models-by-amber

Physics models found by AMBer, an autonomous model builder, as described in 2506.08080. Please used the bibtex citation provided below when using models from this repository.

File Format

Model files are txt files containing a json dictionary with the following fields: - "representations": A matrix encoding the representations of all particles under the non-Abelian and Abelian symmetries. There is a sublist for each particle. In each sublist, the non-Abelian symmetry is one-hot encoded, while the Abelian symmetry charge is given directly from 1-N, where N is the order of the Abelian symmetry. - "associations": A list identifying which particles are packed together in multiplets. Using the "particles" index below, those with the same non-zero integer are in the same multiplet. 0 indicates the particle is in a singlet. - "fixedflavonvevs": A list mapping flavons to their VEV alignment (see below) - "nparams": Number of free parameters in the model, referenced as n_p in 2506.08080. - "paramdict": A dictionary where the keys are the free parameters of the model and the values are the best fit values found by AMBer. - "ZNsymmetries": A list of the order of the Abelian symmetries in the model. - "particles": A list identifying the particles in the model, can be used to index the representation matrix. - "effflav": Number or flavons that contribute to the Lagrangian. - "flavonsnotpresent": A list of flavons specified by the model but not contributing to the Lagrangian. - "total_chisq": The chi-squared fit AMBer found for this model, the value used in the reward function in 2506.08080.

Read-in Code

The notebook modeltxtToLatexTable.ipynb converts a model file into latex code that displays the model in a human readable format. This notebook can also serve as an example for how to interact with model files so that a user can write their own model processing code.

non-Abelian Encoding

A4

In the "representations" matrix, the A4 representations are one hot encoded according to: (1, 1', 1", 3)

T19

In the "representations" matrix, the T19 representations are one hot encoded according to: (1, 1', 1", 3₁, 3̅₁, 3₂, 3̅₂, 3₃, 3̅₃)

VEV Alignment Mapping

The "fixedflavonvevs" list indicates the VEV alignment of the flavons, with integers mapping to VEV alignments following: - 1: flavon is in a singlet - 2: (1, 0, 0) - 3: (1, 1, 1) - 4: (0, 1, 0) - 5: (0, 0, 1) - 6: (0, 0, -1) - 7: (1, ω², ω) - 8: (1, ω, ω²)

ω = exp(2πi/3)

Citation

```bibtex @misc{baretz2025aiassistedneutrinoflavortheory, title={Towards AI-assisted Neutrino Flavor Theory Design}, author={Jason Benjamin Baretz and Max Fieg and Vijay Ganesh and Aishik Ghosh and V. Knapp-Perez and Jake Rudolph and Daniel Whiteson}, year={2025}, eprint={2506.08080}, archivePrefix={arXiv}, primaryClass={hep-ph}, url={https://arxiv.org/abs/2506.08080}, }