54 research outputs found
Rigorous QCD-Potential for the -System at Threshold
Recent evidence for the top mass in the region of 160 for the first
time provides an opportunity to use the full power of relativistic quantum
field theoretical methods, available also for weakly bound systems. Because of
the large decay width \G of the top quark individual energy-levels in
"toponium" will be unobservable. However, the potential for the
system, based on a systematic expansion in powers of the strong coupling
constant \a_s can be rigorously derived from QCD and plays a central role in
the threshold region. It is essential that the neglect of nonperturbative
(confining) effects is fully justified here for the first time to a large
accuracy, also just {\it because} of the large \G. The different
contributions to that potential are computed from real level corrections near
the bound state poles of the -system which for \G \ne 0 move into
the unphysical sheet of the complex energy plane. Thus, in order to obtain the
different contributions to that potential we may use the level corrections at
that (complex) pole. Within the relevant level shifts we especially emphasize
the corrections of order O(\a_s^4 m_t) and numerically comparable ones to
that order also from electroweak interactions which may become important as
well.Comment: 36 pages (mailer uncorrupted version), TUW-94-1
Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
We continue the study of the construction of analytical coefficients of the
epsilon-expansion of hypergeometric functions and their connection with Feynman
diagrams. In this paper, we show the following results:
Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth
(see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions.
Theorem B: The epsilon expansion of a hypergeometric function with one
half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the
harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are
ratios of polynomials. Some extra materials are available via the www at this
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected
and a few references added; v3: few references added
Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions
In this paper, we reconsider the large-argument asymptotic expansions of the
Hankel, Bessel and modified Bessel functions and their derivatives. New
integral representations for the remainder terms of these asymptotic expansions
are found and used to obtain sharp and realistic error bounds. We also give
re-expansions for these remainder terms and provide their error estimates. A
detailed discussion on the sharpness of our error bounds and their relation to
other results in the literature is given. The techniques used in this paper
should also generalize to asymptotic expansions which arise from an application
of the method of steepest descents.Comment: 32 pages, 2 figures, accepted for publication in Acta Applicandae
Mathematica
Über die Zerlegung der aus Wurzeln der Einheit gebildeten complexen Zahlen in ihre Primfactoren.
Allgemeiner Beweis des Fermatschen Satzes, daß die Gleichung x... durch ganze Zahlen unlösbar ist, für alle diejenigen Potenz-Exponenten ..., welche ungerade Primzahlen sind und in den Zählern der ersten ... Bernoullischen zahlen als Factoren nicht vorkommen.
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