Two Invertible Networks for the Matrix Element Method

The matrix element method is widely considered the ultimate LHC inference tool for small event numbers, but computationally expensive. We show how a combination of two conditional generative neural networks encodes the QCD radiation and detector effects without any simplifying assumptions, and allows us to efficiently compute likelihoods for individual events. We illustrate our approach for the CP-violating phase of the top Yukawa coupling in associated Higgs and single-top production. Currently, the limiting factor for the precision of our approach is jet combinatorics.

[1]  A. Butter,et al.  Targeting multi-loop integrals with neural networks , 2021, SciPost Physics.

[2]  U. Köthe,et al.  Inference of cosmic-ray source properties by conditional invertible neural networks , 2021, The European Physical Journal C.

[3]  F. Kling,et al.  Machine learning the Higgs boson-top quark CP phase , 2021, Physical Review D.

[4]  F. Siegert,et al.  Accelerating Monte Carlo event generation -- rejection sampling using neural network event-weight estimates , 2021, SciPost Physics.

[5]  T. Plehn,et al.  Understanding Event-Generation Networks via Uncertainties , 2021, SciPost Physics.

[6]  Jeong Han Kim,et al.  Direct Higgs-top CP-phase measurement with t ¯ th at the 14 TeV LHC and 100 TeV FCC , 2022 .

[7]  H. Bahl.  Constraining CP -violation in the Higgs-top-quark interaction using machine-learning-based inference , 2022 .

[8]  David Shih,et al.  CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows , 2021, ArXiv.

[9]  M. Xiao,et al.  Probing the CP structure of the top quark Yukawa coupling: Loop sensitivity versus on-shell sensitivity , 2021, Physical Review D.

[10]  Blaz Bortolato,et al.  Optimized probes of CP-odd effects in the tt¯h process at hadron colliders , 2021 .

[11]  Rob Verheyen,et al.  Phase space sampling and inference from weighted events with autoregressive flows , 2020, SciPost Physics.

[12]  C. Delaere,et al.  Matrix element regression with deep neural networks — Breaking the CPU barrier , 2020, Journal of High Energy Physics.

[13]  G. Kasieczka,et al.  Getting High: High Fidelity Simulation of High Granularity Calorimeters with High Speed , 2020, Computing and Software for Big Science.

[14]  L. Santi,et al.  Towards a computer vision particle flow , 2020, The European Physical Journal C.

[15]  Michelle P. Kuchera,et al.  Simulation of electron-proton scattering events by a Feature-Augmented and Transformed Generative Adversarial Network (FAT-GAN) , 2020, IJCAI.

[16]  Damian Podareanu,et al.  Event generation and statistical sampling for physics with deep generative models and a density information buffer , 2019, Nature Communications.

[17]  Stefan T. Radev,et al.  Measuring QCD Splittings with Invertible Networks , 2020, SciPost Physics.

[18]  A. Butter,et al.  How to GAN Event Unweighting , 2020, 2012.07873.

[19]  Matthew D. Klimek,et al.  Improved neural network Monte Carlo simulation , 2020, 2009.07819.

[20]  G. Kasieczka,et al.  GANplifying event samples , 2020, SciPost Physics.

[21]  Ullrich Kothe,et al.  Invertible networks or partons to detector and back again , 2020, 2006.06685.

[22]  G. Kasieczka,et al.  Per-object systematics using deep-learned calibration , 2020, SciPost Physics.

[23]  H. Schulz,et al.  Event generation with normalizing flows , 2020, Physical Review D.

[24]  Christina Gao,et al.  i- flow: High-dimensional integration and sampling with normalizing flows , 2020, Mach. Learn. Sci. Technol..

[25]  S. Schumann,et al.  Exploring phase space with Neural Importance Sampling , 2020, SciPost Physics.

[26]  G. Kasieczka,et al.  How to GAN away Detector Effects , 2019, SciPost Physics.

[27]  Patrick T. Komiske,et al.  OmniFold: A Method to Simultaneously Unfold All Observables. , 2019, Physical review letters.

[28]  K. Cranmer,et al.  MadMiner: Machine Learning-Based Inference for Particle Physics , 2019, Computing and Software for Big Science.

[29]  Jennifer Thompson,et al.  Deep-learning jets with uncertainties and more , 2019, SciPost Physics.

[30]  Jin Min Yang,et al.  Unveiling CP property of top-Higgs coupling with graph neural networks at the LHC , 2019, Physics Letters B.

[31]  H. Bahl.  Indirect CP probes of the Higgs–top-quark interaction: current LHC constraints and future opportunities , 2020 .

[32]  A. Butter,et al.  How to GAN event subtraction , 2019, SciPost Physics Core.

[33]  Natalia Gimelshein,et al.  PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.

[34]  P. Uwer,et al.  Matrix element method at NLO for (anti-) kt -jet algorithms , 2019, Physical Review D.

[35]  P. Uwer,et al.  Exploring BSM Higgs couplings in single top-quark production , 2019, 1908.09100.

[36]  Tilman Plehn,et al.  How to GAN LHC events , 2019, SciPost Physics.

[37]  Iain Murray,et al.  Neural Spline Flows , 2019, NeurIPS.

[38]  Sana Ketabchi Haghighat,et al.  DijetGAN: a Generative-Adversarial Network approach for the simulation of QCD dijet events at the LHC , 2019, Journal of High Energy Physics.

[39]  Enrico Bothmann,et al.  Reweighting a parton shower using a neural network: the final-state case , 2018, Journal of High Energy Physics.

[40]  Martin Erdmann,et al.  Precise Simulation of Electromagnetic Calorimeter Showers Using a Wasserstein Generative Adversarial Network , 2018, Computing and Software for Big Science.

[41]  C. Frye,et al.  JUNIPR: a framework for unsupervised machine learning in particle physics , 2018, The European Physical Journal C.

[42]  Nicholay Topin,et al.  Super-convergence: very fast training of neural networks using large learning rates , 2018, Defense + Commercial Sensing.

[43]  M. Spannowsky,et al.  Searching for processes with invisible particles using a matrix element-based method , 2017, Physics Letters B.

[44]  R. Schwienhorst,et al.  Single top-quark production at the Tevatron and the LHC , 2017, Reviews of Modern Physics.

[45]  Michela Paganini,et al.  CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks , 2017, ArXiv.

[46]  P. Uwer,et al.  The Matrix Element Method at next-to-leading order QCD for hadronic collisions: single top-quark production at the LHC as an example application , 2017, 1712.04527.

[47]  Alex Kendall,et al.  What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? , 2017, NIPS.

[48]  Luke de Oliveira,et al.  Learning Particle Physics by Example: Location-Aware Generative Adversarial Networks for Physics Synthesis , 2017, Computing and Software for Big Science.

[49]  S. Weinzierl,et al.  Matrix element method at next-to-leading order for arbitrary jet algorithms , 2016, 1612.07252.

[50]  Andrea Benaglia,et al.  Measurement of spin correlations in tt production using the matrix element method in the muon+jets final state in pp collisions at √s=8 TeV , 2016 .

[51]  M. Xiao,et al.  Constraining anomalous Higgs boson couplings to the heavy flavor fermions using matrix element techniques , 2016, 1606.03107.

[52]  C. Englert,et al.  Measuring the Higgs-bottom coupling in weak boson fusion , 2015, 1512.03429.

[53]  Lino Ferreira Lopes,et al.  Evidence for single top-quark production in the $s$-channel in proton-proton collisions at $\sqrt{s}=$8 TeV with the ATLAS detector using the Matrix Element Method , 2015, 1511.05980.

[54]  M. Buckley,et al.  Boosting the Direct CP Measurement of the Higgs-Top Coupling. , 2015, Physical review letters.

[55]  Yarin Gal,et al.  Uncertainty in Deep Learning , 2016 .

[56]  P. Uwer,et al.  Extending the Matrix Element Method beyond the Born approximation: calculating event weights at next-to-leading order accuracy , 2015, 1506.08798.

[57]  K. Mawatari,et al.  Higgs production in association with a single top quark at the LHC , 2015, The European physical journal. C, Particles and fields.

[58]  S. M. Etesami,et al.  Search for a standard model Higgs boson produced in association with a top-quark pair and decaying to bottom quarks using a matrix element method , 2015, The European physical journal. C, Particles and fields.

[59]  Peter Skands,et al.  An introduction to PYTHIA 8.2 , 2014, Comput. Phys. Commun..

[60]  P. Demin,et al.  DELPHES 3: a modular framework for fast simulation of a generic collider experiment , 2014, Journal of High Energy Physics.

[61]  J. Campbell,et al.  Event-by-event weighting at next-to-leading order , 2013, 1311.5811.

[62]  K. Mawatari,et al.  A framework for Higgs characterisation , 2013, 1306.6464.

[63]  F. Maltoni,et al.  Unravelling tth via the matrix element method. , 2013, Physical review letters.

[64]  J. Campbell,et al.  Finding the Higgs boson in decays to $Z \gamma$ using the matrix element method at Next-to-Leading Order , 2013, 1301.7086.

[65]  C. Englert,et al.  Extracting precise Higgs couplings by using the matrix element method , 2013 .

[66]  J. Campbell,et al.  The matrix element method at next-to-leading order , 2012, 1204.4424.

[67]  M. Cacciari,et al.  FastJet user manual , 2011, 1111.6097.

[68]  O. Mattelaer,et al.  The Matrix Element Method and QCD Radiation , 2010, 1010.2263.

[69]  V. Lemaitre,et al.  Automation of the matrix element reweighting method , 2010, 1007.3300.

[70]  Frank Fiedler,et al.  The matrix element method and its application to measurements of the top quark mass , 2010, 1003.1316.

[71]  M. Cacciari,et al.  The anti-$k_t$ jet clustering algorithm , 2008, 0802.1189.

[72]  E. al.,et al.  Top quark mass measurement from dilepton events at CDF II with the matrix-element method , 2006, hep-ex/0605118.

[73]  J. Latorre,et al.  Unbiased determination of the proton structure function F 2 p with faithful uncertainty estimation , 2005, hep-ph/0501067.

[74]  D. Collaboration.  A precision measurement of the mass of the top quark , 2004, Nature.

[75]  K. Bos,et al.  A precision measurement of the mass of the top quark , 2004 .

[76]  V. Šimák,et al.  Measurement of the Top Quark Mass in Dilepton Channel , 2006 .

[77]  Radford M. Neal.  Bayesian learning for neural networks , 1995 .

[78]  David Mackay,et al.  Probable networks and plausible predictions - a review of practical Bayesian methods for supervised neural networks , 1995 .

[79]  K. Kondo,et al.  Dynamical Likelihood Method for Reconstruction of Events with Missing Momentum. III. Analysis of a CDF High P T eµ Event as t\bar t Production , 1993 .

[80]  Kunitaka Kondo,et al.  Dynamical Likelihood Method for Reconstruction of Events with Missing Momentum. II. Mass Spectra for 2→2 Processes , 1991 .

[81]  K. Kondo.  Dynamical Likelihood Method for Reconstruction of Events with Missing Momentum. I. Method and Toy Models , 1988 .