  We study possibilities to realize a nonvanishing finite Wilson line (WL)
scalar mass in flux compactification. Generalizing loop integrals in the
quantum correction to WL mass at one-loop, we derive the conditions for the
loop integrals and mode sums in one-loop corrections to WL scalar mass to be
finite. We further guess and classify the four-point and three-point
interaction terms satisfying these conditions. As an illustration, the
nonvanishing finite WL scalar mass is explicitly shown in a six dimensional
scalar QED by diagrammatic computation and effective potential analysis. This
is the first example of finite WL scalar mass in flux compactification.
