15,429 research outputs found
Topological Phases in Neuberger-Dirac operator
The response of the Neuberger-Dirac fermion operator D=\Id + V in the
topologically nontrivial background gauge field depends on the negative mass
parameter in the Wilson-Dirac fermion operator which enters
through the unitary operator . We classify
the topological phases of by comparing its index to the topological charge
of the smooth background gauge field. An exact discrete symmetry in the
topological phase diagram is proved for any gauge configurations. A formula for
the index of D in each topological phase is derived by obtaining the total
chiral charge of the zero modes in the exact solution of the free fermion
propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise
Flavor Mixing and the Permutation Symmetry among Generations
In the standard model, the permutation symmetry among the three generations
of fundamental fermions is usually regarded to be broken by the Higgs
couplings. It is found that the symmetry is restored if we include the mass
matrix parameters as physical variables which transform appropriately under the
symmetry operation. Known relations between these variables, such as the
renormalization group equations, as well as formulas for neutrino oscillations
(in vacuum and in matter), are shown to be covariant tensor equations under the
permutation symmetry group.Comment: 12 page
Rephasing invariance and neutrino mixing
A rephasing invariant parametrization is introduced for three flavor neutrino
mixing. For neutrino propagation in matter, these parameters are shown to obey
evolution equations as functions of the induced neutrino mass. These equations
are found to preserve (approximately) some characteristic features of the
mixing matrix, resulting in solutions which exhibit striking patterns as the
induced mass varies. The approximate solutions are compared to numerical
integrations and found to be quite accurate.Comment: 18 pages, 6 figure
Renormalization of the Neutrino Mass Matrix
In terms of a rephasing invariant parametrization, the set of renormalization
group equations (RGE) for Dirac neutrino parameters can be cast in a compact
and simple form. These equations exhibit manifest symmetry under flavor
permutations. We obtain both exact and approximate RGE invariants, in addition
to some approximate solutions and examples of numerical solutions.Comment: 15 pages, 1figur
Properties of the Neutrino Mixing Matrix
For neutrino mixing we propose to use the parameter set
and , with two constraints. These parameters are directly measurable since
the neutrino oscillation probabilities are quadratic functions of them.
Physically, the set signifies a quantitative measure of
asymmetry. Available neutrino data indicate that all the 's are
small , but with large uncertainties. The behavior of
as functions of the induced neutrino mass in matter are found to
be simple, which should facilitate the analyses of long baseline experiments.Comment: 14 pages, 5 figure
Rephasing invariance and the neutrino mu-tau symmetry
The vacuum neutrino mixing is known to exhibit an approximate
symmetry, which was shown to be preserved for neutrino propagating in matter.
This symmetry reduces the neutrino transition probabilities to very simple
forms when expressed in a rephasing invariant parametrization introduced
earlier. Applications to long baseline experiments are discussed.Comment: 12 pages, 4 figure
Signatures of the neutrino mass hierarchy in supernova neutrinos
The undetermined neutrino mass hierarchy may leave an observable imprint on
the neutrino fluxes from a core-collapse supernova (SN). The interpretation of
the observables, however, is subject to the uncertain SN models and the flavor
conversion mechanism of neutrinos in a SN. We attempt to propose a qualitative
interpretation of the expected neutrino events at terrestrial detectors,
focusing on the accretion phase of the neutrino burst. The flavor conversions
due to neutrino self-interaction, the MSW effect, and the Earth regeneration
effect are incorporated in the calculation. It leads to several distinct
scenarios that are identified by the neutrino mass hierarchies and the
collective flavor transitions. Consequences resulting from the variation of
incident angles and SN models are also discussed.Comment: 15 pages, 9 figure
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