Quark fragmentation within an identified jet

Abstract

We derive a factorization theorem that describes an energetic hadron h fragmenting from a jet produced by a parton i, where the jet invariant mass is measured. The analysis yields a “fragmenting jet function” Gih(s,z) that depends on the jet invariant mass s, and on the energy fraction z of the fragmentation hadron. We show that Gih can be computed in terms of perturbatively calculable coefficients, Jij(s,z/x), integrated against standard nonperturbative fragmentation functions, Djh(x). We also show that Sigmah∫dzGih(s,z) is given by the standard inclusive jet function Ji(s) which is perturbatively calculable in QCD. We use soft collinear effective theory and for simplicity carry out our derivation for a process with a single jet, B̅ -->Xhℓν̅ , with invariant mass mXh2≫ΛQCD2. Our analysis yields a simple replacement rule that allows any factorization theorem depending on an inclusive jet function Ji to be converted to a semi-inclusive process with a fragmenting hadron h. We apply this rule to derive factorization theorems for B̅ -->XKγ which is the fragmentation to a Kaon in b→sγ, and for e+e- -->(dijets)+h with measured hemisphere dijet invariant masses.