Fragmentation inside an identified jet

Abstract

Using Soft‐Collinear Effective Theory (SCET) 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.