Jet substructure using semi-inclusive jet functions within SCET

We propose a new method to evaluate jet substructure observables in inclusive jet measurements, based upon semi-inclusive jet functions in the framework of Soft Collinear Effective Theory (SCET). As a first example, we consider the jet fragmentation function, where a hadron $h$ is identified inside a fully reconstructed jet. We introduce a new semi-inclusive fragmenting jet function ${\mathcal G}^h_i(z= \omega_J/\omega,z_h=\omega_h/\omega_J,\omega_J, R,\mu)$, which depends on the jet radius $R$ and the large light-cone momenta of the parton `$i$' initiating the jet ($\omega$), the jet ($\omega_J$), and the hadron $h$ ($\omega_h$). The jet fragmentation function can then be expressed as a semi-inclusive observable, in the spirit of actual experimental measurements, rather than as an exclusive one. We demonstrate the consistency of the effective field theory treatment and standard perturbative QCD calculations of this observable at next-to-leading order (NLO). The renormalization group (RG) equation for the semi-inclusive fragmenting jet function ${\mathcal G}_i^h(z,z_h, \omega_J, R,\mu)$ are also derived and shown to follow exactly the usual timelike DGLAP evolution equations for fragmentation functions. The newly obtained RG equations can be used to perform the resummation of single logarithms of the jet radius parameter $R$ up to next-to-leading logarithmic (NLL$_R$) accuracy. In combination with the fixed NLO calculation, we obtain NLO+NLL$_R$ results for the hadron distribution inside the jet. We present numerical results for $pp\to(\mathrm{jet}\,h)X$ in the new framework, and find excellent agreement with existing LHC experimental data.