Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes

PANDEY, SIDDHARTH

doi:10.23889/SUThesis.67956

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Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes / SIDDHARTH PANDEY

Swansea University Author: SIDDHARTH PANDEY

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DOI (Published version): 10.23889/SUThesis.67956

Abstract

While much progress has been made in the calculation of two-loop amplitudes in Yang-Mills theory, there remain diﬃculties in scaling existing methods to higher numbers of external gluons. A method of calculating two-loop all-plus Yang-Mills amplitudes using 4 dimensional unitarity and augmented recu...

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Published:	Swansea University, Wales, UK 2024
Institution:	Swansea University
Degree level:	Doctoral
Degree name:	Ph.D
Supervisor:	Perkins, W., B.; and Dunbar, D., C.
URI:	https://cronfa.swan.ac.uk/Record/cronfa67956

first_indexed	2024-10-10T15:00:54Z
last_indexed	2025-02-07T05:53:35Z
id	cronfa67956
recordtype	RisThesis
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spelling	2025-02-06T13:27:20.6543483 v2 67956 2024-10-10 Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes c48615a5793627a44c11cbed0d7971ca SIDDHARTH PANDEY SIDDHARTH PANDEY true false 2024-10-10 While much progress has been made in the calculation of two-loop amplitudes in Yang-Mills theory, there remain diﬃculties in scaling existing methods to higher numbers of external gluons. A method of calculating two-loop all-plus Yang-Mills amplitudes using 4 dimensional unitarity and augmented recursion was previously developed that was successful in calculating amplitudes to high gluon multiplicity. This thesis presents the latest developments in extending this method to the two-loop single-minus sector, taking the previously calculated leading in color two-loop ﬁve-point single-minus amplitude as an example. A new technique for calculating the cut-constructible part of this amplitude is presented, with a focus on the ‘pseudo one-loop’ subsector of the cut-constructible part. We calculate this subsector using one-loop reduction methods, and present a new parameterisation that allows for the determination of the coeﬃcients of the one- and two-mass scalar triangle integrals. The bulk of this thesis focuses on the extension of augmented recursion to the calculation of the rational part of single-minus amplitudes. The method is signiﬁcantly extended to include sectors which were absent in previous calculations, and we develop novel techniques to aid in calculating Feynman integrals. Although there are still some unanswered questions, we are able to reconstruct the full rational part of the ﬁve-point amplitude using augmented recursion and universal known properties of scattering amplitudes. E-Thesis Swansea University, Wales, UK Yang-Mills, Scattering, Amplitudes, Rational, Multi-Loop 10 9 2024 2024-09-10 10.23889/SUThesis.67956 A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information. COLLEGE NANME COLLEGE CODE Swansea University Perkins, W., B.; and Dunbar, D., C. Doctoral Ph.D STFC doctoral training grant STFC doctoral training grant 2025-02-06T13:27:20.6543483 2024-10-10T15:54:39.9331540 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics SIDDHARTH PANDEY 1 67956__32590__4afcb1f5ca4745abaaf1c0e6f4df0300.pdf 2024_Pandey_A.final.67956.pdf 2024-10-10T15:59:55.7294671 Output 1511266 application/pdf E-Thesis – open access true Copyright: The Author, Siddharth Pandey, 2024 true eng
title	Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes
spellingShingle	Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes SIDDHARTH PANDEY
title_short	Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes
title_full	Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes
title_fullStr	Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes
title_full_unstemmed	Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes
title_sort	Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes
author_id_str_mv	c48615a5793627a44c11cbed0d7971ca
author_id_fullname_str_mv	c48615a5793627a44c11cbed0d7971ca_***_SIDDHARTH PANDEY
author	SIDDHARTH PANDEY
author2	SIDDHARTH PANDEY
format	E-Thesis
publishDate	2024
institution	Swansea University
doi_str_mv	10.23889/SUThesis.67956
college_str	Faculty of Science and Engineering
hierarchytype
hierarchy_top_id	facultyofscienceandengineering
hierarchy_top_title	Faculty of Science and Engineering
hierarchy_parent_id	facultyofscienceandengineering
hierarchy_parent_title	Faculty of Science and Engineering
department_str	School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str	1
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description	While much progress has been made in the calculation of two-loop amplitudes in Yang-Mills theory, there remain diﬃculties in scaling existing methods to higher numbers of external gluons. A method of calculating two-loop all-plus Yang-Mills amplitudes using 4 dimensional unitarity and augmented recursion was previously developed that was successful in calculating amplitudes to high gluon multiplicity. This thesis presents the latest developments in extending this method to the two-loop single-minus sector, taking the previously calculated leading in color two-loop ﬁve-point single-minus amplitude as an example. A new technique for calculating the cut-constructible part of this amplitude is presented, with a focus on the ‘pseudo one-loop’ subsector of the cut-constructible part. We calculate this subsector using one-loop reduction methods, and present a new parameterisation that allows for the determination of the coeﬃcients of the one- and two-mass scalar triangle integrals. The bulk of this thesis focuses on the extension of augmented recursion to the calculation of the rational part of single-minus amplitudes. The method is signiﬁcantly extended to include sectors which were absent in previous calculations, and we develop novel techniques to aid in calculating Feynman integrals. Although there are still some unanswered questions, we are able to reconstruct the full rational part of the ﬁve-point amplitude using augmented recursion and universal known properties of scattering amplitudes.
published_date	2024-09-10T05:19:35Z
_version_	1851459712475725824
score	11.089572

Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes / SIDDHARTH PANDEY

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