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Gauge-invariant on-shellZ2 in QED, QCD and the effective field theory of a static quark

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

Abstract

We calculate theon-shell fermion wave-function renormalization constantZ2 of a general gauge theory, to two loops, inD dimensions and in an arbitrary covariant gauge, and find it to be gauge-invariant. In QED this is consistent with the dimensionally regularized version of the Johnson-Zumino relation: d logZ2/da0=i(2π)De 0 2 ∫d D k/k4=0. In QCD it is, we believe, a new result, strongly suggestive of the cancellation of the gauge-dependent parts of non-abelian UV and IR anomalous dimensions to all orders. At the two-loop level, we find that the anomalous dimension γ F of the fermion field in minimally subtracted QCD, withNL light-quark flavours, differs from the corresponding anomalous dimension\(\tilde \gamma _F \) of the effective field theory of a static quark by the gauge-invariant amount
$$\begin{gathered} \gamma _F - \tilde \gamma _F \equiv \mu \frac{d}{{d\mu }}\log \left( {\frac{{Z_2^{MS} (\mu )}}{{\tilde Z_2^{MS} (\mu )}}} \right) \hfill \\ = 2\frac{{\bar \alpha _s (\mu )}}{\pi } + \left( {\frac{{41}}{4} - \frac{{11}}{{18}}N_L } \right)\frac{{\bar \alpha _s^2 (\mu )}}{{\pi ^2 }} + O(\bar \alpha _s^3 ) \hfill \\ \end{gathered} $$
.

A complete description of two-loop on-shell renormalization of one-lepton QED, inD dimensions, is also given. More generally, we show that there is no need of integration in the two-loop calculation of on-shell two-and three-point functions.

Keywords

Elementary Particle Gauge Theory Quantum Field Theory Anomalous Dimension Particle Acceleration 
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 1991

Authors and Affiliations

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

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