On the efficiency of parameter space exploration: A scotogenic case study

TL;DR

This paper tackles the problem of efficiently scanning multi-dimensional parameter spaces in scotogenic beyond-Standard Model scenarios by directly comparing Markov Chain Monte Carlo (MCMC) and Deep Neural Network (DNN)–based Active Learning approaches. Both methods are applied to two scotogenic frameworks (T1-2G and T1-2B ext.) that generate radiative neutrino masses and host dark matter candidates, with constraints from Higgs physics, relic density, LFV, EDMs, and (in the G case) anomalous magnetic moments. The study finds broadly compatible phenomenology between MCMC and DNN analyses, though the resulting observable distributions—such as the dark matter mass spectra—differ due to the distinct optimization goals of each method (likelihood maximization vs. boundary mapping). In terms of performance, MCMC delivers higher efficiency in accepting points and faster overall computation, while the DNN/AL approach explores more of the parameter space and efficiently maps viable boundaries, suggesting future enhancements like GAN-based point generation for even faster space exploration. The results illustrate that scotogenic frameworks can accommodate viable fermionic dark matter near current/future experimental reach, highlighting co-annihilation as a key mechanism for relic density and guiding experimental prospects in direct detection and LFV measurements.

Abstract

A common problem in beyond Standard Model phenomenology is the exploration of a multi-dimensional parameter space in view of a large number of constraints. We study and compare two methods applicable to this challenge, namely a Markov Chain Monte Carlo scan (MCMC) and a Deep Neural Network (DNN). We illustrate both methods via their application to different scotogenic frameworks, allowing to extend the Standard Model to include viable dark matter candidates while generating neutrino mass terms at the one-loop level. Our studies allow us to compare the two employed methods, both at the level of phenomenology and at the level of computing effort. We find that, while phenomenologically speaking both methods deliver compatible conclusions, the obtained datasets feature differences at the detail level in the distributions of observables, e.g. the dark matter mass.

Figures (11)

• Figure 1: Radiative generation of neutrino masses within the a scotogenic model, depicted in the interaction basis. Here, $\psi$ is a generic notation for a fermionic field (singlet $F$, doublet $\Psi$, or triplet $\Sigma$), while $\phi$ is a generic notation for a scalar field (singlet $S$, doublet $\eta$, or triplet $\Delta$).
• Figure 2: Schematic representation of our DNN architecture. Each layer is a dense layer, fully connected and feed forward.
• Figure 3: Schema showing the Active Learning process. The input data, of size $K$, are both given to the Discriminator (DNN) and the Oracle (SPheno and MicrOMEGAs). Based on the output we take $pK$ fully randomly and $(1-p)K$ near precedent good points based on a scoring methods.
• Figure 4: A simple flowchart illustrating the AL pipeline for "T1-2G" model and "T1-2B ext." model.
• Figure 5: Histograms of the DM masses obtained from the DNN analysis, within the "T1-2G" model. The colour code indicates the DM nature in terms of fermionic doublet or triplet domination.