QCD Analysis of the Scale-Invariance of Jets

TL;DR

This work uses soft-collinear effective theory (SCET) to perform a global next-to-leading-log (NLL) resummation of the angular correlation function ${\cal G}(R)$, an observable that probes the mass contribution from jet constituents within an angle $R$. By factorizing the cross section into hard, measured jet, and soft functions and computing their anomalous dimensions, the authors obtain a resummed prediction for the ensemble-averaged angular structure function $\langle \Delta {\cal G}_{\alpha}(R)\rangle$, anticipating near scale invariance with $\langle {\cal G}_{\alpha}(R)\rangle \sim R^{\alpha}$ and $\langle \Delta {\cal G}_{\alpha}(R)\rangle \sim \alpha$ up to perturbative and non-perturbative corrections. They compare the SCET result to fixed-order NLO (NLOJet++) and to parton-shower Monte Carlo (Pythia8 and VINCIA), finding that resummation captures the behavior in singular regions while fixed-order and MC show wide-angle radiation effects and non-global log sensitivities. Non-perturbative hadronization tends to reduce the angular structure function, consistent with a modest hadronization correction. The paper also discusses extending the framework to the LHC, noting both the potential and challenges of factorization with initial-state radiation and underlying event, and emphasizes the need for matching to improve accuracy across phase space.

Abstract

Studying the substructure of jets has become a powerful tool for event discrimination and for studying QCD. Typically, jet substructure studies rely on Monte Carlo simulation for vetting their usefulness; however, when possible, it is also important to compute observables with analytic methods. Here, we present a global next-to-leading-log resummation of the angular correlation function which measures the contribution to the mass of a jet from constituents that are within an angle R with respect to one another. For a scale-invariant jet, the angular correlation function should scale as a power of R. Deviations from this behavior can be traced to the breaking of scale invariance in QCD. To do the resummation, we use soft-collinear effective theory relying on the recent proof of factorization of jet observables at e+ e- colliders. Non-trivial requirements of factorization of the angular correlation function are discussed. The calculation is compared to Monte Carlo parton shower and next-to-leading order results. The different calculations are important in distinct phase space regions and exhibit that jets in QCD are, to very good approximation, scale invariant over a wide dynamical range.

Figures (7)

• Figure 1: SCET Feynman diagrams contributing to the quark jet function.
• Figure 2: SCET Feynman diagrams contributing to the gluon jet function. Diagrams (F) and (G) have mirrored counterparts which are not shown.
• Figure 3: Plots of the ratio between the location of the peak in $\frac{d\sigma}{d\cal{G}_\alpha}$ to the maximum value of $\cal{G}_\alpha$ over a range in $R$. For illustration, $\alpha=2$ and the red (blue) curve is quark (gluon) jets. The jet radius is $R_0=1.0$ and we have set the hard, jet and soft scales as in Eq. \ref{['fact_scales1']}.
• Figure 4: Plots of the average angular structure function for quark (red) and gluon (blue) jets. Fig. \ref{['fig:scet_py_comp']} compares the curves from SCET resummation (solid) to anti-$k_T$ jets from Pythia8 (dashed). The Pythia8 curves were computed from 3 jet final states in which all jets had equal energy. Figs. \ref{['fig:scet_py_comp_h']}, \ref{['fig:scet_py_comp_j']} and \ref{['fig:scet_py_comp_s']} compare the Pythia8 curves to SCET bands in which the hard, jet and soft scales have been varied by a factor of 2. To make these curves, the jet radius has been set to be $R_0 = 1.0$ and the energy of the jets is 300 GeV.
• Figure 5: Comparison of NLOJet++ calculation of the event-wide average angular structure function in 3 jet final states to NLO (dotted) to SCET NLL resummation of the average angular structure function for quark jets (solid). Two curves from Pythia8 are shown: the dashed curve is the average angular structure function for quark jets from $e^+e^-\to$ 3 jets and the dot-dashed curve is the average angular structure function from $e^+e^-\to$ 2 jets.