'Deep' Dive into $b \to c$ Anomalies: Standardized and Future-proof Model Selection Using Self-normalizing Neural Networks

TL;DR

This paper introduces the use of self-normalizing neural networks for model selection in $b o c au u_{ au}$ decays, demonstrating superior performance over traditional AIC and Bayesian methods, and providing tools for future analyses.

Contribution

It applies self-normalizing neural networks to model selection in particle physics decays, offering a standardized, robust, and future-proof approach that outperforms traditional criteria.

Findings

SNNs outperform AICc in model selection accuracy.

Parameter spaces differ significantly from Bayesian analyses.

Two-operator tensor scenarios are most probable for the data.

Abstract

Noting the erroneous proclivity of information-theoretic approaches, like the Akaike information criterion (AIC), to select simpler models while performing model selection with a small sample size, we address the problem of new physics model selection in $b\to c \tau \nu_{\tau}$ decays in this paper by employing a specific machine learning algorithm (self-normalizing neural networks, a.k.a. SNN) for supervised classification and regression, in a model-independent framework. While the outcomes of the classification with real data-set are compared with AIC, with the SNNs outperforming AIC$_c$ in all aspects of model selection, the regression-outcomes are compared with the results from Bayesian analyses; the obtained parameter spaces differ considerably while keeping maximum posterior (MAP) estimates similar. A few of the two-operator scenarios with a tensor-type interaction are found to be the most probable solution for the data. We also test the effectiveness of our trained networks with the expected, more precise data in Belle-II. The trained networks and associated functionalities are supplied for the use of the community.