56 research outputs found
Renormalization group evolution of the CKM matrix
We present here the most important ideas, equations and solutions for the
running of all the quark Yukawa couplings and all the elements of the
Cabibbo-Kobayashi-Maskawa matrix, in the approximation of one loop, and up to
order , where is the sine of the Cabibbo
angle. Our purpose is to determine what the evolution of these parameters may
indicate for the physics of the standard model (SM), the minimal supersymmetric
standard model (MSSM) and for the Double Higgs Model (DHM).Comment: Talk given in the X Mexican School of Particles and Fields, Playa del
Carmen, Mexico, 2002. 6 pages, LaTeX, needs aipproc.cls styl
Quark mixings as a test of a new symmetry of quark Yukawa couplings
Based on the hierarchy exhibited by quarks masses at low energies, we assume
that Yukawa couplings of up and down quarks are related by
at grand unification scales. This ansatz gives rise to a symmetrical CKM matrix
at the grand unification (GU) scale. Using three specific models as
illustrative examples for the evolution down to low energies, we obtain the
entries and asymmetries of the CKM matrix which are in very good agreement with
their measured values. This indicates that the small asymmetry of the CKM
matrix at low energies may be the effect of the renormalization group evolution
only.Comment: LaTeX file, 10 pages including 1 tabl
Renormalization Group Equations for the CKM matrix
We derive the one loop renormalization group equations for the
Cabibbo-Kobayashi-Maskawa matrix for the Standard Model, its two Higgs
extension and the minimal supersymmetric extension in a novel way. The derived
equations depend only on a subset of the model parameters of the
renormalization group equations for the quark Yukawa couplings so the CKM
matrix evolution cannot fully test the renormalization group evolution of the
quark Yukawa couplings. From the derived equations we obtain the invariant of
the renormalization group evolution for three models which is the angle
of the unitarity triangle. For the special case of the Standard Model
and its extensions with we demonstrate that also the shape
of the unitarity triangle and the Buras-Wolfenstein parameters
and
are conserved. The invariance of the angles of the unitarity triangle means
that it is not possible to find a model in which the CKM matrix might have a
simple, special form at asymptotic energies.Comment: 9 page
Energy dependence of the quark masses and mixings
The one loop Renormalization Group Equations for the Yukawa couplings of
quarks are solved. From the solution we find the explicit energy dependence on
of the evolution of the {\em down} quark masses from
the grand unification scale down to the top quark mass . These results
together with the earlier published evolution of the {\em up} quark masses
completes the pattern of the evolution of the quark masses. We also find the
energy dependence of the absolute values of the Cabibbo-Kobayashi-Maskawa (CKM)
matrix . The interesting property of the evolution of the CKM matrix
and the ratios of the quark masses: and is that
they all depend on through only one function of energy .Comment: Talk presented at the IX Mexican School on Particles and Fields,
August 9-19, Metepec, Pue., Mexico. To be published in the AIP Conference
Proceedings. 5 pages and 1 eps figure included in the tex
On Weyl Quantization from geometric Quantization
A. Weinstein has conjectured a nice looking formula for a deformed product of
functions on a hermitian symmetric space of non-compact type. We derive such a
formula for symmetric symplectic spaces using ideas from geometric quantization
and prequantization of symplectic groupoids. We compute the result explicitly
for the natural 2-dimensional symplectic manifolds: the euclidean plane, the
sphere and the hyperbolic plane. For the euclidean plane we obtain the well
known Moyal-Weyl product. The other cases show that Weinstein's original idea
should be interpreted with care. We conclude with comments on the status of our
result.Comment: 11 pages. (v2: corrected a couple of typos
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