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 massesMi<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.

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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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