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 [Eθ/Q0], 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 Q0 and on ΛQCD, and we calculate within the coherent branching formalism the identified quark and gluon distributions inside quark and gluon jets.