Exploring Scotogenic Parameter Spaces and Mapping Uncharted Dark Matter Phenomenology with Multi-Objective Search Algorithms

TL;DR

The paper tackles the challenge of scanning highly constrained Beyond-Standard-Model spaces by deploying a multi-objective NSGA-III search alongside CMA-ES, applied to a non-minimal scotogenic model with DM, neutrino masses, and LFV constraints. It shows that multi-objective optimisation yields a richer set of viable solutions and, when augmented by novelty detection, maps novel dark matter realizations near LZ bounds and near the neutrino floor. The authors demonstrate substantial phenomenological diversification, including fermionic and pseudoscalar DM, and provide insights into LHC phenomenology across parameter regions, surpassing previous MCMC studies. The methodological advances—constraint hierarchy, multi- vs single-objective comparison, and novelty-driven exploration—offer a powerful framework for constrained BSM explorations and potential SMEFT applications.

Abstract

We present a novel artificial intelligence approach to explore beyond Standard Model parameter spaces by leveraging a multi-objective optimisation algorithm. We apply this methodology to a non-minimal scotogenic model which is constrained by Higgs mass, anomalous magnetic moment of the muon, dark matter relic density, dark matter direct detection, neutrino masses and mixing, and lepton flavour violating processes. Our results successfully expand on the phenomenological realisations presented in previous work. We compare between multi- and single-objective algorithms and we observe more phenomenologically diverse solutions and an improved search capacity coming from the former. We use novelty detection to further explore sparsely populated regions of phenomenological interest. These results suggest a powerful search strategy that combines the global exploration of multi-objective optimisation with the exploitation of single-objective optimisation.

Figures (20)

• Figure 1: Feynman diagrams depicting the main contributions to the anomalous magnetic moment of the muon (when $i=j=2$) and LFV decays (when $i>j$). Diagram on the left is $\sim \alpha \space g_{\Psi} \space g_R$ while diagram on the right is $\sim y_{1} \space g_F \space g_R$. The $V$ boson line represents the couplings to the $SU(2)_L\times U(1)_Y$ gauge bosons.
• Figure 2: Illustration depicting the scheme for constructing the reference directions ($r_i$, as blue lines) from the reference points (red points) in NSGA-III, and how points in the constraint space ($p_i$, as green) are assigned to a reference direction.
• Figure 3: Absolute values for the components of the couplings $g_{F_1}$ (upper left and upper right) and $g_{\Psi}$ (lower left and lower right) resulting from h-CMA-ES (left) and h-CMA-ES-CI (right) scans. The box shows the region which encompasses the distribution obtained from MCMC in Alvarez:2023dzz.
• Figure 4: Absolute values for the components of the couplings $g_{F_1}$ (upper left and upper right) and $g_{\Psi}$ (lower left and lower right) resulting from h-NSGA-III (left) and h-NSGA-III-CI (right) scans. The box shows the region which encompasses distribution obtained from MCMC in Alvarez:2023dzz.
• Figure 5: Trilinear coupling correlation with absolute values for the second component of the couplings $g_{\Psi}$ and $g_R$ (upper left and upper right) and the absolute value of $g_{\Psi}$ and $g_{F_1}$ couplings (lower left and lower right) resulting from h-NSGA-III (left) and h-NSGA-III-CI (right) scans. The box show region which encompass distribution obtained from MCMC in Alvarez:2023dzz.