Quark and Lepton Masses from Gaussian Landscapes

TL;DR

A class of simple models, "Gaussian landscapes," where Yukawa couplings derive from overlap integrals of Gaussian wave functions on extra-dimensions are proposed, where Gaussian landscapes can account for all observed flavor patterns with few free parameters.

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.

Figures (1)

• Figure 1: Distributions of observables in the $S^1$ Gaussian landscape. The width parameters are set at $d_h = d_{\bf 10} = d_{\bar{\nu}} = d_\phi = 0.08 L$ and $d_{\bar{\bf 5}} = 0.3 L$, and we use $r=3$ and $g=0.2$. Numbers in brackets are the experimentally measured values (or limits), with the leading renormalization effects up to the Planck scale partially taken into account. All logarithms are base ten.