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<p>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 <i>γ</i><sub>5</sub> (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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>O</mi> <mfenced close=")" open="("> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( O\left({\alpha}_s^2\right) \)</EquationSource> </InlineEquation>, <i>O</i>(<i>α</i><sub><i>s</i></sub><i>α</i>) and <i>O</i>(<i>α</i><sup>2</sup>) corrections. The method employed is an extension of a common approach to deal with traces containing <i>γ</i><sub>5</sub> 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.</p>

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Two-loop anomalous dimensions in the LEFT: dimension-six four-fermion operators in NDR

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月6日

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  • Jason Aebischer,
  • Pol Morell,
  • Marko Pesut,
  • Javier Virto

摘要

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 γ5 (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 \( O\left({\alpha}_s^2\right) \) , O(αsα) and O(α2) corrections. The method employed is an extension of a common approach to deal with traces containing γ5 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.