12,308 research outputs found
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
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
Solutions of the Ginsparg-Wilson Relation
We analyze general solutions of the Ginsparg-Wilson relation for lattice
Dirac operators and formulate a necessary condition for such operators to have
non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13
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