Recalculation of pion Compton scattering in perturbative QCD

We recalculated pion virtual Compton scattering in perturbative QCD in this Letter. Our calculation avoids some deficiencies in existing literature, and treats real Compton scattering as a limit case in which the mass of the virtual photon equals to zero. Expressions of the hard scattering amplitudes from 10 independent diagrams are given explicitly in the text. By comparing the effects of different distribution amplitudes on the physical observables, we studied the self-consistence of pQCD calculation of this problem.