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<p>We compute template formulae of all four-loop <i>β</i>-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27389_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>MS</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \overline{\textrm{MS}} \)</EquationSource> </InlineEquation> scheme. Using these results, novel contributions to the <i>β</i>-functions of the Higgs and top coupling are extracted. We discuss how four loops present a challenge to dimensional continuation from four to three dimensions and propose a solution.</p>

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Four loop renormalisation group equations in general Gross-Neveu-Yukawa theories

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  • 发表日期：

    2025年10月14日

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  • Tom Steudtner

摘要

We compute template formulae of all four-loop β-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the MS ¯ \( \overline{\textrm{MS}} \) scheme. Using these results, novel contributions to the β-functions of the Higgs and top coupling are extracted. We discuss how four loops present a challenge to dimensional continuation from four to three dimensions and propose a solution.