Semileptonic decays of pseudoscalar particles (M→M′+ℓ+νℓ) and short-distance behaviour of quantum chromodynamics

The form factors which govern the semileptonic decays of pseudoscalar particles (M→M′+?+ν_?) are constrained by the knowledge of the two-point function Π^μν(q) = i ∫ d⁴x e^iqx〈06TV^μ(x) V^ν+ (0)60〉 in the deep euclidean region, where V^μ(x) denotes the vector current responsible for the transition M→M′. We derive the precise constraints from a QCD calculation of Π^μν which includes perturbative contributions to two loops as well as leading non-perturbative contributions. Applications to π_?3, K_?3 and $\text{D}{}^{\mathrm{+}}\text{→}\text{K}{}^0\text{e}{}^{\mathrm{+}}\text{ν}{}_{\mathrm{<mtext>e</mtext>}}$ decays are discussed.