Pre-Processing and Re-Weighting Jet Images with Different Substructure Variables

Transcription

1 Pre-Processing and Re-Weighting Jet Images with Different Substructure Variables Lynn Huynh University of California, Davis Department of Mechanical Engineering CERN Work Project Report CERN, ATLAS, Jet Substructure Group Supervisor: Mario Campanelli (Dated: August 19, 2016) ABSTRACT This work is an extension of Monte Carlo simulation based studies in tagging boosted, hadronically decaying W bosons at a center of mass energy of s = 13 TeV. Two preprocessing techniques used with jet images, translation and rotation, are first examined. The generated jet images for W signal jets and QCD background jets are then rescaled and weighted with five different substructure variables for visual comparison. I. INTRODUCTION At the Large Hadron Collider (LHC), high energy collisions can produce sprays of particles known as jets. Theories beyond the Standard Model (SM) predict new particles that decay into the heavy SM particles - including the top quark, W, Z and Higgs bosons. The new particles are typically more massive than their SM daughter particles, and are therefore highly boosted and tightly collimated. This means they can be reconstructed as a single hadronic jet, with a maximum opening angle of roughly twice the jet mass divided by the transverse momentum: 2M/p T R [3]. Distinguishing these jets from the Quantum Chromodynamic (QCD) multijet background is one of the major challenges at the LHC. Prior studies have examined different substructure variables and methods to determine how to effectively tag hadronically decaying boosted particles. Machine Learning (ML) and Computer Vision (CV) techniques are one such way to address the challenge of jet tagging. With this approach, jets are represented as images. Deep neural networks (DNN) have the ability to learn rich high-level representations of these jet images, and feature greater discriminating power than previous analyses using Fisher discriminants [2]. It is important to pre-process the jet images so that machine learning algorithms can focus on identifying the discriminating features between background and signal. Here, a less rigorous procedure consisting of a translational and rotational transformation has been applied. The jets were also rescaled by the transverse momentum. Nonetheless, these corrections were sufficient for the purposes of building an intuition for jet tagging procedures and observing the effect of different substructure variable weights. A. Decay Case Data The specific case examined here was to differentiate between the decay of highly Lorentz boosted W bosons into quarks, and a background of generically produced quarks and gluons. The highly boosted W boson can be simulated by a hypothetical W boson that decays to a W and Z boson [3]. This W boson subsequently decays hadronically (W qq ), while the Z boson decays invisibly (Z ν ν). II. PRE-PROCESSING FIG. 1: Production and Decay Angles of W Bosons [1] The data studied was indirectly based on the work carried out with both real and simulated data from Run 1. To tag vector bosons in Run 2, jets recon-

2 2 (a) Raw Clusters (b) Translated W Jet Clusters (c) Rotated W Jet Clusters FIG. 2: Pre-Processing Jets with the Signal W Sample (a) Raw Clusters (b) Translated QCD Jet Clusters (c) Rotated QCD Jet Clusters FIG. 3: Pre-Processing Jets with the QCD Background Sample tructed with the anti-k T, R = 1.0 algorithm were used [4]. The signal W jet was simulated using the PYTHIA (8.186) generator. This process was produced with different W resonance masses (400 GeV 5 TeV), and with p T up to 2 TeV from s = 13 TeV simulated samples under Run 2 conditions [4]. To remove any bias, the simulated sample was weighted and combined so that the leading (highest p T ) jet and the background sample had the same p T distribution. The QCD background sample was comprised of high-p T multijets initiated by light quarks and gluons. This was simulated using the same setup as the W signal sample. The generated events were passed through a GEANT4 based simulation of the ATLAS detector. The topoclustering used in Run 2 was adjusted to prevent the local hadronic calibration from heavily weighing the presampler cells, thereby reducing the topoclusters energy contribution from pileup [4]. B. Translation To correct for the Monte Carlo data spread, the clusters were first all centrally translated, such that the jet is located at (η, φ) = (0,0). It should also be noted that the azimuthal angle periodicity must be accounted for. This translational shift can be seen with FIG. 2. Subfigure (a) shows the raw clusters from the signal sample. Subfigure (b) shows these clusters, after a translational transformation applied with a cut for the W jets. The bin size used in all three sample cases here was 50 x 50. To better demonstrate the pre-processing procedure, the clusters in FIG. 2 and FIG. 3 were all weighted by the same variable: transverse energy, defined as p T = E i /cosh(η i ). This was used as pixel intensity because it is invariant under translations in η (which are actually Lorentz boosts along the z axis). C. Rotation The next pre-processing step was to rotate the images about the jet center. The pixel intensity was unaffected because translations in φ are simply rotations about the z axis. Note that the subleading subjet is rotated to π/2 and is typically located using the FASTJET package. In this instance, the highest energy cluster was found and used as a proxy for this subleading subjet; this was sufficient for the purpose of obtaining azimuthal invariance. The angle of rotation was determined by rotating this cluster to π/2. This angle should be adjusted across the four quadrants, as the rotated grid aligns with original grid only when the rotation is an integer multiple of π/4. This rotational shift can be seen with FIG.

