Order p6 chiral couplings from the scalar Kpi form factor

Employing results from a recent determination of the scalar Kpi form factor F ₀ ^Kpi within a coupled channel dispersion relation analysis [1], in this work we calculate the slope and curvature of F ₀ ^Kpi(t) at zero momentum transfer. Knowledge of the slope and curvature of the scalar Kpi form factor, together with a recently calculated expression for F ₀ ^Kpi(t) in chiral perturbation theory at order p ⁶ , enable to estimate the Script O(p ⁶) chiral constants C ₁₂ ^r (M _rho) = (0.3+/-5.4).10^-7 and (C ₁₂ ^r +C ₃₄ ^r )(M _rho) = (3.2+/-1.5).10^-6 . Our findings also allow to estimate the contribution coming from the C _i to the vector form factor F ₊ ^Kpi(0) which is a crucial ingredient for a precise determination of |V _us | from K _l3 decays. Our result F ₊ ^Kpi(0)| _{C i ^r} = - 0.018+/-0.009, though inflicted with large uncertainties, is in perfect agreement with a previous estimate by Leutwyler and Roos already made twenty years ago.