Abstract
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.
Highlights
Appealing to cut corners by computing RGEs directly for QFTs of interest instead, which fails to deliver a contribution to the bigger picture
It is found that the graphs (13)–(15) in figure 1 do not contribute to the anomalous dimension, which can be readily understood from the momentum flow
We have completely determined the general result for all field anomalous dimensions, Yukawa and fermion mass β-functions, as well as terms ∝ λ4, ∝ y2λ3 and ∝ y4λ2 for scalar quartics
Summary
Being the Levi-Civita symbol, is closely tied to four dimensions. Different approaches to reconcile the γ5 problem — see [17] for a review and [43] for a recent list of works — in general lead to ambiguous computational results; this includes renormalisation group equations, see e.g. [44, 45]. In [28, 46], a semi-naïve scheme has been chosen that renders the ambiguity evanescent (∝ d − 4) and drop out when computing three-loop Yukawa β-functions This scheme has been employed in [27, 32,33,34], which serve as input in this work. Tensor structures that explicitly distinguish the chiralities of the included fermion lines have to be considered in the ansatz in order to account for possible γ5 corrections This could be achieved by inserting the quantity χij = ± δij on fermion lines, providing opposite signs for left- and right-chiral fermions. The γ5 issue can be neglected both in our ansatz as well as in the input data we use, as the gauge sector will be projected out
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