Two-Loop Anomalous Dimensions in the LEFT: Dimension-Six Four-Fermion Operators in NDR
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| Format: | Preprint |
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2025
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| _version_ | 1866917465307480064 |
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| author | Aebischer, Jason Morell, Pol Pesut, Marko Virto, Javier |
| author_facet | Aebischer, Jason Morell, Pol Pesut, Marko Virto, Javier |
| contents | We derive the complete set of two-loop anomalous dimensions describing the mixing of four-fermion operators in the Low Energy Effective Field Theory (LEFT). The calculation is performed in Naive Dimensional Regularization with anticommuting $γ_5$ (the NDR scheme), and the results are given in the "JMS basis" of dimension-six operators. The derivation relies on known results for UV poles in two-loop diagrams in QCD, which are then used to derive the two-loop Anomalous Dimension Matrix (ADM) for the full set of four-fermion operators including $O(α_s^2)$, $O(α_sα)$ and $O(α^2)$ corrections. The method employed is an extension of a common approach to deal with traces containing $γ_5$ in NDR. Our results have been implemented in the public code DsixTools. We also discuss and provide the results in the LEFT with 5, 4 and 3 active quark flavors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_08384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Loop Anomalous Dimensions in the LEFT: Dimension-Six Four-Fermion Operators in NDR Aebischer, Jason Morell, Pol Pesut, Marko Virto, Javier High Energy Physics - Phenomenology High Energy Physics - Experiment We derive the complete set of two-loop anomalous dimensions describing the mixing of four-fermion operators in the Low Energy Effective Field Theory (LEFT). The calculation is performed in Naive Dimensional Regularization with anticommuting $γ_5$ (the NDR scheme), and the results are given in the "JMS basis" of dimension-six operators. The derivation relies on known results for UV poles in two-loop diagrams in QCD, which are then used to derive the two-loop Anomalous Dimension Matrix (ADM) for the full set of four-fermion operators including $O(α_s^2)$, $O(α_sα)$ and $O(α^2)$ corrections. The method employed is an extension of a common approach to deal with traces containing $γ_5$ in NDR. Our results have been implemented in the public code DsixTools. We also discuss and provide the results in the LEFT with 5, 4 and 3 active quark flavors. |
| title | Two-Loop Anomalous Dimensions in the LEFT: Dimension-Six Four-Fermion Operators in NDR |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2501.08384 |