Constraints from jet calculus on quark recombination

Abstract

Within the quantum-chromodynamic jet-calculus formalism, we deduce an equation describing recombination of quarks and antiquarks into mesons within a quark or gluon jet. This equation relates the recombination function $R(x_1,x_2,x)$ used in current literature to the fragmentation function for producing that same meson out of the parton initiating the jet. We submit currently used recombination functions to our consistency test, taking as input mainly the $u$-quark fragmentation "data" into ${\pi }^{+}$ mesons. The $q\overline{q}\to \pi$ recombination functions popular in the literature are consistent with measured fragmentation functions, but they must be supplemented by other contributions to provide the full $D_u^{\pi +}$. We also discuss the $Q^2$ dependence of the resulting fragmentation functions.