20 research outputs found
Sweeping the Space of Admissible Quark Mass Matrices
We propose a new and efficient method of reconstructing quark mass matrices
from their eigenvalues and a complete set of mixing observables. By a
combination of the principle of NNI (nearest neighbour interaction) bases which
are known to cover the general case, and of the polar decomposition theorem
that allows to convert arbitrary nonsingular matrices to triangular form, we
achieve a parameterization where the remaining freedom is reduced to one
complex parameter. While this parameter runs through the domain bounded by a
circle with radius R determined by the up-quark masses around the origin in the
complex plane one sweeps the space of all mass matrices compatible with the
given set of data.Comment: 18 page
Leptonic Generation Mixing, Noncommutative Geometry and Solar Neutrino Fluxes
Triangular mass matrices for neutrinos and their charged partners contain
full information on neutrino mixing in a most concise form. Although the scheme
is general and model independent, triangular matrices are typical for reducible
but indecomposable representations of graded Lie algebras which, in turn, are
characteristic for the standard model in noncommutative geometry. The mixing
matrix responsible for neutrino oscillations is worked out analytically for two
and three lepton families. The example of two families fixes the mixing angle
to just about what is required by the Mikheyev-Smirnov-Wolfenstein resonance
oscillation of solar neutrinos. In the case of three families we classify all
physically plausible choices for the neutrino mass matrix and derive
interesting bounds on some of the moduli of the mixing matrix.Comment: LaTeX, 12 page
Physical renormalization condition for the quark-mixing matrix
We investigate the renormalization of the quark-mixing matrix in the
Electroweak Standard Model. We show that the corresponding counterterms must be
gauge independent as a consequence of extended BRS invariance. Using rigid
SU(2)_L symmetry, we proof that the ultraviolet-divergent parts of the
invariant counterterms are related to the field renormalization constants of
the quark fields. We point out that for a general class of renormalization
schemes rigid SU(2)_L symmetry cannot be preserved in its classical form, but
is renormalized by finite counterterms. Finally, we discuss a genuine physical
renormalization condition for the quark-mixing matrix that is gauge independent
and does not destroy the symmetry between quark generations.Comment: 20 pages, LaTeX, minor changes, references adde
Bimaximal mixing from the leptonic new texture for triangular mass matrices
An analysis of the leptonic texture for the new triangular mass matrices has
been carried out. In particular, it is shown that both bimaximal and nearly
bimaximal solutions for solar and atmospheric neutrino anomalies can be
generated within this pattern. We have also derived exact and compact
parametrization of the leptonic mixing matrix in terms of the lepton masses and
the parameters and . A consistency with the CHOOZ
reactor result for and a smallness of the Jarlskog's invariant
parameter are obtained.Comment: 16 pages, late
Width and Partial Widths of Unstable Particles in the Light of the Nielsen Identities
Fundamental properties of unstable particles, including mass, width, and
partial widths, are examined on the basis of the Nielsen identities (NI) that
describe the gauge dependence of Green functions. In particular, we prove that
the pole residues and associated definitions of branching ratios and partial
widths are gauge independent to all orders. A simpler, previously discussed
definition of branching ratios and partial widths is found to be gauge
independent through next-to-next-to-leading order. It is then explained how it
may be modified in order to extend the gauge independence to all orders. We
also show that the physical scattering amplitude is the most general
combination of self-energy, vertex, and box contributions that is gauge
independent for arbitrary s, discuss the analytical properties of the NI
functions, and exhibit explicitly their one-loop expressions in the Z-gamma
sector of the Standard Model.Comment: 20 pages (Latex); minor changes included, accepted for publication in
Phys. Rev.
A Grassmann integral equation
The present study introduces and investigates a new type of equation which is
called Grassmann integral equation in analogy to integral equations studied in
real analysis. A Grassmann integral equation is an equation which involves
Grassmann integrations and which is to be obeyed by an unknown function over a
(finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann
integral equations is explicitly studied for certain low-dimensional Grassmann
algebras. The choice of the equation under investigation is motivated by the
effective action formalism of (lattice) quantum field theory. In a very general
setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional
analogues of the generating functionals of the Green functions are worked out
explicitly by solving a coupled system of nonlinear matrix equations. Finally,
by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi},
{\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the
generators of the Grassmann algebra G_2n), between the finite-dimensional
analogues G_0 and G of the (``classical'') action and effective action
functionals, respectively, a special Grassmann integral equation is being
established and solved which also is equivalent to a coupled system of
nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann
integral equation exist for n=2 (and consequently, also for any even value of
n, specifically, for n=4) but not for n=3. If \lambda=1, the considered
Grassmann integral equation has always a solution which corresponds to a
Gaussian integral, but remarkably in the case n=4 a further solution is found
which corresponds to a non-Gaussian integral. The investigation sheds light on
the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the
reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54],
[61], [64], [139] added