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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.
Highlights
The tiny neutrino mass is a remaining mystery of the SM
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
We consider a mixture of two supersymmetric Yang-Mills (SYM) theories defined in different dimensions of spacetime to get the strong suppression, especially, we focus on a system consisting of 6D and 10D SYM theories which is well motivated by stable D-brane systems in type IIB superstring theory
Summary
This section gives an overview of magnetized toroidal compactifications on the basis of sixdimensional (6D) SYM theories compactified on a two-dimensional (2D) torus, following ref. [9] (See [11] for a review of magnetized toroidal compactifications). Yukawa couplings of the SM are expected to be given by an overlap integral of the zero-mode wavefunctions of a left-handed matter field, a right-handed matter field and a Higgs field. When their wavefunctions are localized far away from each other on the magnetized torus, a suppressed Yukawa coupling will be obtained. Overlaps of gaussian wavefunctions of the matters and Higgs fields determine the Yukawa couplings, and the gaussians of three generations are localized with a constant interval in the compact space shown as figure 1. Tiny neutrino masses (ν O(1eV)) cannot be obtained with these Yukawa couplings, without heavy Majorana masses for the right-handed neutrinos [6,7,8]. (The masses of the bottom and tau can be realized by using the degree of freedom of tan β ≡ Hu / Hd , where Hu (Hd) represents the up- (down-) type Higgs field.) This paper provides a way to yield the absolutely tiny Yukawa couplings in the magnetized toroidal compactifications, which has a global strong suppression factor
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