Dimensionally Regulated On-Shell Renormalisation In QCD And QED

This thesis describes a technical advance in the treatment of massive fermion two-loop calculations in QED and QCD, which allows us to reduce complicated on-shell Feynman integrals to a large number of simple integrals, and one particularly complicated, but evaluable, one. The method extends the work of Chetyrkin and Tkachov to massive integrals, and is applicable to on-shell mass and wavefunction renormalisation. After an extensive review of the relevant areas of renormalisation, and of the rôle of quark masses in current algebra, we go on to use the extended technique to extract the fermion mass and wavefunction renormalisation constants to O(α2s), and to relate the running and pole masses to the bare mass and to each other. We find that the ratio of the running to the pole mass may be rather smaller than might be expected, which allows us to claim a perturbative source for a larger proportion of the strange quark constituent mass than has been usual before. In passing, we extract a number of two-loop renormalisation group coefficients, and find ourselves to be in agreement with other calculations. We also find that the on-shell fermion wavefunction renormalisation constant is quite unexpectedly gauge invariant to two loops, and that it is relatively simply related to the mass renormalisation constant. We suggest that this is the result of such intricate calculations that there must be a field-theoretic explanation waiting to be uncovered. We relate our results to the effective theory of a static quark