Status of chiral perturbation theory for light mesons

The status of chiral perturbation theory in the meson sector is illustrated with several topical examples. The longtime discrepancy between theory and experiment for the charged pion polarizabilities has now been resolved in favour of the chiral SU(2) result to next-to-next-to-leading order. For chiral SU(3), the main obstacles are the large number of badly known coupling constants (LECs) and the lack of convergence of the low-energy expansion in many cases of interest. I describe a new global fit of the LECs in the strong sector that leads to a prediction of the CKM matrix element $V_{us}$ in agreement with the latest lattice determinations. The slow convergence of the chiral series is particularly acute in transitions with strong final-state interactions calling for dispersive treatments. The status of dispersive approaches is reviewed for $K_{\ell 4}$ decays and for $η-> 3 π$ decays where precise measurements of Dalitz plot distributions have recently become available.

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