The MSR mass and the \( \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) \) renormalon sum rule

  • André H. Hoang
  • Ambar Jain
  • Christopher Lepenik
  • Vicent Mateu
  • Moritz Preisser
  • Ignazio Scimemi
  • Iain W. Stewart
Open Access
Regular Article - Theoretical Physics
  • 21 Downloads

Abstract

We provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark Q. In contrast to earlier low-scale short-distance mass schemes, the MSR scheme has a direct connection to the well known \( \overline{\mathrm{MS}} \) mass commonly used for high-energy applications, and is determined by heavy quark on-shell self-energy Feynman diagrams. Indeed, the MSR mass scheme can be viewed as the simplest extension of the \( \overline{\mathrm{MS}} \) mass concept to renormalization scales ≪ m Q . The MSR mass depends on a scale R that can be chosen freely, and its renormalization group evolution has a linear dependence on R, which is known as R-evolution. Using R-evolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the \( \mathcal{O}\left({\varLambda}_{\mathrm{QCD}}\right) \) renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the \( \mathcal{O}\left({\varLambda}_{\mathrm{QCD}}\right) \) renormalon sum rule, and can be applied to any perturbative series. The relations of the MSR mass scheme to other low-scale short-distance masses are analyzed as well.

Keywords

Heavy Quark Physics Perturbative QCD Quark Masses and SM Parameters Renormalization Regularization and Renormalons 

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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© The Author(s) 2018

Authors and Affiliations

  1. 1.University of Vienna, Faculty of PhysicsWienAustria
  2. 2.Erwin Schrödinger International Institute for Mathematical PhysicsUniversity of ViennaWienAustria
  3. 3.Indian Institute of Science Education and Research BhopalBhopalIndia
  4. 4.Departamento de Física Fundamental e IUFFyMUniversidad de SalamancaSalamancaSpain
  5. 5.Instituto de Física Teórica UAM-CSICMadridSpain
  6. 6.Center for Theoretical Physics, Massachusetts Institute of TechnologyCambridgeU.S.A.
  7. 7.Departamento de Física Teórica IIUniversidad Complutense de Madrid (UCM)MadridSpain

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