When high-energy single-hadron production takes place inside an identified jet, there are important correlations between the fragmentation and phase-space cuts. For example, when one-hadron yields are measured in on-resonance B-factory data, a cut on the thrust event shape T is required to remove the large b-quark contribution. This leads to a dijet final state restriction for the light-quark fragmentation process. Here we complete our analysis of unpolarized fragmentation of (light) quarks and gluons to a light hadron h with energy fraction z in e+ e- -> dijet + h at the center-of-mass energy Q=10.58 GeV. In addition to the next-to-next-to-leading order resummation of logarithms of 1-T, we include the next-to-leading order (NLO) nonsingular O(1-T) contribution to the cross section, the resummation of threshold logarithms of 1-z, and the leading nonperturbative contribution to the soft function. Our results for the correlations between fragmentation and the thrust cut are presented in a way that can be directly tested against B-factory data. These correlations are also observed in Pythia, but are surprisingly smaller at NLO.
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