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 J_i(z, ω_J, μ), which describes how a parton i is transformed into a jet with a jet radius R and energy fraction z = ω_J/ω, with ω_J and ω 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, ω_J, μ) and J_g (z, ω_J, μ) 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, ω_J, μ) follow exactly the usual DGLAP evolution, which can be used to perform the ln 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, ω_J, μ) and those for the so-called unmeasured jet functions J_i(ω_J, μ), 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, μ) replaced by J_i(z, ω_J, μ). This can facilitate more efficient higher-order analytical computations of jet cross sections. We further match our ln R resummation at both LL_R and NLL_R to fixed NLO results and present the phenomenological implications for single inclusive jet production at the LHC.