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<p>We present a procedure g5anchor to anchor <i>γ</i><sub>5</sub> in the definition of a Dirac trace with <i>γ</i><sub>5</sub> 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) <i>γ</i><sub>5</sub> in a given Feynman diagram, g5anchor returns a definite set of anchor points for <i>γ</i><sub>5</sub>, in terms of pairs of ordered fermion propagators; at each of these <i>γ</i><sub>5</sub> 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 <i>γ</i><sub>5</sub> from their original places (dictated by the Feynman rules) to this anchor point. The defining expressions for the cyclic <i>γ</i><sub>5</sub>-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.</p>

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A procedure g5anchor to anchor γ5 in Feynman diagrams for the Standard Model

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  • 发表日期：

    2025年5月13日

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  • Long Chen

摘要

We present a procedure g5anchor to anchor γ5 in the definition of a Dirac trace with γ5 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) γ5 in a given Feynman diagram, g5anchor returns a definite set of anchor points for γ5, in terms of pairs of ordered fermion propagators; at each of these γ5 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 γ5 from their original places (dictated by the Feynman rules) to this anchor point. The defining expressions for the cyclic γ5-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.