Hadronic single inclusive kt distributions inside one jet beyond MLLA

The hadronic kt-spectrum inside one jet is determined including corrections of relative magnitude sqrt{alpha_s} with respect to the Modified Leading Logarithmic Approximation (MLLA), at and beyond the limiting spectrum (assuming an infrared cut-off Q_0 = Lambda_QCD and Q_0 not = Lambda_QCD). The agreement between our results and preliminary measurements by the CDF collaboration is impressive, much better than at MLLA, pointing out very small overall non-perturbative contributions.