Matching chiral perturbation theory and the dispersive representation of the scalar Kπ form factor

We perform a matching of the two loop-chiral perturbation theory representation of the scalar Kπ   form factor to a dispersive one. Knowing the value of FK/FπFK/Fπ and f+(0)f+(0) in the Standard Model (SM) allows to determine two O(p6)O(p6) LECs, the slope of the scalar form factor and the deviation of the Callan–Treiman theorem. Going beyond the SM and assuming the knowledge of the slope of the scalar form factor from experiment, the matching allows us to determine the ratio of FK/FπFK/Fπ, f+(0)f+(0), a certain combination of non-standard couplings, the deviation of the Callan–Treiman theorem and the two O(p6)O(p6) LECs.