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.

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We use recent data on K + → π + e + e − , together with known values for the pion form factor, to derive the kaon electromagnetic form factor for 0 < q 2 < 0.125 (GeV/c) 2 . The results are then compared with predictions of the Linear σ Model, a quark-triangle model and Vector Meson Dominance. The first two models describe the data at least qualitatively, but the simple Vector Meson Dominance picture gives a detailed quantitative fit to the experimental results.

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavours, 23 terms for three and 5 for two flavours. In the two flavour case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.Comment: 12 pages, misprint in table 2 correcte

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