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

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.