SHORT-DISTANCE QCD CONTRIBUTION TO THE ELECTROWEAK MASS DIFFERENCE OFPIONS

It is known that the short distance QCD contribution to the mass diffe rence of pions is quadratic on the quark masses, and irrelevant with r espect to the long distance part. It is also considered in the literat ure that its calculation contains infinities, which should be absorbed by the quark mass renormalization. Following a prescription by Craigi e, Narison, and Riazuddin of a renormalization-group-improved perturba tion theory to deal with the electromagnetic mass shift problem in QCD , we show that the short distance QCD contribution to the electroweak pion mass difference (with m(u) = m(d) not equal 0) is finite and, of course, its value is negligible compared to other contributions.