Gaining (Mutual) Information about Quark/Gluon Discrimination

Abstract: Discriminating quark jets from gluon jets is an important but challenging problem in jet substructure. In this paper, we use the concept of mutual information to illuminate the physics of quark/gluon tagging. Ideal quark/gluon separation requires only one bit of truth information, so even if two discriminant variables are largely uncorrelated, they can still share the same "truth overlap". Mutual information can be used to diagnose such situations, and thus determine which discriminant variables are redundant and which can be combined to improve performance. Using both parton showers and analytic resummation, we study a two-parameter family of generalized angularities, which includes familiar infrared and collinear (IRC) safe observables like thrust and broadening, as well as IRC unsafe variants like $p_T^D$ and hadron multiplicity. At leading-logarithmic (LL) order, the bulk of these variables exhibit Casimir scaling, such that their truth overlap is a universal function of the color factor ratio $C_A/C_F$. Only at next-to-leading-logarithmic (NLL) order can one see a difference in quark/gluon performance. For the IRC safe angularities, we show that the quark/gluon performance can be improved by combining angularities with complementary angular exponents. Interestingly, LL order, NLL order, Pythia 8, and Herwig++ all exhibit similar correlations between observables, but there are significant differences in the predicted quark/gluon discrimination power. For the IRC unsafe angularities, we show that the mutual information can be calculated analytically with the help of a nonperturbative "weighted-energy function", providing evidence for the complementarity of safe and unsafe observables for quark/gluon discrimination.

Analyzing Quark/Gluon Discrimination by Utilizing Mutual Information

This paper addresses the challenging but crucial problem of distinguishing quark jets from gluon jets in the field of jet substructure. The authors employ mutual information as a theoretical framework to better understand the intricacies of quark/gluon tagging and analyze the discrimination power of various observables for this purpose.

Key Observations and Methodology

• Motivation and Framework: Quark/gluon discrimination is non-trivial due to the different showering and fragmentation behaviors of quarks and gluons. It is essential for many applications in high-energy physics contexts like those observed at the Large Hadron Collider (LHC). The authors propose using mutual information to evaluate the redundancy and effectiveness of different discriminant variables, offering insights into combining these variables for improved performance.

• Generalized Angularities: The paper introduces a two-parameter family of generalized angularities characterized by $(\kappa, \beta)$, enabling exploration of both IRC safe and unsafe observables. The authors focus on understanding the mutual information and discrimination capabilities of these angularities through their scaling properties, notably identifying instances of Casimir scaling at leading-logarithmic order, which is indicative of uniform performance across different angularities.

• Analytic and Simulation Studies: Through both analytic calculations and parton shower simulations performed with Pythia{8} and Herwig++, the study highlights significant variance in predicted discrimination power. The generalized angularities were evaluated for their truth overlap with quark/gluon classification to assess their individual and collective discriminant powers.

• Evidence of Model Variability: The results from simulations using Pythia{8} and Herwig++ revealed discrepancies, underlining the sensitivity of quark/gluon discrimination to the model used. This variability points to the need for precise real-world measurements to refine and validate the theoretical predictions.

Implications

This comprehensive study of mutual information in quark/gluon discrimination suggests significant theoretical and practical implications:

1. Optimization of Substructure Observables: By identifying redundant variables and optimizing combinations of substructure observables, researchers can achieve more accurate and reliable quark/gluon discrimination, which is vital for the physics analyses at the LHC.

2. Guidance for Experimental Studies: The observed discrepancies between simulation models hint at the importance of empirical data for tuning and validating theoretical models. It recommends measuring the distributions of observables like recoil-free angularities to benchmark simulation predictions.

3. Potential for Expanding Calculability: The highlighted techniques allow a broader understanding of collinear and infrared unsafe variables by introducing nonperturbative objects like the weighted-energy function. This insight could be pivotal for expanding calculability in jet physics.

4. Future Directions in Soft Radiation Handling: The study proposes potential methodologies to address the soft radiation component, possibly through procedures like soft drop declustering, to enhance theoretical control over quark/gluon tagging precision.

Conclusion

This paper offers a significant contribution to understanding quark/gluon discrimination through the lens of mutual information and generalized angularities. The combination of analytic and simulation approaches presents a thorough investigation, setting the stage for further theoretical and empirical exploration in high-energy particle physics contexts. While discrepancies between simulation models necessitate real-world validation and adjustment, the insights provided pave the way for optimized jet tagging strategies that can more effectively discern between quark and gluon jets.