Abstract
Unbroken gauge theories containing light as well as heavy fermions are considered in the limit of the mass of the heavy fermions tending to infinity. The effective coupling constant of the decoupled low-energy theory thus obtained, has been calculated up to two-loop level using the light particle irreducible vertex function and the background field formalism. In addition, to simplify the computation, a background field gauge-fixing term has been used, because in such a gauge the effective coupling constant can be calculated from a two-point function only. Our analysis reveals that in the non-abelian theory, the simple algorithm proposed by Ovrut and Schnitzer for computing the effective coupling constant up to the two-loop level is valid only in the α = 0 or α = −3 background field gauge. A general procedure correct for all values of α is described.
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