Jet Shapes in Dijet Events at the LHC in SCET

TL;DR

This work develops a Soft-Collinear Effective Theory (SCET) factorization for jet shapes (angularities) in dijet production at the LHC, using boost-invariant angularities and a hadron-collider specific soft function with an out-of-jet p_T veto. It introduces unmeasured beam functions and a universal, color-space soft function, and performs fixed-order O(α_s) calculations alongside a robust RG evolution to achieve NLL' resummation in a regime where non-global logarithms are not enhanced. A key advancement is the refactorization of the soft function, which separates global soft and soft-collinear pieces and reduces normalization and scale uncertainties, with explicit results shown for the qq' → qq' channel. The framework is positioned to attain NNLL with known anomalous dimensions and can be extended to other jet-substructure observables and heavy-flavor jets, enabling meaningful comparisons with data and Monte Carlo simulations.

Abstract

We consider the class of jet shapes known as angularities in dijet production at hadron colliders. These angularities are modified from the original definitions in e+e- collisions to be boost invariant along the beam axis. These shapes apply to the constituents of jets defined with respect to either k_T-type (anti-k_T, C/A, and k_T) algorithms and cone-type algorithms. We present an SCET factorization formula and calculate the ingredients needed to achieve next-to-leading-log (NLL) accuracy in kinematic regions where non-global logarithms are not large. The factorization formula involves previously unstudied "unmeasured beam functions," which are present for finite rapidity cuts around the beams. We derive relations between the jet functions and the shape-dependent part of the soft function that appear in the factorized cross section and those previously calculated for e+e- collisions, and present the calculation of the non-trivial, color-connected part of the soft-function to O(α_s). This latter part of the soft function is universal in the sense that it applies to any experimental setup with an out-of-jet p_T veto and rapidity cuts together with two tagged jets and it is independent of the choice of jet (sub-)structure measurement. In addition, we implement the recently introduced soft-collinear refactorization to resum logarithms of the jet size, valid in the region of non-enhanced non-global logarithm effects. While our results are valid for all 2 \to 2 channels, we compute explicitly for the qq' \to qq' channel the color-flow matrices and plot the NLL resummed differential dijet cross section as an explicit example, which shows that the normalization and scale uncertainty is reduced when the soft function is refactorized. For this channel, we also plot the jet size R dependence, the p_T^{\rm cut} dependence, and the dependence on the angularity parameter a.