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arXiv · 2106.14711

Divergences in anomalous dimension matrices of quarks at three loops: Explanation and simple solution

Adrian Lewandowski
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Abstract

Three-loop counterterms for the Standard Model (SM) revealed that the matrix of anomalous dimensions ($\gamma$) of quarks is divergent in the $d \to 4$ limit unless a carefully chosen non-Hermitian square-root of $Z$ matrix is used in the textbook formula for $\gamma$. Here, an alternative prescription is given, which expresses $\gamma$ and $\beta$ functions directly in terms of counterterms (instead of $\sqrt{Z}$ and conventional `bare couplings') and produces finite results. In the SM, this prescription $automatically$ reproduces results obtained previously by adjusting $\sqrt{Z}$.

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Adrian Lewandowski. 2021-06-28. Divergences in anomalous dimension matrices of quarks at three loops: Explanation and simple solution. https://doi.org/10.1103/physrevd.104.056029

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