Showing papers by "W. G. Scott published in 2018"
TL;DR: In this article, a Majorana neutrino mass matrix (a symmetric symmetric matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of the discrete group, and specific vacuum alignments of the flavons are used to obtain the desired mass matrices.
Abstract: In 2002, two neutrino mixing ansatze having trimaximally mixed middle (
$$
u _2$$
) columns, namely tri-chi-maximal mixing (
$$\text {T}\chi \text {M}$$
) and tri-phi-maximal mixing (
$$\text {T}\phi \text {M}$$
), were proposed. In 2012, it was shown that $$\text {T}\chi \text {M}$$
with $$\chi =\pm \,\frac{\pi }{16}$$
as well as $$\text {T}\phi \text {M}$$
with $$\phi = \pm \,\frac{\pi }{16}$$
leads to the solution, $$\sin ^2 \theta _{13} = \frac{2}{3} \sin ^2 \frac{\pi }{16}$$
, consistent with the latest measurements of the reactor mixing angle, $$\theta _{13}$$
. To obtain $$\text {T}\chi \text {M}_{(\chi =\pm \,\frac{\pi }{16})}$$
and $$\text {T}\phi \text {M}_{(\phi =\pm \,\frac{\pi }{16})}$$
, the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, $$m_1:m_2:m_3=\frac{\left( 2+\sqrt{2}\right) }{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left( 2+\sqrt{2}\right) }{-1+\sqrt{2(2+\sqrt{2})}}$$
. In this paper we construct a flavour model based on the discrete group $$\varSigma (72\times 3)$$
and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric $$3\times 3$$
matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of $$\varSigma (72\times 3)$$
. Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.
5 citations
TL;DR: In this paper, the authors constructed a flavour model based on the discrete group of the Majorana neutrino mass matrices and obtained the aforementioned results, where the type~I see-saw framework was used to obtain the desired mass matrix.
Abstract: In 2002, two neutrino mixing ansatze having trimaximally-mixed middle ($
u_2$) columns, namely tri-chi-maximal mixing ($\text{T}\chi\text{M}$) and tri-phi-maximal mixing ($\text{T}\phi\text{M}$), were proposed. In 2012, it was shown that $\text{T}\chi\text{M}$ with $\chi=\pm \frac{\pi}{16}$ as well as $\text{T}\phi\text{M}$ with $\phi = \pm \frac{\pi}{16}$ leads to the solution, $\sin^2 \theta_{13} = \frac{2}{3} \sin^2 \frac{\pi}{16}$, consistent with the latest measurements of the reactor mixing angle, $\theta_{13}$. To obtain $\text{T}\chi\text{M}_{(\chi=\pm \frac{\pi}{16})}$ and $\text{T}\phi\text{M}_{(\phi=\pm \frac{\pi}{16})}$, the type~I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, $m_1:m_2:m_3=\frac{\left(2+\sqrt{2}\right)}{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left(2+\sqrt{2}\right)}{-1+\sqrt{2(2+\sqrt{2})}}$. In this paper we construct a flavour model based on the discrete group $\Sigma(72\times 3)$ and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric $3\times 3$ matrix with 6 complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex 6 dimensional representation of $\Sigma(72\times 3)$. Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.
4 citations