For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the \( \overline{\mathrm{MS}} \) scheme are investigated at three-loop order in perturbation theory. Collecting literature results, general expressions are obtained for field anomalous dimensions, Yukawa interactions, as well as fermion masses. The renormalisation group evolution of scalar quartic, cubic and mass terms is determined up to a few unknown coefficients. The combined results are applied to compute the renormalisation group evolution of the gaugeless Litim-Sannino model.

A preprint version of the article is available at ArXiv.

中文翻译：

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三环阶上的一般标量-Yukawa重整化群方程

对于带有标量和费米子的任意四维量子场论，在扰动理论中以三环阶研究了\（\ overline {\ mathrm {MS}}} \）中的重整化群方程。收集文献结果，获得了场异常尺寸，Yukawa相互作用以及费米子质量的一般表达式。标量四次方，三次方和质量项的重整化组演化确定为几个未知系数。合并后的结果将用于计算无轨距Litim-Sannino模型的重归一化组演化。

该文章的预印本可在ArXiv上获得。