Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractionalized time reversal, parity and charge conjugation symmetry in
  topological superconductor: a possible origin of three generations of
  neutrinos and mass mixing   The existence of three generations of neutrinos(charged leptons/quarks) and
their mass mixing are deep mysteries of our universe. Recently, Majorana's
spirit returns in modern condensed matter physics -- in the context of
topological Majorana zero modes in certain classes of topological
superconductors(TSCs). In this paper, we attempt to investigate the topological
nature of the neutrino by assuming that a relativistic Majorana fermion can be
divided into four topological Majorana zero modes at cutoff energy scale, e.g.
planck scale. We begin with an exactly solvable $1$D lattice model which
realizes a $T^2=-1$ time reversal symmetry protected TSC, and show that a pair
of topological Majorana zero modes can realize a $T^4=-1$ time reversal
symmetry.Moreover, we find that a pair of topological Majorana zero modes can
also realize a $P^4=-1$ parity symmetry and even a nontrivial $\overline
C^4=-1$ charge conjugation symmetry. Next, we argue that the origin of three
generations of neutrinos(charged leptons and quarks) can be naturally explained
as three distinguishable ways of forming a pair of complex fermions(with
opposite spin polarizations) out of four topological Majorana zero modes,
characterized by the $T^4=-1$, $(TP)^4=-1$ and $(T \overline C)^4=-1$
fractionalized symmetries that each complex fermion carries at cutoff energy
scale. Finally, we use a semiclassical approach to compute the neutrino mass
mixing matrix at leading order(LO), e.g., in the absence of $CP$ violation
correction. We obtain $\theta_{12}=31.7^\circ, \theta_{23}=45^\circ$ and
$\theta_{13}=0^\circ$(the golden ratio pattern), which is consistent with an
$A_5$ flavor symmetry pattern. We further predict an exact mass ratio of the
three mass eigenstates of neutrinos with $m_1/m_3=m_2/m_3=3/\sqrt{5}$ and an
effective mass of neutrinoless double beta decay
$m_{0\nu\beta\beta}=m_1/\sqrt{5}$.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph