65 research outputs found
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
The Poisson equations in the nonholonomic Suslov problem: Integrability, meromorphic and hypergeometric solutions
We consider the problem of integrability of the Poisson equations describing
spatial motion of a rigid body in the classical nonholonomic Suslov problem. We
obtain necessary conditions for their solutions to be meromorphic and show that
under some further restrictions these conditions are also sufficient. The
latter lead to a family of explicit meromorphic solutions, which correspond to
rather special motions of the body in space. We also give explicit extra
polynomial integrals in this case.
In the more general case (but under one restriction), the Poisson equations
are transformed into a generalized third order hypergeometric equation. A study
of its monodromy group allows us also to calculate the "scattering" angle: the
angle between the axes of limit permanent rotations of the body in space
Criteria equivalent to the Riemann Hypothesis
We give a brief overview of a few criteria equivalent to the Riemann
Hypothesis. Next we concentrate on the Riesz and B{\'a}ez-Duarte criteria. We
proof that they are equivalent and we provide some computer data to support
them. It is not compressed to six pages version of the talk delivered by M.W.
during the XXVII Workshop on Geometrical Methods in Physics, 28 June -- 6 July,
2008, Bia{\l}owie{\.z}a, Poland.Comment: It is not compressed to six pages version of the talk delivered by
M.W. during the XXVII Workshop on Geometrical Methods in Physics, 28 June --
6 July, 2008, Bia{\l}owie{\.z}a, Poland. New Fig.1 is include
RG Invariance of the Pole Mass in the Minimal Subtraction Scheme
We prove the renormalization group(RG) invariance of the pole mass with
respect to the RG functions of the minimal subtraction(MS) scheme and
illustrate this in case of the the neutral scalar field theory both in the
symmetric and in the broken symmetry phase
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
The analytic continuation of the Lippmann-Schwinger bras and kets is obtained
and characterized. It is shown that the natural mathematical setting for the
analytic continuation of the solutions of the Lippmann-Schwinger equation is
the rigged Hilbert space rather than just the Hilbert space. It is also argued
that this analytic continuation entails the imposition of a time asymmetric
boundary condition upon the group time evolution, resulting into a semigroup
time evolution. Physically, the semigroup time evolution is simply a (retarded
or advanced) propagator.Comment: 32 pages, 3 figure
Testing the Standard Model and Schemes for Quark Mass Matrices with CP Asymmetries in B Decays
The values of and , where and
are angles of the unitarity triangle, will be readily measured in a B
factory (and maybe also in hadron colliders). We study the standard model
constraints in the plane. We use the results
from recent analyses of and which take into account
heavy quark symmetry considerations. We find and
most likely \sin (2 \beta) \roughly{>} 0.6, and emphasize the strong
correlations between and . Various schemes
for quark mass matrices allow much smaller areas in the plane. We study the schemes of Fritzsch, of Dimopoulos, Hall and
Raby, and of Giudice, as well as the ``symmetric CKM'' idea, and show how CP
asymmetries in B decays will crucially test each of these schemes.Comment: 11 pages and 4 postscript figures available on request, LaTeX,
WIS-92/52/Jun-PH, LBL-3256
Wolfenstein Parametrization Re-examined
The Wolfenstein parametrization of the Kobayashi-Maskawa (KM)
matrix is modified by keeping its unitarity up to the accuracy of
. This modification can self-consistently lead to the
off-diagonal asymmetry of : =
with , which is comparable in magnitude with the Jarlskog parameter of
violation . We constrain the ranges of
and by using the current experimental data, and point out that the
possibility of a symmetric KM matrix has almost been ruled out.Comment: 5 Latex pages including a figure; Two references are adde
On the inconsistency of the Bohm-Gadella theory with quantum mechanics
The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum
Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom
asserts that the solutions of the Lippmann-Schwinger equation are functionals
over spaces of Hardy functions. The preparation-registration arrow of time
provides the physical justification for the Hardy axiom. In this paper, it is
shown that the Hardy axiom is incorrect, because the solutions of the
Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also
shown that the derivation of the preparation-registration arrow of time is
flawed. Thus, Hardy functions neither appear when we solve the
Lippmann-Schwinger equation nor they should appear. It is also shown that the
Bohm-Gadella theory does not rest on the same physical principles as quantum
mechanics, and that it does not solve any problem that quantum mechanics cannot
solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
We exemplify the way the rigged Hilbert space deals with the
Lippmann-Schwinger equation by way of the spherical shell potential. We
explicitly construct the Lippmann-Schwinger bras and kets along with their
energy representation, their time evolution and the rigged Hilbert spaces to
which they belong. It will be concluded that the natural setting for the
solutions of the Lippmann-Schwinger equation--and therefore for scattering
theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur
Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''
In this reply, we show that when we apply standard distribution theory to the
Lippmann-Schwinger equation, the resulting spaces of test functions would
comply with the Hardy axiom only if classic results of Paley and Wiener, of
Gelfand and Shilov, and of the theory of ultradistributions were wrong. As
well, we point out several differences between the ``standard method'' of
constructing rigged Hilbert spaces in quantum mechanics and the method used in
Time Asymmetric Quantum Theory.Comment: 13 page
- …