The shape of quark flavors
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, 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 𝒪(1) separations in the extra dimensions.
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BibTeX
@misc{kawai2026shape,
title = {{The shape of quark flavors}},
author = {Shinsuke Kawai and Nobuchika Okada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22812},
eprint = {2609.22812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22812},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The shape of quark flavors
AU - Shinsuke Kawai
AU - Nobuchika Okada
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22812
UR - https://arxiv.org/abs/2609.22812
AB - 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 𝒪(1) separations in the extra dimensions.
ER -