0000000000768799
AUTHOR
Norman Gray
Gauge-invariant on-shellZ 2 in QED, QCD and the effective field theory of a static quark
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 0 2 ∫d D 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 anomalou…
Three-loop relation of quark $$\overline {MS} $$ and pole masses
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 forN F−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…