  We discuss the gauge dependence of physical parameter's definitions under the
on-shell and pole mass renormalization prescriptions. By two-loop-level
calculations we prove for the first time that the on-shell mass renormalization
prescription makes physical result gauge dependent. On the other hand, such
gauge dependence doesn't appear in the result of the pole mass renormalization
prescription. Our calculation also implies the difference of the physical
results between the two mass renormalization prescriptions cannot be neglected
at two-loop level.
