Jet substructure with analytical methods

TL;DR

This work provides a comprehensive analytical study of jet-mass distributions after boosted-object substructure techniques (MDT, pruning, trimming) at next-to-leading order. It shows that the modified mass drop tagger (mMDT) yields a pure single-logarithmic structure with no non-global logs, while pruning exhibits challenging double-logarithmic and non-global effects, and trimming retains substantial double-log behavior with complex region-dependent transitions. The findings illuminate how these tools alter the QCD background and guide the development of resummation and fixed-order matching for LHC phenomenology. Overall, the paper establishes explicit logarithmic patterns across techniques and validates them against fixed-order results, providing a foundation for improved substructure methods and phenomenological studies.

Abstract

We consider the mass distribution of QCD jets after the application of jet substructure methods, specifically the mass-drop tagger, pruning, trimming and their variants. In contrast to most current studies employing Monte Carlo methods, we carry out analytical calculations at the next-to-leading order level, which are sufficient to extract the dominant logarithmic behaviour for each technique, and compare our findings to exact fixed-order results. Our results should ultimately lead to a better understanding of these jet substructure methods which in turn will influence the development of future substructure tools for LHC phenomenology.

Figures (12)

• Figure 1: Comparison of the analytic calculation Eq. (\ref{['LOmdtcomplete']}) with Event2 at LO in the region $v< \frac{y_\text{cut}}{1+y_\text{cut}}\Delta_R^2$, for different values of $y_\text{cut}$. The red curve shows the fixed-order result alone which is flat for small $v$ and hence indicates a single logarithmic behaviour for the integrated distribution. The green curve indicates that, after subtracting our analytical calculation, the result vanishes at small $v$ as expected.
• Figure 2: NLO configuration that gives rise to an extra logarithm for the MDT.
• Figure 3: Comparison of the NLO analytic calculations Eq. (\ref{['MDJg1']}), on the left, and Eq. (\ref{['MDJg2']}), on the right, with Event2 , in the region $v< \frac{y_\text{cut}^3}{(1+y_\text{cut})^3}\Delta_R^2$, for different values of $y_\text{cut}$. The plots demonstrate that the extra logarithm for MDT in the $C_F C_A$ and $C_F n_f$ channels, is correctly captured by the our calculation: the difference between analytical and Event2 results (in green) is consistent with a linear behaviour at small $v$ corresponding to a single-logarithmic leftover, $\alpha_s^2 \ln^2 1/v$, in the integrated distribution.
• Figure 4: Real and virtual contributions to the NLO jet-mass distribution in the $C_F^2$ channel.
• Figure 5: Comparison of the analytic calculation Eq. (\ref{['MDTCF2final']}) with Event2 for the coefficient of $C_F^2$, in the region $v< \frac{y_\text{cut}}{1+y_\text{cut}}\Delta_R^2$, for different values of $y_\text{cut}$. The red curve shows the fixed-order result alone which behaves like a straight line at small $v$ and hence indicates a single logarithmic behaviour for the integrated distribution. The green curve indicates that, after subtracting our analytical calculation, the result is flat at small $v$, as expected.