# The shape of quark flavors

arXiv: https://arxiv.org/abs/2609.22812 · HTML: https://mlsanity.com/paper/2609.22812/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 14 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Truth, beauty, and goodness in grand unification: a machine learning approach](https://mlsanity.com/paper/2411.06718/) (2024)
- [Good flavor search in SU(5): a machine learning approach](https://mlsanity.com/paper/2511.08154/) (2025)

## Abstract (arXiv)

We construct the Yukawa couplings of the quark sector as overlap integrals of Gaussian wave functions in extra spatial dimensions. Assuming that the wave function of each chiral fermion is localised at a point in the extra dimensions, while that of the Higgs doublet is flat, the Yukawa matrix elements are determined by the relative positions of the three left-handed quark doublets, q1, q2, q3, and the six right-handed quark singlets, u1, u2, u3, d1, d2, d3. We employ numerical optimisation techniques from machine learning to identify field configurations that satisfy all current experimental constraints on the quark Yukawa sector. In this framework, the large hierarchy of quark masses arises naturally, since the overlap integrals of Gaussian wave functions are exponentially sensitive to mathcal O(1) separations in the extra dimensions.