Fragmentation inside an identified jet

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Using Soft-Collinear Effective Theory we derive factorization formulae for semi-inclusive processes where a light hadron h fragments from a jet whose invariant mass is measured. Our analysis yields a novel "fragmenting jet function" Gᵢʰ(s,z) that depends on the jet invariant mass √s, and on the fraction z of the large light-cone momentum components of the hadron and the parent parton i. We show that Gᵢʰ(s,z) can be computed in terms of perturbatively calculable coefficients, Jij(s,z/x), integrated against standard non-perturbative fragmentation functions, Dⱼʰ(x). Our analysis yields a simple replacement rule that allows any factorization theorem depending on a jet function Jᵢ to be converted to a semi-inclusive process with a fragmenting hadron h.