Neutrino oscillations in the scheme of mass mixings and problem of smallness of angle mixing $\theta_{1 3}$

TL;DR

This paper explores neutrino oscillations within a mass mixing framework, suggesting that the smallness of the mixing angle θ13 may be due to a more complex mass structure, and that θ13 could be larger than traditionally thought.

Contribution

It introduces a mass mixing scheme allowing for different oscillation lengths, proposing that θ13 need not be very small and can be larger if neutrino mass differences are more complex.

Findings

Oscillation lengths L23 and L13 are not necessarily equal.

θ13 can be larger than traditionally assumed.

Different neutrino mass difference relations can explain the smallness of θ13.

Abstract

In the framework of the mass mixing scheme we have considered mixings and oscillations of $\nu_e, \nu_\mu, \nu_\tau$ neutrinos and obtained expressions for angle mixings and lengths of oscillations in dependence on components of the nondiagonal mass matrix. Then analysis of these obtained results was done by using modern experimental data on neutrino oscillations. It has been shown that in this approach the lengths of neutrino oscillations $L_{2 3}$ and $L_{1 3}$ are not compulsory to be equal. It means that the angle mixing $\theta_{1 3}$ can be not very small, i.e., $L_{1 3}$ can be larger than $L_{2 3}$. In the conventional approach $L_{1 3} \approx L_{2 3}$ ($L_{1 2} \gg L_{2 3}$) and angle mixing of $\theta_{1 3}$ is very small. Angle mixings $\theta_{2 3}, \theta_{1 2}$ are big. Then there ia a problem: why is mixing angle $\theta_{1 3}$ so small? A natural solution of the problem is to suppose that $(m_2^2 - m_1^2) \neq (m_3^2 - m_1^2) - (m_3^2 - m_2^2)$, then $L_{1 3} > L_{2 3}$. It will be realized if there are 4 neutrino oscillations instead of 3 neutrino oscillations. Then the value of $\theta_{1 3}$ is necessary to search at distances more than $L_{2 3}$.