Two Flavon Froggatt-Nielsen Models with Genetic Algorithms

High Energy Physics - Phenomenology [Submitted on 18 Jun 2026] Title:Two Flavon Froggatt-Nielsen Models with Genetic Algorithms View PDF HTML (experimental)Abstract:We present the first systematic and comprehensive scan of two-flavon Froggatt-Nielsen (FN) models, employing artificial intelligence techniques to explore the high-dimensional, mixed discrete-continuous parameter space. Extending the standard single-flavon FN framework to a two-flavon setup in which separate flavon fields couple independently to the up- and down-type sectors, we demonstrate that the relative phase between their vacuum expectation values (vevs) provides a natural and generic source of CP violation absent in single-flavon models. To explore this enlarged model space, we cast the search for phenomenologically viable models as a multi-objective optimisation problem, formulating each experimental constraint as a separate objective, and employ the Non-dominated Sorting Genetic Algorithm III to simultaneously fit all 18 FN charges, 45 Wilson coefficients, and flavon parameters to both the quark and lepton sectors. Our approach requires no separate training phase and identifies phenomenologically viable models orders of magnitude faster than prior reinforcement learning methods. Imposing experimental constraints on CKM and PMNS mixing angles and CP phases, charged fermion masses, and neutrino squared-mass differences, we discover over $100\,000$ unique viable models with a remarkably low duplication rate, indicating that the space of valid two-flavon FN realisations has not been exhausted. Both Normal and Inverted neutrino mass squared orderings are realised, with the relative hierarchy between the flavon vevs producing qualitatively distinct predictions for the effective neutrinoless double beta decay mass $m_{ee}$. We further demonstrate the existence of minimal FN realisations with maximal flavon exponent as small as three, and of models reproducing charged fermion masses to within $6\%$ without any dedicated continuous parameter optimisation. Submission history From: Miguel Crispim Romão [view email][v1] Thu, 18 Jun 2026 09:35:38 UTC (6,042 KB) Current browse context: hep-ph Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.