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Journal of High Energy Physics

, 2016:105 | Cite as

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

  • Piotr H. Chankowski
  • Adrian Lewandowski
  • Krzysztof A. Meissner
Open Access
Regular Article - Theoretical Physics

Abstract

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional \( \overline{\mathrm{MS}} \) scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the \( \overline{\mathrm{MS}} \) scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

Keywords

BRST Quantization Renormalization Regularization and Renormalons Renormalization Group Anomalies in Field and String Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Piotr H. Chankowski
    • 1
  • Adrian Lewandowski
    • 1
    • 2
  • Krzysztof A. Meissner
    • 1
  1. 1.Institute of Theoretical Physics, Faculty of PhysicsUniversity of WarsawWarsawPoland
  2. 2.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany

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