Zijlstra, Jelmer (2024) On Duality and Unity: Constructing Hybrid Soft Behaviour with the Double Copy and Transmutation Operators. Master's Thesis / Essay, Physics.
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Abstract
This thesis delves into the unifying relations for these amplitudes and applies the BCJ bootstrap method to construct kinematic numerators that respect the colour-kinematics duality. We began with a detailed analysis of Yang-Mills (gluon) and pion (NLSM) amplitudes, investigating their duality and behaviour under specific kinematic conditions. We then applied the BCJ bootstrap method to derive amplitudes for the gauged nonlinear sigma model, observing a hybrid soft degree where some amplitudes conform to σ = 0 while others exhibit pion contact terms with σ = 1. In this work we have developed of a generalised transmutation (GT) operator, which allowed us to generate and analyze mixed amplitudes of scalars and pions interacting through gluons. The GT operator was validated by computing 6-point amplitudes and tracking Mandelstam variables, revealing correct results for Yang-Mills-Scalar (YMS) and Nonlinear Sigma Model (NLSM) amplitudes, and uncovering unexpected terms like the 4-point φ 4 amplitude. We found that while the GT operator reconstructs some interactions observed in the BCJ bootstrap method, there are contributions to the σ = 0 amplitude that are not generated by the BCJ bootstrap. We therefore conclude that the BCJ bootstrap does not uniquely determine amplitudes based solely on the soft degree σ = 0.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Roest, D. and Bergshoeff, E.A. |
| Degree programme: | Physics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 06 Aug 2024 09:43 |
| Last Modified: | 06 Aug 2024 09:43 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33864 |
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