The 1-Jettiness DIS Spectrum: Factorization, Resummation, and Jet Algorithm Dependence
Abstract
The 1-Jettiness (tau1) event shape for Deep Inelastic Scattering (DIS), allows for a quantitative and global description of the pattern of QCD radiation for single jet (J) production in electron-nucleus (NA) collisions e- + NA e- + J + X. It allows for precision studies of QCD and is a sensitive probe of nuclear structure and dynamics. The large transverse momentum (PJT) of the final state jet J, characterizes the hard scale in the problem. The region of phase space where tau1 << PJT, corresponds to configurations where energetic radiation (E~ PJT) is only along either the single jet direction or the beam direction with only soft radiation (E ~ τ1 <<PJT) in between. Thus, the restriction tau1 << PJT corresponds to a veto on additional jets and leads to large Sudakov logarithms of τ1/PJT that must be resummed. Based on a factorization framework, derived using the Soft Collinear Effective Theory (SCET), we provide resummation results at the NNLL level of accuracy and match them onto the NLO result in fixed order perturbation theory, appropriate in the τ1 PJT region where additional jets and hard radiation are allowed. The τ1-distribution depends on the jet algorithm used to find the leading jet in the region tau1 ~ PJT, unlike the resummation region where this dependence is power suppressed in tau1/PJT << 1. We give results for the entire tau1 spectrum, with a smooth matching between the resummation region and fixed-order region, where we make use of the anti-kt jet algorithm. The 1-Jettiness event shape can be a powerful probe of nuclear and QCD dynamics at future electron-ion colliders and by analyzing existing HERA data.