A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard Model
Abstract We present a procedure g5anchor to anchor γ 5 in the definition of a Dirac trace with γ 5 in Dimensional Regularization (DR) in Feynman diagrams for the Standard Model, based on a recent revision of the works by Kreimer, Gottlieb and Donohue. For each closed fermion chain with an odd number...
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2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)109 |
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| author | Long Chen |
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| description | Abstract We present a procedure g5anchor to anchor γ 5 in the definition of a Dirac trace with γ 5 in Dimensional Regularization (DR) in Feynman diagrams for the Standard Model, based on a recent revision of the works by Kreimer, Gottlieb and Donohue. For each closed fermion chain with an odd number of primitive (i.e. not-yet-clearly-defined) γ 5 in a given Feynman diagram, g5anchor returns a definite set of anchor points for γ 5, in terms of pairs of ordered fermion propagators; at each of these γ 5 anchor points a fixed expression in terms of the Levi-Civita tensor and elementary Dirac matrices will be inserted together with a sign determined by anticommutatively shifting all γ 5 from their original places (dictated by the Feynman rules) to this anchor point. The defining expressions for the cyclic γ 5-odd Dirac traces in DR associated with closed fermion chains in amplitudes, or more generally squared amplitudes, thus follow from this procedure, where the Levi-Civita tensors are not necessarily treated strictly in 4-dimensions. We propose utilizing this definition in practical perturbative calculations in the Standard Model at least to two-loop orders with the current implementation. Certain limitations and modifications of the KKS and/or the Kreimer scheme are addressed, as well as the possible caveats with g5anchor. |
| format | Article |
| id | doaj-art-e6957e71d72c42978b27e25b4db88873 |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-e6957e71d72c42978b27e25b4db888732025-08-20T03:10:27ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025513910.1007/JHEP05(2025)109A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard ModelLong Chen0School of Physics, Shandong UniversityAbstract We present a procedure g5anchor to anchor γ 5 in the definition of a Dirac trace with γ 5 in Dimensional Regularization (DR) in Feynman diagrams for the Standard Model, based on a recent revision of the works by Kreimer, Gottlieb and Donohue. For each closed fermion chain with an odd number of primitive (i.e. not-yet-clearly-defined) γ 5 in a given Feynman diagram, g5anchor returns a definite set of anchor points for γ 5, in terms of pairs of ordered fermion propagators; at each of these γ 5 anchor points a fixed expression in terms of the Levi-Civita tensor and elementary Dirac matrices will be inserted together with a sign determined by anticommutatively shifting all γ 5 from their original places (dictated by the Feynman rules) to this anchor point. The defining expressions for the cyclic γ 5-odd Dirac traces in DR associated with closed fermion chains in amplitudes, or more generally squared amplitudes, thus follow from this procedure, where the Levi-Civita tensors are not necessarily treated strictly in 4-dimensions. We propose utilizing this definition in practical perturbative calculations in the Standard Model at least to two-loop orders with the current implementation. Certain limitations and modifications of the KKS and/or the Kreimer scheme are addressed, as well as the possible caveats with g5anchor.https://doi.org/10.1007/JHEP05(2025)109Higher-Order Perturbative CalculationsElectroweak Precision PhysicsHigher Order Electroweak Calculations |
| spellingShingle | Long Chen A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard Model Journal of High Energy Physics Higher-Order Perturbative Calculations Electroweak Precision Physics Higher Order Electroweak Calculations |
| title | A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard Model |
| title_full | A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard Model |
| title_fullStr | A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard Model |
| title_full_unstemmed | A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard Model |
| title_short | A procedure g5anchor to anchor γ 5 in Feynman diagrams for the Standard Model |
| title_sort | procedure g5anchor to anchor γ 5 in feynman diagrams for the standard model |
| topic | Higher-Order Perturbative Calculations Electroweak Precision Physics Higher Order Electroweak Calculations |
| url | https://doi.org/10.1007/JHEP05(2025)109 |
| work_keys_str_mv | AT longchen aprocedureg5anchortoanchorg5infeynmandiagramsforthestandardmodel AT longchen procedureg5anchortoanchorg5infeynmandiagramsforthestandardmodel |