Inclusive hadronic distributions inside one jet at high energy colliders at 'modified leading logarithmic approximation' of quantum chromodynamics

After demonstrating their general expressions valid at all x, double differential 1-particle inclusive distributions inside a quark and a gluon jet produced in a hard process, together with the inclusive kperpendicular distributions, are calculated at small x in the Modified Leading Logarithmic Approximation (MLLA), as functions of the transverse momentum kperpendicular of the outgoing hadron. Results are compared with the Double Logarithmic Approximation (DLA) and a naive DLA-inspired evaluation; sizable corrections are exhibited, which, associated with the requirement to stay in a perturbative regime, set the limits of the interval where our calculations can be trusted. We give predictions for the LHC and Tevatron colliders