[Paper Review] Precision-Machine Learning for the Matrix Element Method

Theo Heimel, Nathan Huetsch+3 more|arXiv (Cornell University)|Oct 11, 2023

Particle physics theoretical and experimental studies11 citations

TL;DR

The paper develops a three-network MEM-ML framework that combines a conditional invertible neural network, a transfer/diffusion network, and an acceptance classifier to enable high-precision likelihood extraction in MEM analyses, demonstrated on a CP-phase in tHj production with H→γγ.

ABSTRACT

The matrix element method is the LHC inference method of choice for limited statistics. We present a dedicated machine learning framework, based on efficient phase-space integration, a learned acceptance and transfer function. It is based on a choice of INN and diffusion networks, and a transformer to solve jet combinatorics. We showcase this setup for the CP-phase of the top Yukawa coupling in associated Higgs and single-top production.

Motivation & Objective

• Improve MEM analyses by integrating ML-based phase-space integration with learned acceptance and transfer functions.
• Achieve high-precision likelihood extraction from limited event samples for LHC processes.
• Demonstrate applicability to a CP-phase measurement in top Yukawa coupling via tHj with H→γγ decay.
• Address jet combinatorics and detector effects within a unified ML MEM framework.

Proposed method

• Use a three-network MEM integrator comprising a Sampling-cINN conditioned on CP-angle α and reco-level x_reco, a Transfer network conditioned on x_hard, and an Acceptance network estimating ε(x_hard).
• Express the reco-level likelihood p(x_reco|α) via dσ_fid(α)/dx_reco and the forward transfer r(x_reco|x_hard) with ε(x_hard).
• Train the Acceptance network to output acceptance probabilities for x_hard.
• Model the transfer function with a conditional generative network (cINN or diffusion) to map x_hard to x_reco.
• Incorporate a second conditional normalizing flow to optimize sampling q_φ(x_hard|x_reco,α) for efficient Monte Carlo integration.
• Apply Vegas latent-space refinement to reduce integral variance and improve convergence.
• Exploit factorization of dσ(x_hard|α)/dx_hard into α-dependent and x_hard-dependent parts to accelerate computation (operator morphing).

Experimental results

Research questions

• RQ1 Can a three-network MEM-ML framework achieve near-optimal likelihood extraction for MEM analyses with limited event samples?
• RQ2 How can learned acceptance and transfer functions be integrated into MEM to handle detector effects and phase-space integration efficiently?
• RQ3 What is the impact of using a diffusion/transfer network and jet combinatorics transformer on CP-phase sensitivity in tHj production?
• RQ4 How does Vegas refinement and importance sampling trained on the transfer probability affect convergence and uncertainty in MEM integrals?
• RQ5 Can the MEM be reformulated to exploit factorization properties of the differential cross section for CP-violating top Yukawa studies?

Key findings

• A three-network MEM framework with a Sampling-cINN, a Transfer network, and an Acceptance network enables efficient and precise fiducial cross-section integration and event likelihood evaluation.
• Training the Sampling-cINN on the learned transfer probability and applying Vegas refinement improves convergence and achieves target precision (approximately 2%) within a practical number of iterations for most events.
• Increased event samples reveal residual systematic deviations between hard-process truth and reconstructed likelihoods, motivating architectural and training improvements for the transfer probability.
• Acceptance modeling via a dedicated network improves the MEM likelihoods compared to a two-network baseline, enabling closer-to-optimal performance in CP-phase inference.
• The method can exploit factorization of dσ/dx_hard into α-dependent and x_hard-dependent components to simplify and accelerate the computation, aiding CP-phase studies.