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Zeitschrift für Physik C Particles and Fields

, Volume 48, Issue 4, pp 673–679 | Cite as

Three-loop relation of quark\(\overline {MS} \) and pole masses

  • N. Gray
  • D. J. Broadhurst
  • W. Grafe
  • K. Schilcher
Article

Abstract

We calculate, exactly, the next-to-leading correction to the relation between the\(\overline {MS} \) quark mass,\(\bar m\), and the scheme-independent pole mass,M, and obtain
$$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$
as an accurate approximation forNF−1 light quarks of massesM i <M. Combining this new result with known three-loop results for\(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the\(\overline {MS} \) mass,\(\bar m\)(μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom\(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.

Keywords

Field Theory Elementary Particle Quantum Field Theory Accurate Approximation Quark Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • N. Gray
    • 1
  • D. J. Broadhurst
    • 1
  • W. Grafe
    • 2
  • K. Schilcher
    • 2
  1. 1.Physics DepartmentOpen UniversityMilton KeynesUK
  2. 2.Institut für Physik der Universität MainzMainzFederal Republic of Germany

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