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We introduce a jet tagger based on a neural network analyzing the Minkowski Functionals (MFs) of pixellated jet images. The MFs are geometric measures of binary images, and they can be regarded as a generalization of the particle multiplicity, which is an important quantity in jet tagging. Their changes by dilation encode the jet constituents geometric structures that appear at various angular scales. We explicitly show that this analysis using the MFs together with mathematical morphology can be considered a constrained convolutional neural network (CNN). Conversely, CNN could model the MFs in a certain limit, and we show their correlation in the example of tagging semi-visible jets emerging from the strong interaction of a hidden valley scenario. The MFs are independent of the IRC-safe observables commonly used in jet physics. We combine this morphological analysis with an IRC-safe relation network which models two-point energy correlations. While the resulting network uses constrained input parameters, it shows comparable dark jet and top jet tagging performances to the CNN. The architecture has significant computational advantages when the available data is limited. We show that its tagging performance is much better than that of the CNN with a small number of training samples. We also qualitatively discuss their parton-shower model dependency. The results suggest that the MFs can be an efficient parameterization of the IRC-unsafe feature space of jets.
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Classification of jets with deep learning has gained significant attention in recent times. However, the performance of deep neural networks is often achieved at the cost of interpretability. Here we propose an interpretable network trained on the jet spectrum $S_{2}(R)$ which is a two-point correlation function of the jet constituents. The spectrum can be derived from a functional Taylor series of an arbitrary jet classifier function of energy flows. An interpretable network can be obtained by truncating the series. The intermediate feature of the network is an infrared and collinear safe C-correlator which allows us to estimate the importance of a $S_{2}(R)$ deposit at an angular scale R in the classification. The performance of the architecture is comparable to that of a convolutional neural network (CNN) trained on jet images, although the number of inputs and complexity of architecture is significantly simpler than the CNN classifier. We consider two examples: one is the classification of two-prong jets which differ in color charge of the mother particle, and the other is a comparison between Pythia 8 and Herwig 7 generated jets.
We present a new approach to jet definition as an alternative to methods that exploit kinematic data directly, such as the anti-$k_T$ scheme; we use the kinematics to represent the particles in an event in a new multidimensional space. The latter is constituted by the eigenvectors of a matrix of kinematic relations between particles, and the resulting partition is called spectral clustering. After confirming its Infra-Red (IR) safety, we compare its performance to the anti-$k_T$ algorithm in reconstructing relevant final states. We base this on Monte Carlo (MC) samples generated from the following processes: $(ggto H_{125,text{GeV}} rightarrow H_{40,text{GeV}} H_{40,text{GeV}} rightarrow b bar{b} b bar{b}), (ggto H_{500,text{GeV}} rightarrow H_{125,text{GeV}} H_{125,text{GeV}} rightarrow b bar{b} b bar{b})$ and $(gg,qbar qto tbar tto bbar b W^+W^-to bbar b jj ell u_ell)$. Finally, we show that the results for spectral clustering are obtained without any change in the algorithms parameter settings, unlike the anti-$k_T$ case, which requires the cone size to be adjusted to the physics process under study.
Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside $Z$-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction $z_h$ of the jet carried by the hadron and the transverse momentum $j_perp$ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the $z_h$-dependence provides information on standard collinear fragmentation functions, while $j_perp$-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate $z_h$ region. For $j_perp$-dependence, we suggest binning in both $z_h$ and $j_perp$, which would lead to a more direct probing of TMD fragmentation functions.
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.
Observables which distinguish boosted topologies from QCD jets are playing an increasingly important role at the Large Hadron Collider (LHC). These observables are often used in conjunction with jet grooming algorithms, which reduce contamination from both theoretical and experimental sources. In this paper we derive factorization formulae for groomed multi-prong substructure observables, focusing in particular on the groomed $D_2$ observable, which is used to identify boosted hadronic decays of electroweak bosons at the LHC. Our factorization formulae allow systematically improvable calculations of the perturbative $D_2$ distribution and the resummation of logarithmically enhanced terms in all regions of phase space using renormalization group evolution. They include a novel factorization for the production of a soft subjet in the presence of a grooming algorithm, in which clustering effects enter directly into the hard matching. We use these factorization formulae to draw robust conclusions of experimental relevance regarding the universality of the $D_2$ distribution in both $e^+e^-$ and $pp$ collisions. In particular, we show that the only process dependence is carried by the relative quark vs. gluon jet fraction in the sample, no non-global logarithms from event-wide correlations are present in the distribution, hadronization corrections are controlled by the perturbative mass of the jet, and all global color correlations are completely removed by grooming, making groomed $D_2$ a theoretically clean QCD observable even in the LHC environment. We compute all ingredients to one-loop accuracy, and present numerical results at next-to-leading logarithmic accuracy for $e^+e^-$ collisions, comparing with parton shower Monte Carlo simulations. Results for $pp$ collisions, as relevant for phenomenology at the LHC, are presented in a companion paper.
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