Seesaw mechanism in magnetic compactifications

In this paper, we explore a new avenue to a natural explanation of the observed tiny neutrino masses with a dynamical realization of the three-generation structure in the neutrino sector. Under the magnetized background based on $T^2/Z_2$, matter consists of multiply-degenerated zero modes and the whole intergenerational structure is dynamically determined. In this sense, we can conclude that our scenario is favored by minimality, where no degree of freedom remains to deform the intergenerational structure by hand freely. Under the consideration of brane-localized Majorana-type mass terms for an $SU(2)_L$ singlet neutrino, it is sufficient to introduce one Higgs doublet for reproducing the observed neutrino data. In all reasonable flux configurations with three right-handed neutrinos, phenomenologically acceptable parameter configurations are found.Comment: 20 pages, 3 figures, 4 tables; published version from JHEP (v2

Class numbers of algebraic number fields of Eisenstein type, II

AbstractLet K be an algebraic number field, of degree n, with a completely ramifying prime p, and let t be a common divisor of n and (p − 1)2. Then it is proved that if K does not contain the unique subfield, of degree t, of the p-th cyclotomic number field, then we have (hK, n) > 1, where hK is the class number of K. As applications, we give several results on hK of such algebraic number fields K

Vitrectomy combined with glial tissue removal at the optic pit in a patient with optic disc pit maculopathy: a case report

<p>Abstract</p> <p>Introduction</p> <p>We present a case of a man with optic disc pit maculopathy, whose vision improved after vitrectomy combined with glial tissue removal from the optic pit area, and without the use of photocoagulation.</p> <p>Case presentation</p> <p>A 45-year-old man complained of blurred vision, and ophthalmoscopy revealed a retinal detachment and retinoschisis extending from an optic disc pit through the macula in his left eye. He was diagnosed with optic disc pit maculopathy, and vitrectomy was performed. A posterior vitreous detachment was created, glial tissue at the optic pit was removed, and octafluoropropane (C₃F₈) was injected as a gas tamponade. The retinal detachment and retinoschisis disappeared after six months, and vision improved to 20/20 without any visual field defects (Goldmann perimetry). A cataractous lens was extracted 2 years after the vitrectomy, and vision has remained 20/20 for 10 years without any recurrence.</p> <p>Conclusion</p> <p>The removal of glial tissue during vitrectomy may be beneficial in patients with optic disc pit maculopathy.</p

Effects of localized {\mu}-terms at the fixed points in magnetized orbifold models

We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called $\mu$-term, is localized at the orbifold fixed points, and study the effects on the zero-mode spectra. The zero-mode degeneracy to be identified as the generation in four-dimensional (4D) effective theories is determined by the magnetic fluxes. It is known that multiple Higgs zero-modes appear in general in magnetized orbifold models. We derive the analytic form of the $\mu$-term matrix in the 4D effective theory generated by the localized sources on $T^2/Z_2$ orbifold fixed points, and find that this matrix can lead to a distinctive pattern of the eigenvalues that yields hierarchical $\mu$-terms for the multiple Higgs fields. The lightest ones can be exponentially suppressed due to the localized wavefunctions of zero-modes determined by the fluxes, while the others are of the order of the compactification scale, which can provide a dynamical origin of the electroweak scale as well as a simultaneous decoupling of extra Higgs fields. We also show that a certain linear combination of the lightest Higgs fields could generate the observed mass ratios of down-type quarks through their Yukawa couplings determined by the wavefunctions.Comment: 23 pages, 4 figures, 7 table