Quark flavor shapes explained by extra dimensional wave overlaps
The shape of quark flavors
Machine Learning
Summary
Scientists studied why quarks, the tiny building blocks of matter, have different masses. They proposed that these differences come from how quark particles are positioned in tiny hidden dimensions beyond our usual space. By treating each quark’s presence as a small Gaussian bump and the Higgs field as uniform, the overlap of these bumps in extra space determines interaction strengths, explaining mass differences naturally. They used machine learning to find quark arrangements that match observed particle behaviors.
What this means in practice
- •For particle physicists: Model quark mass hierarchies using spatial wave localization in extra dimensions to inform new physics theories.
- •For machine learning engineers: Use numerical optimization techniques inspired by this framework to solve complex parameter arrangement problems in high-dimensional spaces.
Authors
Shinsuke Kawai, Nobuchika Okada
Abstract
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, $q_1$, $q_2$, $q_3$, and the six right-handed quark singlets, $u_1$, $u_2$, $u_3$, $d_1$, $d_2$, $d_3$. 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.