Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalizable $A_4$ Model for Lepton Sector   We revisit $A_4$ flavor symmetry for the lepton sector with minimal Higgs
sector, namely just one $A_4-$triplet SU(2)-doublet scalar. To increase
predictivity even further, we impose the constraint of renormalizability. A
geometric interpretation of an $A_4-$triplet aids our understanding of
tribimaximal mixing. To increase predictivity even further, we impose the
constraint of renormalizability. We investigate the neutrino mass hierarchy in
such a minimal $A_4$ model and find there are two solutions: one with $m_2 \gg
m_1 = m_3$ is phenomenologically unacceptable; the other with $m_3 \gg m_1 =
m_2$ is a normal hierarchy. An inverted hierarchy is impossible without
addition of more parameters by either more Higgs scalars or higher-order
irrelevant operators.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph