Likelihood free inference with advanced machine learning techniques - Diplomarbeit

Aug 3, 2026

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Hypothetical particles outside the Standard Model can manifest as small deviations in the data tails collected with the Compact Muon Solenoid experiment at the Large Hadron Collider. These deviations are modeled by effective operators of mass dimension higher than four, with the Standard Model treated as a low-energy approximation. The thesis develops simulation-based inference to learn optimal test statistics for four-fermion operator insertions in four-top and tt/tb channels, using polynomial structures in Wilson coefficients and nuisance-free unbinned likelihood-ratio limits up to quadratic order. Deep neural networks combined with LSTM layers extract information from variable-length jet systems as well as scalar observables, validated through training workflows and projected limits on Wilson coefficients for multiple scenarios.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages80

Reading Time3 h 22 min

AccessFree to download

Introduction

CERN, LHC and CMS

CERN-The European Council for Nuclear Research

LHC-The Large Hadron Collider

CMS-The Compact Muon Solenoid

The Standard Model and Standard Model Eﬀective Field Theory

The Standard Model and beyond

Standard Model Eﬀective Field Theory

Multi-classiﬁcation in tt and backgrounds

Learning the SMEFT with Simulation-based Inference

Simulation based inference

Limit setting in 1D and 2D

Multivariate Analysis

Basic Priniciples of MVA

The MVA architecture

Data Generation and Training

The input data

Hyperparameter optimization

Results

Training for signal only

Training with signal and background

Summary of the limit setting

Conclusion and Outlook

Diplomarbeit Likelihood free inference with advanced machine learning techniques zur Erlangung des akademischen Grades Diplom-Ingenieurin im Rahmen des Studiums Technische Physik eingereicht von Lena Wild, BSc MA MA Matrikelnummer: 11824551 ausgeführt am Institut für Hochenergiephysik der Österreichischen Akademie der Wissenschaften Betreuung Betreuer: Privatdoz. DI Dr. Robert Schöfbeck Wien, 12.06.2023 Unterschrift Verfasserin Unterschrift Betreuer Abstract Although many theories locate hypothetical phenomena beyond the Standard Model at energy scales far above the current experimental reach, tiny deviations from the Standard Model prediction are expected to show in the tails of data collected with the Compact Muon Solenoid experiment atthe Large Hadron Collider at CERN. These deviations can be described through the insertion of eﬀective operators of mass dimension higher than four, treating the Standard Model as a low-energy approximation of the hypothetical high energy theory. In this thesis, we adopt novel machine learning techniques based on simulation (simulation-based inference) to teach the machine the optimal test statistic according to the Neyman-Pearson lemma for four-fermion operator insertions in four-top production and production of two top and two bottom quarks. The centerpiece of this approach consists in exploiting the polynomial structure of the eﬀective ﬁeld theory prediction as a function of the coeﬃcients of the operators, i.e. , the Wilson coeﬃcients. Hence, learning only a small number of coeﬃcient functions allows to parametrize an optimal classiﬁer in the full parameter space. With the learned coeﬃcient functions at hand, we then set nuisance-free limits in an unbinned likelihood ratio test up to quadratic order in the polynomial expansion. In this way, we investigate the neural network’s performance in learning the yield-and shape-related modiﬁcations, thus probing new forces between four heavy quarks. On the machine learning side, we combine Deep Neural Networks with Long Short Time Memory layers to extract information not only from scaler observables, but also from the variable length jet system in analogy to speech recognition. By also probing this Multivariate Analysis setup in the simpler, more robust setting of multi-classiﬁcation, we test, optimize and cross-validate the conﬁguration of the network. In instantiating a complete workﬂow of sample generation, training with simulation-based inference, and the limit setting procedure, we obtain projected limits on the Wilson coeﬃcients of four-fermion operators in tt and tb with and without t background. Thus, we demonstrate the potential of these novel neural network architectures and machine learning techniques for future analyses. Contents 1 Introduction 1 2 CERN, LHC and CMS 2 2.1 CERN-The European Council for Nuclear Research .................. 2 2.2 LHC-The Large Hadron Collider ............................ 2 2.3 CMS-The Compact Muon Solenoid ........................... 5 2.3.1 CMS detection systems .............................. 6 2.3.2 Trigger and Data Acquisition at CMS ...................... 8 3 The Standard Model and Standard Model Eﬀective Field Theory 9 3.1 The Standard Model and beyond ............................. 9 3.2 Standard Model Eﬀective Field Theory .......................... 10 3.2.1 The SMEFT Lagrangian at mass dimension 6 .................. 10 3.3 The physics cases: tt and tb ............................. 10 3.4 Multi-classiﬁcation in tt and backgrounds ....................... 11 3.5 SMEFT in tt / tb ................................... 12 4 Learning the SMEFT with Simulation-based Inference 15 4.1 Simulation based inference ................................. 15 4.1.1 The optimal test statistic ............................. 15 4.1.2 Learning EFT eﬀects from simulation ...................... 16 4.1.3 Learning the polynomial dependence ..................

FAQs

What is the main goal of this thesis?

To learn optimal test statistics for SMEFT effects using likelihood-free, simulation-based machine learning, and to derive projected limits on Wilson coefficients for four-fermion operators in tt and tb-related production channels.

How does the approach use effective field theory structure?

It exploits the polynomial dependence of EFT predictions on Wilson coefficients, enabling learning of a small set of coefficient functions and constructing an optimal classifier across the full parameter space.

What machine learning architecture is used and what data does it extract from?

The work combines Deep Neural Networks with Long Short Term Memory layers to learn from both scalar observables and variable-length jet system inputs, validated via training, cross-validation, and hyperparameter optimization.

Aug 3, 2026

Upload by Riley