E-Thesis 53 views 23 downloads
Analyticity and Recursion in Multi-Loop Yang-Mills Amplitudes / SIDDHARTH PANDEY
Swansea University Author: SIDDHARTH PANDEY
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...
| Published: |
Swansea University, Wales, UK
2024
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| 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 |
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| 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 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. |
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| Item Description: |
A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information. |
| Keywords: |
Yang-Mills, Scattering, Amplitudes, Rational, Multi-Loop |
| College: |
Faculty of Science and Engineering |
| Funders: |
STFC doctoral training grant |