Stability Analysis of Sum Rules for Compton Scattering

We perform a stability analysis of a recently proposed sum rule for pion Compton scattering at fixed angle and moderate Mandelstam invariants. The sum rule is found to be sensitive to the parameter $\lambda^2$, the contour radius of a generalized Borel transform. A modified phenomenological model for the continuum contribution is proposed to remove this dependence. It is shown that the best value of the quark-hadron duality interval $s_0=0.6$ GeV$^2$ is close to that in the form factor case ($s_0=0.7$ GeV$^2$). The application of this new model to the pion form factor is examined. A comparison of our predictions with those derived from a modified perturbative calculation including Sudakov suppression is also briefly considered.