The semi-inclusive jet function in SCET and small radius resummation for inclusive jet production

We introduce a new kind of jet function: the semi-inclusive jet function Ji(z, omega(J), mu), which describes how a parton i is transformed into a jet with a jet radius R and energy fraction z = omega(J)/omega with omega(J) and omega being the large light-cone momentum component of the jet and the corresponding parton i that initiates the jet, respectively. Within the framework of Soft Collinear Effective Theory (SCET) we calculate both J(q)(z, omega(J), mu) and Jg(z, omega(J), mu) to the next-to-leading order (NLO) for cone and anti-k(T) algorithms. We demonstrate that the renormalization group (RG) equations for J(i)(z, omega(J), mu) follow exactly the usual DGLAP evolution, which can be used to perform the In R resummation for inclusive jet cross sections with a small jet radius R. We clarify the difference between our RG equations for J(i)(z, omega(J), mu) and those for the so-called unmeasured jet functions J(i)(omega(J), mu), widely used in SCET for exclusive jet production. Finally, we present applications of the new semi-inclusive jet functions to inclusive jet production in e(+)e(-) and pp collisions. We demonstrate that single inclusive jet production in these collisions shares the same short-distance hard functions as single inclusive hadron production, with only the fragmentation functions D-i(h) (z, mu) replaced by J(i)(z, omega(J), mu) . This can facilitate more efficient higher-order analytical computations of jet cross sections. We further match our In R resummation at both LLR and NLLR to fixed NLO results and present the phenomenological implications for single inclusive jet production at the LHC.