Abstract
We consider a version of dimensional regularization (reduction) in which the dimensionful regularization parameter Λ is in general different from the renormalization scale μ. Then in the scheme analogous to the minimal subtraction the renormalization constants contain ε-poles, powers of ln Λ/μ, and mixed terms of the structure ε−q lnp Λ/μ. For the MS-like schemes we present explicit expressions for the coefficients at all these structures which relate them to the coefficients in the renormalization group functions, namely in the β-function and in the anomalous dimension. In particular, for the pure ε-poles we present explicit solutions of the ’t Hooft pole equations. Also we construct simple all-loop expressions for the renormalization constants (also written in terms of the renormalization group functions) which produce all ε-poles and logarithms and establish a number of relations between various coefficients at ε-poles and logarithms. The results are illustrated by some examples.
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Acknowledgments
K.S. is very grateful to A.L.Kataev and D.I.Kazakov for indicating the problem addressed in this paper.
This work has been supported by Foundation for Advancement of Theoretical Physics and Mathematics “BASIS”, grant No. 21-2-2-25-1 (N.M.) and by Russian Science Foundation, grant No. 21-12-00129 (K.S.).
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Meshcheriakov, N.P., Shatalova, V.V. & Stepanyantz, K.V. Higher logarithms and ε-poles for the MS-like renormalization prescriptions. J. High Energ. Phys. 2023, 97 (2023). https://doi.org/10.1007/JHEP12(2023)097
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DOI: https://doi.org/10.1007/JHEP12(2023)097