Towards an understanding of jet substructure (1307.0007v2)

Abstract: We present first analytic, resummed calculations of the rates at which widespread jet substructure tools tag QCD jets. As well as considering trimming, pruning and the mass-drop tagger, we introduce modified tools with improved analytical and phenomenological behaviours. Most taggers have double logarithmic resummed structures. The modified mass-drop tagger is special in that it involves only single logarithms, and is free from a complex class of terms known as non-global logarithms. The modification of pruning brings an improved ability to discriminate between the different colour structures that characterise signal and background. As we outline in an extensive phenomenological discussion, these results provide valuable insight into the performance of existing tools and help lay robust foundations for future substructure studies.

• The paper presents resummed calculations of jet-tagging rates for methods like trimming, pruning, and a novel modified mass-drop tagger.
• It demonstrates that trimming and pruning exhibit distinct logarithmic behaviors that align well with Monte Carlo simulations.
• The modified mass-drop tagger simplifies the analysis by eliminating non-global logarithms, offering higher perturbative accuracy in collider studies.

An Analysis of Jet Substructure Techniques

The paper under discussion presents a theoretical analysis of jet substructure techniques used in high-energy physics, especially in the context of experiments at the Large Hadron Collider (LHC). Notably, it addresses the behavior and analytical understanding of various jet-tagging algorithms—trimming, pruning, and the mass-drop tagger (MDT)—that have been developed to identify substructure within jets originating from the decays of highly boosted heavy particles, like electroweak bosons and top quarks.

Analytical Framework and Tools

The main focus of this paper is to perform a resummed calculation of the rates at which these algorithms tag Quantum Chromodynamics (QCD) jets. The paper introduces modified tools, such as a variant of the MDT, with improved analytical properties. The standard tools' resummation structures are thoroughly discussed, highlighted by their typical double-logarithmic behavior. In contrast, the modified MDT is noted for a unique feature—it involves only single logarithms and is free from non-global logarithms that typically complicate such calculations.

Key Findings and Results

1. Trimming: The paper finds that for the trimmed-mass distribution, the analytical results exhibit distinctive regions characterized by different logarithmic dependencies on the jet mass parameter $\rho$. These regions are well captured by the resummation technique, and the comparison with Monte Carlo simulations shows good agreement.
2. Pruning: Two scenarios, $sane-pruning$ and $anomalous-pruning$, are introduced to account for different kinematic configurations under pruning. $Anomalous-pruning$ can produce terms with double-logarithmic divergences. The analytical results align well with simulations, capturing the transition between the dominant logarithmic structures.
3. Modified Mass-Drop Tagger (mMDT): A significant contribution of the paper is the introduction of the mMDT, which simplifies the tagging process by following the prong with the larger transverse mass. This modification importantly leads to results characterized only by single logarithms and eliminates non-global logarithms, making it a calculationally appealing option.

Theoretical Implications and Practical Use

The paper’s rich phenomenological discussion provides valuable insights into the performance of existing jet substructure techniques. It underscores the potential benefits of these methods for tagging jets in complex environments like the LHC. By eliminating terms associated with non-global logarithms, the mMDT offers a method that can be calculated to higher perturbative accuracy without the challenges posed by resummations at finite $N_C$.

Future Directions

The development and validation of these jet-tagging algorithms highlight the path forward for jet substructure analysis. Further work could involve incorporating these tools into actual collider data analyses to refine their performance and applicability. Additionally, exploring higher-order analytical corrections or integrating these techniques within machine learning frameworks for real-time data analysis could bring substantial benefits.

This paper establishes a robust foundation for the theoretical understanding of jet substructure, providing an essential toolkit for further studies and improvements in experimental high-energy physics analyses.