12,965 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
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
Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator
A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac
operator does not possess any topological zero modes in
topologically-nontrivial gauge backgrounds, it can reproduce correct axial
anomaly for sufficiently smooth gauge configurations, provided that it is
exponentially-local, doublers-free, and has correct continuum behavior. In this
paper, we calculate the axial anomaly of this lattice Dirac operator in weak
coupling perturbation theory, and show that it recovers the topological charge
density in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge
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Quark Mass Matrices with Four and Five Texture Zeroes, and the CKM Matrix, in terms of Mass Eigenvalues
Using the triangular matrix techniques of Kuo et al and Chiu et al for the
four and five texture zero cases, with vanishing (11) elements for U and D
matrices, it is shown, from the general eigenvalue equations and hierarchy
conditions, that the quark mass matrices, and the CKM matrix can be expressed
(except for the phases) entirely in terms of quark masses. The matrix
structures are then quite simple and transparent. We confirm their results for
the five texture zero case but find, upon closer examination of all the CKM
elements which our results provide, that six of their nine patterns for the
four texture zero case are not compatible with experiments. In total, only one
five-texture zero and three four-texture zero patterns are allowed.Comment: 15 pages, 3 table
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