Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermion masses and mixings in a $U(1)_X$ model based on the $\Sigma(18)$
  discrete symmetry   We have built a renormalizable $U(1)_X$ model with a $\Sigma (18)\times Z_4$
symmetry, whose spontaneous breaking yields the observed SM fermion masses and
fermionic mixing parameters. The tiny masses of the light active neutrinos are
produced by the type I seesaw mechanism mediated by very heavy right handed
Majorana neutrinos. To the best of our knowledge, this model is the first
implementation of the $\Sigma (18)$ flavor symmetry in a renormalizable
$U(1)_X$ model. Our model allows a successful fit for the SM fermion masses,
fermionic mixing angles and CP phases for both quark and lepton sectors. The
obtained values for the physical observables of both quark and lepton sectors
are in accordance with the experimental data. We obtain an effective neutrino
mass parameter of $\langle m_{ee}\rangle=1.51\times 10^{-3}\, \mathrm{eV}$ for
normal ordering and $\langle m_{ee}\rangle =4.88\times 10^{-2} \, \mathrm{eV}$
for inverted ordering which are well consistent with the recent experimental
limits on neutrinoless double beta decay.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