Non-Global Logarithms in Filtered Jet Algorithms

TL;DR

This work analyzes how perturbative QCD radiation affects the Filtering analysis used to identify boosted Higgs decays to $b\bar{b}$ at the LHC, focusing on non-global logarithms in the leading soft limit within the large-$N_c$ approximation. It develops both analytic insights (for low filter multiplicities) and all-orders numerical results to capture the non-global structure of the observable, and compares them with fixed-order calculations to understand convergence. The study then combines perturbative widths with underlying-event/pile-up and hadronisation effects to propose optimized filtering parameters $(n,\eta)$ that minimize the overall Higgs mass peak width while preserving the perturbative content, offering practical guidance for boosted-Higgs analyses and potential extensions to other boosted colorless resonances. The results highlight the delicate balance between retaining perturbative radiation and suppressing soft contamination, and they reveal notable features such as the saturation of perturbative width at large $\,\eta$ and the strong influence of non-global dynamics on optimal filtering choices.

Abstract

We analytically and numerically study the effect of perturbative gluons emission on the "Filtering analysis", which is part of a subjet analysis procedure proposed two years ago to possibly identify a low-mass Higgs boson decaying into b\bar{b} at the LHC. This leads us to examine the non-global structure of the resulting perturbative series in the leading single-log large-N_c approximation, including all-orders numerical results, simple analytical approximations to them and comments on the structure of their series expansion. We then use these results to semi-analytically optimize the parameters of the Filtering analysis so as to suppress as much as possible the effect of underlying event and pile-up on the Higgs mass peak reconstruction while keeping the major part of the perturbative radiation from the b\bar{b} dipole.

Figures (25)

• Figure 1: The Mass Drop and Filtering analysis in the procedure used to enhance the signal from a light Higgs decaying into $b\bar{b}$ at the LHC.
• Figure 2: Configurations leading to non-global logarithms when \ref{['NG_nfilt2']}$n_{\hbox{\tiny filt}}=2$ and \ref{['NG_nfilt3']}$n_{\hbox{\tiny filt}}=3$. In each case, the hardest gluon $1$, which is inside the filtered jet region, emits a softer gluon $2$ outside the filtered jet region.
• Figure 3: The coefficient $J(\eta)$ in front of the primary soft logarithm $\ln\frac{M_H}{\Delta M}$.
• Figure 4: How to compute the leading behavior of $\Sigma^{(3)}(L,t)$ from $\Sigma^{(2)}(L,t)$ when $L\gg 1$ and $N_c\gg 1$. In the second term, $t'$ is the gluon's emission scale.
• Figure 5: Comparison between numerical all-orders result (obtained using $C/A$ algorithm) and leading collinear logarithm estimate of $\Sigma(t)$ derived with anti-$k_t$ for \ref{['ao_vs_an_nf2']}$n=2$ and \ref{['ao_vs_an_nf3']}$n=3$ for $2$ values of $\eta$: $0.1$ and $0.5$.