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CP violation in semileptonic tau lepton decays
The leading order contribution to the direct CP asymmetry in tau^{+/-} ->
K^{+/-} pi^0 nu_{tau} decay rates is evaluated within the Standard Model. The
weak phase required for CP violation is introduced through an interesting
mechanism involving second order weak interactions, which is also responsible
for tiny violations of the Delta S= Delta Q rule in K_{l3} decays. The
calculated CP asymmetry turns out to be of order 10^{-12}, leaving a large
window for studying effects of non-standard sources of CP violation in this
observable.Comment: 5 pages, 3 figures, version published in Phys.Rev.
Convergent Asymptotic Expansions of Charlier, Laguerre and Jacobi Polynomials
Convergent expansions are derived for three types of orthogonal polynomials:
Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for
large values of the degree. The expansions are given in terms of functions that
are special cases of the given polynomials. The method is based on expanding
integrals in one or two points of the complex plane, these points being saddle
points of the phase functions of the integrands.Comment: 20 pages, 5 figures. Keywords: Charlier polynomials, Laguerre
polynomials, Jacobi polynomials, asymptotic expansions, saddle point methods,
two-points Taylor expansion
Multi-point Taylor Expansions of Analytic Functions
Taylor expansions of analytic functions are considered with respect to
several points, allowing confluence of any of them. Cauchy-type formulas are
given for coefficients and remainders in the expansions, and the regions of
convergence are indicated. It is explained how these expansions can be used in
deriving uniform asymptotic expansions of integrals. The method is also used
for obtaining Laurent expansions in several points as well as Taylor-Laurent
expansions.Comment: 20 pages, 7 figures. Keywords: multi-point Taylor expansions,
Cauchy's theorem, analytic functions, multi-point Laurent expansions, uniform
asymptotic expansions of integral
Radiative corrections of to decays
The electromagnetic radiative corrections to the ( is a vector meson and a charged
lepton) decay rates are evaluated using the cutoff method to regularize virtual
corrections and incorporating intermediate resonance states in the real-photon
amplitude to extend the region of validity of the soft-photon approximation.
The electromagnetic and weak form factors of hadrons are assumed to vary
smoothly over the energies of virtual and real photons under consideration. The
cutoff dependence of radiative corrections upon the scale that
separates the long- and short-distance regimes is found to be mild and is
considered as an uncertainty of the calculation. Owing to partial cancellations
of electromagnetic corrections evaluated over the three- and four-body regions
of phase space, the photon-inclusive corrected rates are found to be dominated
by the short-distance contribution. These corrections will be relevant for a
precise determination of the quark mixing angles by testing isospin
symmetry when measurements of semileptonic rates of charged and neutral
mesons at the few percent level become available. For completeness, we also
provide numerical values of radiative corrections in the three-body region of
the Dalitz plot distributions of these decays.Comment: Further comments and two references adde
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