Consistency constraints on ms from QCD dispersion relations and chiral perturbation theory in Kℓ3 decays

We use both old and new theoretical developments in QCD dispersion relation constraints on the scalar form factor in the decay K→πℓνℓ to obtain constraints on the strange quark mass. The perturbative QCD side of the calculation incorporates up to four-loop corrections, while the hadronic side uses a recently developed parameterization constructed explicitly to satisfy the dispersive constraints. Using chiral perturbation theory (χPT) as a model for soon-to-be measured data, we find a series of lower bounds on ms increasing with the accuracy to which one believes χPT to represent the full QCD result.