Angular Scaling in Jets

TL;DR

This work defines an infrared- and collinear-safe ensemble jet observable from two-particle angular correlations, encoding the angular mass distribution inside jets as a scaling exponent with a resolution parameter $R$. The authors show the leading small-$R$ behavior yields $\langle \Delta \mathcal{G}(R) \rangle \approx 2$, with running coupling, higher-order corrections, and factorization providing systematic deformations. They develop a practical method to extract the uncorrelated radiation density $\Lambda_{\rm UE}$ from measurements of $\langle \mathcal{G}(R) \rangle$ and $\langle \Delta \mathcal{G}(R) \rangle$, and study UE in the transverse region using the Feynman-Wilson gas, a toy Monte Carlo, and full Pythia8/Herwig++ simulations. The results highlight the observable’s sensitivity to jet substructure, UE/PU, and shower modeling, suggesting it as a valuable tool for MC tuning and QCD studies at the LHC.

Abstract

We introduce a jet shape observable defined for an ensemble of jets in terms of two-particle angular correlations and a resolution parameter R. This quantity is infrared and collinear safe and can be interpreted as a scaling exponent for the angular distribution of mass inside the jet. For small R it is close to the value 2 as a consequence of the approximately scale invariant QCD dynamics. For large R it is sensitive to non-perturbative effects. We describe the use of this correlation function for tests of QCD, for studying underlying event and pile-up effects, and for tuning Monte Carlo event generators.

Figures (8)

• Figure 1: Splitting diagram for the ${\cal O}(\alpha_s^2)$ contribution to $\langle {\cal G}(R) \rangle$.
• Figure 2: Average angular structure functions for ensembles of jets with $p_T>$ 200 GeV and no underlying event or initial state radiation. Red curves denote quark jets and blue curves denote gluon jets. These are anti-kT jets with jet radius $R_0=1.0$ as generated with Pythia8 (left) and Herwig++ (right). See Appendix \ref{['mc']} for more details about the Monte Carlo.
• Figure 3: Average angular structure functions for three different ensembles of jets with $p_T>$ 200 GeV and no underlying event or initial state radiation. These are anti-kT jets with jet radius $R_0=1.0$ as generated with Pythia8 (solid) and Herwig++ (dashed). See Appendix \ref{['mc']} for more details about the Monte Carlo.
• Figure 4: Average angular structure functions for ensembles of jets with $p_T>$ 200 GeV. The black curves have no underlying event nor any ISR. In contrast to the previous section, here underlying event and ISR are turned on for the colored curves. On the LHS, the Pythia8 samples make use of tune 4C, with the red curve having twice as much UE activity as the blue curve. On the RHS, the purple curve corresponds to Herwig++ tune LHC-UE7-2. For comparison, the bottom figure overlays the Pythia8 and Herwig++ curves. These are anti-kT jets with jet radius $R_0=1.0$. See Appendix \ref{['mc']} for more details about the Monte Carlo.
• Figure 5: $\Lambda_{\rm UE}(R)$ curves as extracted via the procedure detailed in Sec. \ref{['proc']}. The solid curves correspond to the Pythia8 samples in Fig. \ref{['pyher_ue']}, while the dashed curve corresponds to the Herwig++ sample. The dotted curve corresponds to the same Herwig++ sample as the dashed curve, the difference being that the power law of the underlying event ansatz is changed from $R^4$ to $R^{3.3}$. The matching was done at $R_{\rm min}=0.25$.