Energy Correlation Functions for Jet Substructure (1305.0007v3)

Abstract: We show how generalized energy correlation functions can be used as a powerful probe of jet substructure. These correlation functions are based on the energies and pair-wise angles of particles within a jet, with (N+1)-point correlators sensitive to N-prong substructure. Unlike many previous jet substructure methods, these correlation functions do not require the explicit identification of subjet regions. In addition, the correlation functions are better probes of certain soft and collinear features that are masked by other methods. We present three Monte Carlo case studies to illustrate the utility of these observables: 2-point correlators for quark/gluon discrimination, 3-point correlators for boosted W/Z/Higgs boson identification, and 4-point correlators for boosted top quark identification. For quark/gluon discrimination, the 2-point correlator is particularly powerful, as can be understood via a next-to-leading logarithmic calculation. For boosted 2-prong resonances the benefit depends on the mass of the resonance.

• The paper introduces a novel method using generalized energy correlation functions to probe jet substructure by leveraging pair-wise angular information and energy measurements.
• It demonstrates significant enhancements in quark/gluon discrimination and boosted boson tagging by optimizing correlation parameters and outperforming traditional observables.
• Additionally, the study explores boosted top quark tagging with 4-point correlators, providing computational insights and paving the way for future jet physics advancements.

An Overview of Energy Correlation Functions for Jet Substructure

The paper "Energy Correlation Functions for Jet Substructure" by Larkoski, Salam, and Thaler introduces a novel approach to jet substructure analysis using generalized energy correlation functions. These functions serve as observables for probing the intrinsic complexity of jets, particularly their substructure, by employing pair-wise angular information and energy measurements of particles within jets. The method is particularly sensitive to the prong structure of jets, with $(N+1)$-point correlators designed to detect $N$-prong substructures.

The primary innovation in this work is the application of energy correlation functions to identify complex jets without necessitating explicit subjet identification, rendering them more adaptable to diverse physics environments, notably where conventional methods face limitations due to soft and collinear masking. Importantly, these correlation functions retain infrared and collinear safety, adding robustness across a range of scenarios.

Key Achievements and Contributions

The paper outlines the analytical and computational framework of energy correlation functions through three core studies:

1. Quark/Gluon Discrimination: Utilizing 2-point correlators, the paper capitalizes on the differentiation in radiation patterns between quark- and gluon-initiated jets. It demonstrates that using a small value of the angular exponent $\beta$, specifically $\beta \simeq 0.2$, remarkably enhances discrimination. This is confirmed via a leading and next-to-leading logarithmic calculation that outlines theoretical underpinnings, suggesting superiority to traditional jet observables such as angularities.
2. Boosted Boson Tagging: For identifying jets arising from boosted $W$, $Z$, or Higgs bosons, the authors employ 3-point correlators and apply these observables in mass rescaling analyses to show discriminative features compared to QCD jets. They report substantial improvements over $N$-subjettiness ratios, particularly in phase spaces where the resonance mass is relatively low. Furthermore, these findings highlight how color-singlet property recognition becomes accessible with higher point correlators.
3. Boosted Top Quark Tagging: Utilizing 4-point correlators, the exploration into distinguishing top quark jets from generic QCD jets displays potential, although their findings indicate that the complexity within the 4-point correlator structure can dilute its sensitivity compared to other taggers. The computational feasibility suggests practical viability, albeit with room for methodological enhancement.

Implications and Future Directions

This paper carries both practical and theoretical implications for jet physics in high-energy colliders like the LHC. Practically, the findings suggest promising improvements in the accuracy and reliability of jet classification tasks, which could be extended to detect new physics events beyond the Standard Model. One implication lies in refining Monte Carlo models based on experimental measurements informed by energy correlation observables, which could enhance parton shower algorithms and guide the tuning of event generators.

Theoretically, the robustness of energy correlation functions in probing both soft and collinear emissions implies further opportunities for elucidating QCD dynamics. The paper highlights potential for extending these functions to more complex jet topologies, opening avenues for both analytical explorations across different energy scales and experimental settlements, potentially aligning with future upgrades in collider facilities.

Considering the scalability and computational demands, future developments may need to encompass more efficient algorithms for extracting significant variables from detector data without compromising the robustness intrinsic to higher-point correlations. Moreover, establishing a detailed theoretical groundwork using effective theories or further enhancing NLL calculations may incentivize wider adoption in jet substructure profiling tasks.

In summary, this work delivers a substantive advancement in jet physics, furnishing state-of-the-art methodologies that reveal intricate jet signatures with enhanced precision, offering heightened understanding and capability in particle physics analyses.