Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Testing the minimal $S_4$ model of neutrinos with the Dirac and Majorana
  phases   We propose two new simple lepton flavor models in the framework of the $S_4$
flavor symmetry. The neutrino mass matrices, which are given by two complex
parameters, lead to the inverted mass hierarchy. The charged lepton mass matrix
has the 1-2 lepton flavor mixing, which gives the non-vanishing reactor angle
$\theta_{13}$. These models predict the Dirac phase and the Majorana phases,
which are testable in the future experiments. The predicted magnitudes of the
effective neutrino mass for the neutrino-less double beta decay are in the
regions as $32~\text{meV}\lesssim |m_{ee}|\lesssim 49~\text{meV}$ and
$34~\text{meV}\lesssim |m_{ee}|\lesssim 59~\text{meV}$, respectively. These
values are close to the expected reaches of the coming experiments. The total
sum of the neutrino masses are predicted in both models as
$0.0952~\text{eV}\lesssim \sum m_i\lesssim 0.101~\text{eV}$ and
$0.150~\text{eV}\lesssim \sum m_i\lesssim 0.160~\text{eV}$, respectively.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
14
The categories of this paper are: math-ph