Abstract:We calculate the vector and scalar form factors of the pion to two loops in Chiral Perturbation Theory. We estimate the unknown O(p 6 ) constants using resonance exchange. We make a careful comparison to the available data and determine two O(p 4 ) constants rather precisely, and two O(p 6 ) 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 r 2 π V = 0.437 ± 0.016 fm 2 .

The procedure to calculate masses and matrix-elements in the presence of mixing of the basis states is explained in detail. We then apply this procedure to the twoloop calculation in Chiral Perturbation Theory of pseudoscalar masses and decay constants including quark mass isospin breaking. These results are used to update our analysis of K ℓ4 done previously and obtain a value of m u /m d in addition to values for the low-energy-constants L r i .

The vector and axial-vector two-point functions are calculated to nextto-next-to-leading order in Chiral Perturbation Theory for three light flavours. We also obtain expressions at the same order for the masses, m 2 π , m 2 K and m 2 η , and the decay constants, F π , F K and F η . We present some numerical results after a simple resonance estimate of some of the new O(p 6 ) constants.