Quark fragmentation within an identified jet

Authors:
  • MPMassimiliano Procura
    Massimiliano Procura
  • ISIain W. Stewart
    Iain W. Stewart
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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 $\sum${}h$\int${}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, B\ifmmode\bar\else\textasciimacron\fi{}$\rightarrow${}Xh$\ell${}$\nu${}\ifmmode\bar\else\textasciimacron\fi{}, with invariant mass mXh2$\gg${}$\Lambda${}QCD2. 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 B\ifmmode\bar\else\textasciimacron\fi{}$\rightarrow${}XK$\gamma${} which is the fragmentation to a Kaon in b$\rightarrow${}s$\gamma${}, and for e+e-$\rightarrow${}(dijets)+h with measured hemisphere dijet invariant masses.

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