb92534b2b9aedc86c1be8bee0fMD52unal/64025oai:repositorio.unal.edu.co:unal/640252024-05-02 23:24:13.793Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co