The 1-Jettiness DIS Spectrum: Factorization, Resummation, and Jet Algorithm Dependence

TL;DR

This paper develops a theoretical framework for the 1-Jettiness event shape in DIS, enabling precise QCD radiation analysis and jet algorithm dependence, with applications to nuclear structure studies at electron-ion colliders.

Contribution

It provides a NNLL resummation and NLO matching for the 1-Jettiness spectrum in DIS, incorporating jet algorithm effects and full spectrum analysis.

Findings

Resummation at NNLL accuracy achieved.

Matching with NLO fixed-order results.

Dependence on jet algorithm analyzed.

Abstract

The 1-Jettiness (tau_1) 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 (N_A) collisions e^- + N_A \to e^- + J + X. It allows for precision studies of QCD and is a sensitive probe of nuclear structure and dynamics. The large transverse momentum (P_{J_T}) of the final state jet $J$, characterizes the hard scale in the problem. The region of phase space where tau_1 << P_{J_T}, corresponds to configurations where energetic radiation (E~ P_{J_T}) is only along either the single jet direction or the beam direction with only soft radiation (E ~ \tau_1 <<P_{J_T}) in between. Thus, the restriction tau_1 << P_{J_T} corresponds to a veto on additional jets and leads to large Sudakov logarithms of \tau_1/P_{J_T} 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 \tau_1 \sim P_{J_T} region where additional jets and hard radiation are allowed. The \tau_1-distribution depends on the jet algorithm used to find the leading jet in the region tau_1 ~ P_{J_T}, unlike the resummation region where this dependence is power suppressed in tau_1/P_{J_T} << 1. We give results for the entire tau_1 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.