Two Loop Calculation of Decoupling in Unbroken Gauge Theories with Fermions.

The low energy effects of heavy fermions in unbroken gauge theories are investigated in the dimensional regularization scheme. Using the light-particle irreducible vertex functional scheme suitably modified to incorporate the background field formalism, the coupling constant g* of the low energy effective theory is calculated completely upto two loop orders. A curious cancellation of the infrared divergent terms within the fermionic sector of the two point background field function, without which the effective Lagrangian would be nonlocal, is shown to occur for all values of the gauge fixing parameter. Finally, the gauge independence of g* is explicitly demonstrated.