The vector and scalar form factors of the pion to two loops

Abstract

We calculate the vector and scalar form factors of the pion to two loops in Chiral Perturbation Theory. We estimate the unknown O(p6) constants using resonance exchange. We make a careful comparison to the available data and determine two O(p4) constants rather precisely, and two O(p6) constants less precisely. We also use Chiral Perturbation Theory to two loops to extract in a model-independent manner the charge radius of the pion from the available data, and obtain 〈r2〉vπ = 0.437 ± 0.016 fm2.