  In the previous works, we proposed the stochastic quantization method (SQM)
approach to N=1 supersymmetric Yang-Mills theory (SSYM). In four dimensions, in
particular, we obtained the superfield Langevin equation and the corresponding
Fokker-Planck equation which describe the underlying stochastic process
manifestly preserving the global supersymmetry as well as the local gauge
symmetry. The stochastic gauge fixing procedure was also applied to SSYM_4 in
the superfield formalism. In this note, we apply the background field methd to
SSYM_4 in terms of the stochastic action principle in SQM approach. The
one-loop $\beta$-function for the gauge coupling agrees with that given by the
path-integral approach, thereby confirming that the stochastic gauge fixing
procedure with the background local gauge invariant Zwanziger's gauge fixing
functions simulates the contributions from the Nielsen-Kallosh ghost as well as
the Faddeev-Popov ghost at the one-loop level. We also show the equivalence of
the stochastic effective action in the background field method to the standard
one in SQM.
