Quasi-localized wavefunctions on magnetized tori and tiny neutrino Yukawa couplings

TL;DR

This paper demonstrates how quasi-localized wavefunctions in magnetized tori can generate highly suppressed Yukawa couplings, providing a natural mechanism for tiny neutrino masses without fine-tuning.

Contribution

It introduces a novel method to induce an extremely small global factor in Yukawa matrices through wavefunction overlaps in magnetized SYM theories, enabling tiny neutrino masses.

Findings

Suppression factors can be strong enough to produce tiny neutrino masses.

Wavefunction overlaps in different dimensions lead to variable Yukawa coupling magnitudes.

A concrete model for tiny neutrino Yukawa couplings is proposed.

Abstract

This paper shows that, a quasi-localization of wavefunctions in toroidal compactifications with magnetic fluxes can lead to a strong suppression for relevant Yukawa couplings, and it is applicable to obtain tiny neutrino masses. Although it is known that magnetic fluxes lead to a Gaussian profile of zero-modes on a torus and that can yield a suppressed coupling in higher-dimensional supersymmetric Yang-Mills (SYM) theories, the largest (diagonal) entry of Yukawa matrices is always of $\mathcal O(1)$. In this paper, we propose a way to induce an absolutely tiny global factor of Yukawa matrices. In two SYM theories defined in different dimensional spacetime, their bifundamental representations must be localized as a point in some directions. Overlaps of such point-like localized wavefunctions and Gaussian zero-modes give a global factor of Yukawa matrices, and it can be a strong suppression factor or a usual $\mathcal O(1)$ factor, corresponding to their distance. Our numerical analysis shows that it is possible to obtain a suppression strong enough to realize the tiny neutrino masses without a hard fine-tuning. Furthermore, we propose a concrete model of the tiny neutrino Yukawa couplings in a magnetized SYM system.