640 research outputs found
Lepton masses, mixings and FCNC in a minimal S_3-invariant extension of the Standard Model
The mass matrices of the charged leptons and neutrinos, previously derived in
a minimal S_3-invariant extension of the Standard Model, were reparametrized in
terms of their eigenvalues. We obtained explicit, analytical expressions for
all entries in the neutrino mixing matrix, V_PMNS, the neutrino mixing angles
and the Majorana phases as functions of the masses of charged leptons and
neutrinos in excellent agreement with the latest experimental values. The
resulting V_PMNS matrix is very close to the tri-bimaximal form of the neutrino
mixing matrix. We also derived explicit analytical expressions for the matrices
of the Yukawa couplings and computed the branching ratios of some selected
flavour changing neutral current processes as functions of the masses of the
charged leptons and the neutral Higgs bosons. We find that the S_3 x Z_2
flavour symmetry and the strong mass hierarchy of the charged leptons strongly
suppress the FCNC processes in the leptonic sector well below the present
experimental upper bounds by many orders of magnitude.Comment: One paragraph added with comparison to tri-bimaximal mixing, two
lines changed in abstract, references added, typographical errors correcte
Berry Phase of a Resonant State
We derive closed analytical expressions for the complex Berry phase of an
open quantum system in a state which is a superposition of resonant states and
evolves irreversibly due to the spontaneous decay of the metastable states. The
codimension of an accidental degeneracy of resonances and the geometry of the
energy hypersurfaces close to a crossing of resonances differ significantly
from those of bound states. We discuss some of the consequences of these
differences for the geometric phase factors, such as: Instead of a diabolical
point singularity there is a continuous closed line of singularities formally
equivalent to a continuous distribution of `magnetic' charge on a diabolical
circle; different classes of topologically inequivalent non-trivial closed
paths in parameter space, the topological invariant associated to the sum of
the geometric phases, dilations of the wave function due to the imaginary part
of the Berry phase and others.Comment: 28 pages Latex, three uuencoded postcript figure
Covariant canonical formalism for four-dimensional BF theory
The covariant canonical formalism for four-dimensional BF theory is
performed. The aim of the paper is to understand in the context of the
covariant canonical formalism both the reducibility that some first class
constraints have in Dirac's canonical analysis and also the role that
topological terms play. The analysis includes also the cases when both a
cosmological constant and the second Chern character are added to the pure BF
action. In the case of the BF theory supplemented with the second Chern
character, the presymplectic 3-form is different to the one of the BF theory in
spite of the fact both theories have the same equations of motion while on the
space of solutions they both agree to each other. Moreover, the analysis of the
degenerate directions shows some differences between diffeomorphisms and
internal gauge symmetries.Comment: Latex file, 22 pages (due to the macro). Revised version to match
published versio
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