Inclusive hadronic distributions in jets and sub-jets with jet axis from color current

The hadronic kperpendicular-spectrum and the gluon to quark average multiplicity ratio r=Ng/Nq inside a high energy sub-jet are determined from a precise definition of the jet axis, including corrections of relative magnitude O(√(αs)) with respect to the Modified Leading Logarithmic Approximation (MLLA), in the limiting spectrum approximation (assuming an infrared cut-off Q0=ΛQCD). The results for the kperpendicular-spectrum in the limiting spectrum approximation are found to be, after normalization, in impressive agreement with measurements by the CDF collaboration, and the ratio has not been measured yet.