Quark and Lepton Masses from Gaussian Landscapes

TL;DR

This paper introduces Gaussian landscapes, a model where Yukawa couplings originate from overlap integrals of Gaussian wavefunctions in extra dimensions, explaining flavor structures with minimal parameters.

Contribution

It proposes a simple, statistical framework for flavor hierarchies in the Standard Model using Gaussian landscapes, connecting extra-dimensional wavefunctions to observed flavor patterns.

Findings

Broad probability distributions for flavor observables

Correlations among flavor parameters sharpen predictions

Model accounts for quark and neutrino flavor structures

Abstract

The flavor structure of the Standard Model might arise from random selection on a landscape. We propose a class of simple models, ``Gaussian landscapes,'' where Yukawa couplings derive from overlap integrals of Gaussian wavefunctions on extra-dimensions. Statistics of vacua are generated by scanning the peak positions of these zero-modes, giving probability distributions for all flavor observables. Gaussian landscapes can broadly account for all observed flavor patterns with very few free parameters. For example, the generation structure in the quark sector follows from the overlap integrals for both the up and down type Yukawas sharing the localized wavefunctions of the quark doublets and the Higgs boson. Although Gaussian landscapes predict broad probability distributions, the flavor observables are correlated and we show that accounting for measured flavor parameters creates sharper distributions for future neutrino measurements.