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Applying Normalizing Flows for spin correlations reconstruction in associated top-quark pair and dark matter production

E. Abasov, L. Dudko, E. Iudin, A. Markina, P. Volkov, G. Vorotnikov, M. Perfilov, A. Zaborenko

TL;DR

The paper addresses reconstructing invisible momenta in $t\bar{t}$+DM events to access spin-sensitive observables. It applies Normalizing Flows to learn the full conditional density $p( ext{invisible}| ext{visible})$ and compares against an MLP baseline, demonstrating improved preservation of high-dimensional correlations. The study demonstrates robust reconstruction of the entanglement marker $D=\text{Tr}[C]/3$ and the angular observable $\cos\varphi$ in dileptonic $t\bar{t}$ across different $m_{t\bar{t}}$ regions, with the $\nu$-Flows variant often excelling in histogram-level metrics. It also outlines extensions to 3- and 4-top final states, suggesting transformer-based unfolding and resonance matching to handle combinatorial challenges and enhance sensitivity to dark matter in complex topologies.

Abstract

We apply a unified machine-learning framework based on Normalizing Flows (NFs) for the event-by-event reconstruction of invisible momenta and the subsequent evaluation of spin-sensitive observables in top-quark pair and dark-matter (DM) associated production processes. Building on recent studies in single-top + DM topologies, we extend the research to $t\bar{t}$ + DM final states. Inputs to our networks combine low-level four-momenta and missing transverse energy with high-level kinematic and angular variables. We compare a baseline multilayer perceptron (MLP) regressor, an autoregressive flow, and the conditional $ν$-Flows model -- trained to learn the full conditional density. In these final states all the models perform well and demonstrate high reconstruction quality in independent regions split by $m_{t\bar{t}}$ for validation purposes. We highlight the potential of this approach to be extended to three- and four-top-quark production.

Applying Normalizing Flows for spin correlations reconstruction in associated top-quark pair and dark matter production

TL;DR

The paper addresses reconstructing invisible momenta in +DM events to access spin-sensitive observables. It applies Normalizing Flows to learn the full conditional density and compares against an MLP baseline, demonstrating improved preservation of high-dimensional correlations. The study demonstrates robust reconstruction of the entanglement marker and the angular observable in dileptonic across different regions, with the -Flows variant often excelling in histogram-level metrics. It also outlines extensions to 3- and 4-top final states, suggesting transformer-based unfolding and resonance matching to handle combinatorial challenges and enhance sensitivity to dark matter in complex topologies.

Abstract

We apply a unified machine-learning framework based on Normalizing Flows (NFs) for the event-by-event reconstruction of invisible momenta and the subsequent evaluation of spin-sensitive observables in top-quark pair and dark-matter (DM) associated production processes. Building on recent studies in single-top + DM topologies, we extend the research to + DM final states. Inputs to our networks combine low-level four-momenta and missing transverse energy with high-level kinematic and angular variables. We compare a baseline multilayer perceptron (MLP) regressor, an autoregressive flow, and the conditional -Flows model -- trained to learn the full conditional density. In these final states all the models perform well and demonstrate high reconstruction quality in independent regions split by for validation purposes. We highlight the potential of this approach to be extended to three- and four-top-quark production.

Paper Structure

This paper contains 5 sections, 3 equations, 8 figures.

Table of Contents

  1. Reconstructing spin-sensitive observables with machine learning
  2. From single-top to $t\bar{t}$ spin correlations
  3. Application of machine learning reconstruction
  4. Prospects: 3 and 4 top-quark production
  5. Conclusion

Figures (8)

  • Figure 1: Entanglement marker $cos\varphi$ in parton-level samples for $t\bar{t}$ (SM) and $t\bar{t}\Phi$ (DM) signatures, whole dataset is used.
  • Figure 2: Entanglement marker $cos\varphi$ in parton-level samples for $t\bar{t}$ (SM) and $t\bar{t}\Phi$ (DM) signatures, data is split into distinct $m_{t\bar{t}}$ regions.
  • Figure 3: Loss functions of the neural networks by epoch. L1 loss is used to train the MLP, NF-based architectures use the likelihood.
  • Figure 4: Reconstructed $\cos\varphi$ for both SM and DM samples and 3 types of neural networks - MLP, Basic Flows and $\nu$-Flows.
  • Figure 5: Reconstructed $\cos\varphi$ for both SM and DM samples with $m_{t\bar{t}}$ splits for the Basic Flows.
  • ...and 3 more figures