Abstract
We calculate theon-shell fermion wave-function renormalization constantZ 2 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 logZ 2/da 0=i(2π)−D e 20 ∫dD k/k 4=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, withN L 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
.
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.
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Broadhurst, D.J., Gray, N. & Schilcher, K. Gauge-invariant on-shellZ 2 in QED, QCD and the effective field theory of a static quark. Z. Phys. C - Particles and Fields 52, 111–122 (1991). https://doi.org/10.1007/BF01412333
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DOI: https://doi.org/10.1007/BF01412333