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Complete Physics Results

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Abstract and 1. Introduction

  1. Unfolding

    2.1 Posing the Unfolding Problem

    2.2 Our Unfolding Approach

  2. Denoising Diffusion Probabilistic Models

    3.1 Conditional DDPM

  3. Unfolding with cDDPMs

  4. Results

    5.1 Toy models

    5.2 Physics Results

  5. Discussion, Acknowledgments, and References


Appendices

A. Conditional DDPM Loss Derivation

B. Physics Simulations

C. Detector Simulation and Jet Matching

D. Toy Model Results

E. Complete Physics Results

E Complete Physics Results

In fig. 11 and fig. 12 we present the unfolding results for the remaining particle properties (η, ϕ, E, px, py, pz) that were not shown in the main text. These additional plots demonstrate the cDDPM’s ability to successfully unfold the full particle vector, providing a comprehensive view of its performance across all dimensions.


The tables in this appendix (table 3 and table 4) provide a detailed breakdown of the unfolding performance metrics for each particle property and dataset. Furthermore, these metrics (Energy distance, Wasserstein distance between histograms, and KL divergence between histograms) offer a more in-depth perspective on the unfolding quality.


Figure 10: Complete unfolding results for the multidimensional toy model tests using a class of exponential functions. The cDDPM is trained on datasets with different exponential distributions (characterized by βi) and conditioned on the moments of the pT distributions. The successful unfolding of the test datasets demonstrates the cDDPM’s ability to interpolate and extrapolate within the class of distributions based on the provided moments.


Figure 11: Unfolding performance of a single cDDPM on the remaining particle properties (η, ϕ, px, py, pz) for various simulated physics processes with detector effects simulated using DELPHES CMS. These plots show the particle vector properties that were not included in the main results in fig. 5.


Figure 12: Unfolding performance of a single cDDPM on the remaining particle properties (η, ϕ, px, py, pz) for various simulated physics processes with detector effects simulated using an analystical data-driven approach. These plots show the particle vector properties that were not included in the main results in fig. 6.


Table 3: Metrics for evaluating the unfolding performance on datasets with the DELPHES CMS detector simulation. The Wasserstein distance, Energy distance, Wasserstein distance between histograms, and KL divergence between histograms are reported for each observable (pT , η, ϕ, E, px, py, pz) of the unfolded and detector-level datasets, compared to the truth-level dataset.


Authors:

(1) Camila Pazos, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts;

(2) Shuchin Aeron, Department of Electrical and Computer Engineering, Tufts University, Medford, Massachusetts and The NSF AI Institute for Artificial Intelligence and Fundamental Interactions;

(3) Pierre-Hugues Beauchemin, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts and The NSF AI Institute for Artificial Intelligence and Fundamental Interactions;

(4) Vincent Croft, Leiden Institute for Advanced Computer Science LIACS, Leiden University, The Netherlands;

(5) Martin Klassen, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts;

(6) Taritree Wongjirad, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts and The NSF AI Institute for Artificial Intelligence and Fundamental Interactions.


This paper is available on arxiv under CC BY 4.0 DEED license.


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