Soft Drop (1402.2657v2)

Abstract: We introduce a new jet substructure technique called "soft drop declustering", which recursively removes soft wide-angle radiation from a jet. The soft drop algorithm depends on two parameters--a soft threshold $z_\text{cut}$ and an angular exponent $\beta$--with the $\beta = 0$ limit corresponding roughly to the (modified) mass drop procedure. To gain an analytic understanding of soft drop and highlight the $\beta$ dependence, we perform resummed calculations for three observables on soft-dropped jets: the energy correlation functions, the groomed jet radius, and the energy loss due to soft drop. The $\beta = 0$ limit of the energy loss is particularly interesting, since it is not only "Sudakov safe" but also largely insensitive to the value of the strong coupling constant. While our calculations are strictly accurate only to modified leading-logarithmic order, we also include a discussion of higher-order effects such as multiple emissions and (the absence of) non-global logarithms. We compare our analytic results to parton shower simulations and find good agreement, and we also estimate the impact of non-perturbative effects such as hadronization and the underlying event. Finally, we demonstrate how soft drop can be used for tagging boosted W bosons, and we speculate on the potential advantages of using soft drop for pileup mitigation.

• The paper presents soft drop declustering, a method that recursively removes soft wide-angle emissions to clarify jet substructure.
• It employs the C/A clustering algorithm with an adjustable angular exponent (β) to control logarithmic scaling and tagging conditions.
• Numerical results confirm improved discrimination in observables, enhancing boosted W boson tagging and ensuring IRC safety.

An Insightful Overview of the "Soft Drop" Jet Substructure Technique

In particle physics, understanding the substructure of jets—collimated streams of particles produced in high-energy processes—is crucial for unraveling intricate mechanisms in quantum chromodynamics (QCD) and beyond. The paper "Soft Drop" by Larkoski, Marzani, Soyez, and Thaler introduces a jet grooming technique called "soft drop declustering," expanding on previous methodologies like the modified mass drop tagger (mMDT). This technique prioritizes the removal of soft wide-angle emissions within jets, providing a refined approach to jet substructure analysis.

Key Concepts and Methodology

The soft drop method is predicated on the principle of recursively declustering a jet to eliminate soft wide-angle radiation, defined by a pair of parameters—$cut$ as a soft threshold and $\beta$ as an angular exponent. This approach builds on the C/A jet clustering algorithm, ensuring a robust iterative process. For $\beta=0$, the algorithm approximates the mass drop procedure, iteratively shedding mass or transverse momentum drop parameters to decluster jets.

The analytic focus of the paper centers on the impact of the soft drop on various observables, including energy correlation functions $(#2){1}{\alpha}$, the groomed jet radius $R_g$, and the jet energy loss $\Delta_E$. A comprehensive examination of these observables highlights significant interplay with the angular exponent $\beta$. The calculations are performed to a modified leading-logarithmic order, with consideration of higher-order effects such as multiple emissions, showcasing notable parity with parton shower simulations.

Numerical Results and Observations

Numerical analyses within the paper reveal that for $\beta > 0$, the groomed jets exhibit significant reductions of double logarithm terms, paradigmatic of improved Sudakov peak positioning and reduced sensitivity to non-global logarithms. This is a profound affirmation of the analytic robustness of soft drop jets, especially when evaluated against untamed backgrounds. Within these trials, a marked deviation from standard $R_0$ approximations is evident, furthering the precision in extracting jet mass distributions or energy correlations.

As $\beta$ transitions towards zero, the declustering technique effectively nullifies soft-collinear divergences, resulting in single-logarithmic scaling behaviors. Conversely, $\beta < 0$ predicates stringent tagging conditions, manifesting as thresholds for observable scales like $(#2){1}{\alpha}$. Importantly, the manuscript finds that $\Delta_E$, which measures energy reduction after grooming, retains IRC safety with $\beta > 0$ and exhibits remarkable independence from $\alpha_s$ in the $\beta=0$ regime—a notion the authors refer to as "Sudakov safe."

Theoretical and Practical Implications

The dual capacity of soft drop declustering to groom jet substructure while mitigating pileup effects presents profound practical implications. Its superior discrimination power in boosted $W$ boson tagging augurs well for experimental applications, particularly in the enhanced energy and luminosity context of LHC Run II. Empirically, the resilience against both hadronization and UE corrections, as quantified by empirical distributions, offers a compelling argument for the soft drop's adaptability in addressing contamination from pileup.

From a theoretical perspective, this approach illuminates new pathways in the paper of singularities within QCD. Specifically, the demarcation of phase spaces and the attenuation of non-global logarithms underscore soft drop as a pivotal tool for isolating perturbative signatures whilst remaining practical for real-world analytic continuations.

Future Directions and Developments

This work paves the way for future inquiries into jet grooming techniques, especially as interactions grow increasingly complex. Future prospects could involve the application of soft drop methodologies to other composites like gluon or quark-gluon mixed jets and their subvarieties. Furthermore, the paper suggests potential benefits in extending the soft drop procedure to an event-wide frame, circumventing traditional jet definitions to provide holistic event analyses.

In summary, the soft drop algorithm introduces a versatile, theoretically sound, and empirically validated framework for jet grooming, offering meaningful contributions to both the phenomenological interpretations and experimental procedures within high-energy particle physics.