Small-x single-particle distributions in jets from the coherent branching formalism

We calculate single parton distributions inside quark and gluon jets within the coherent branching formalism, which resums leading and next-to-leading logarithmic contributions. This formalism is at the basis of the modified leading logarithmic approximation (MLLA), and it conserves energy exactly. For a wide preasymptotic range of the evolution variable Y=ln[E\theta/Q_0], we find marked differences in the shape and norm of single parton distributions calculated in the MLLA or in the coherent branching formalism, respectively. For asymptotically large values Y>5-10, the difference in norm persists, while differences in shape disappear. In this way, our numerical study delineates the jet energy scale needed for a reliable application of both approaches. We also study the dependence of the single parton distributions on the hadronization scale Q_0 and on \Lambda_QCD, and we calculate within the coherent branching formalism the identified quark and gluon distributions inside quark and gluon jets.