3 3 (a) EM Probability (b) Transverse Energy (c) Isolation (d) LCE over EME (e) Longitudinal FIG. 4: Weighted W Signal Jets (a) EM Probability (b) Transverse Energy (c) Isolation (d) LCE over EME (e) Longitudinal FIG. 5: Weighted QCD Background Jets 2. Subfigure (c) shows the clusters, after a subsequent rotational transformation applied with a cut for the W jets. III. SUBSTRUCTURE VARIABLES In prior studies involving these DNN architectures, the jet image pixel intensities were represented by the particle energy depositions. There however exists thirteen other observables that may be used for weighting: clus E clus rawe clus LCEoverEME clus ISOLATION clus LATERAL clus LONGITUDINAL clus SECOND LAMBDA clus SECOND R clus CENTER LAMBDA clus CENTER MAG clus ENG POS clus EM PROBABILITY

4 4 (a) Scaled Energy (b) Unscaled Energy (c) Scaled Transverse Energy (d) Unscaled Transverse Energy FIG. 6: (Un)scaled W Signal Jets weighted with (Transverse) Energy (a) Scaled Energy (b) Unscaled Energy (c) Scaled Transverse Energy (d) Unscaled Transverse Energy FIG. 7: (Un)scaled QCD Background Jets weighted with (Transverse) Energy clus ENG FRAC MAX clus FIRST ENG DENS Here, the jet image re-weighting was compared with four of these substructure variables, as well as the transverse energy. The selected variables include: clus EM PROBABILITY clus ISOLATION clus LCEoverEME clus LONGITUDINAL IV. VISUALIZATION The clusters were then rescaled by 300 GeV over the jet transverse momentum. Once pre-processed, the weighted jet images were used to visualize these clusters. FIG. 4 (signal W jets) and FIG. 5 (QCD background jets) contain the set of these jet images, individually weighted by each of the five aforementioned substructure variables. These were visually compared between the W signal and QCD background jets, as well as between the variable weights. Differences in weighting by energy and transverse

5 5 energy, and for scaling and not scaling, are depicted in FIG. 4 (signal W jets) and FIG. 7 (QCD background jets). VI. CONCLUSION In the CV and image processing fields, a particular weighted average of the pixels intensities is known as an image moment. These moments are used to find image properties such as the area (total intensity), centroid and orientation. The generated jet images, as processed and weighted here, can be used to further explore these image moments for analysis of W signal and QCD background jet differences. When weighted by each of the substructure variables, characteristic differences in the jet substructures can be seen between the signal W and QCD background jets. These variances in the image weights prove interesting for further analysis. With a more thorough pre-processing procedure, the jet tagging methods driven by these physically motivated features can be incorporated into DNN architectures. The goal of increasing sensitivity in jet tagging methods motivates future studies in machine learning techniques targeting these physical substructure observables. References [1] Couchman, J. (2002, November 4). W Boson Decays. Retrieved August 18, 2016, from jpc/all/ulthesis/node45.h tml [2] De Oliveira, L., Kagan, M., Mackey, L., Nachman, B., and Schwartzman, A. (n.d.). Jet-Images Deep Learning Edition (arxiv: v2 [hepex]) (Tech.). [3] Identification of boosted, hadronically decaying W bosons and comparisons with ATLAS data taken at s = 8 TeV (Rep.). (2016). [4] Identification of Boosted, Hadronically-Decaying W and Z Bosons in s = 13 TeV Monte Carlo Simulations for ATLAS (Rep. No. ATL-PHYS- PUB ). (2015). Acknowledgments The invaluable guidance of Mario Campanelli, Samuel Meehan, Benjamin Nachman, Fiona Pons, Ece Akilli, Amal Vaidya, and the rest of the Jet Substructure Group is gratefully acknowledged. Special thanks to Phil Rubin for making this opportunity possible. This work is supported by the International Research Experiences for Students (IRES) grant from the National Science Foundation under Grant No