πK sum rules and the SU(3) chiral expansion

A recently proposed set of sum rules, based on the pion-kaon scattering amplitudes and their crossing symmetric conjugates are analyzed in detail. A key role is played by the l=0 ππ→K/line K amplitude which requires an extrapolation to be performed. It is shown how this is tightly constrained from analyticity, chiral counting and the available experimental data, and its stability is tested. A re-evaluation of the O(p4) chiral couplings L1, L2, L3 is obtained, as well as a new evaluation of the large Nc suppressed coupling L4. (orig.)