1,182 research outputs found

### Tuning FORM with large calculations

Some recent additions to FORM are discussed. In particular large file support
and the tablebases are presented.Comment: 5 pages, LaTeX. Talk given at RADCOR02, Kloster Ban

### - XSummer - Transcendental Functions and Symbolic Summation in Form

Harmonic sums and their generalizations are extremely useful in the
evaluation of higher-order perturbative corrections in quantum field theory. Of
particular interest have been the so-called nested sums,where the harmonic sums
and their generalizations appear as building blocks, originating for example
from the expansion of generalized hypergeometric functions around integer
values of the parameters. In this Letter we discuss the implementation of
several algorithms to solve these sums by algebraic means, using the computer
algebra system Form.Comment: 21 pages, 1 figure, Late

### Harmonic sums, Mellin transforms and Integrals

This paper describes algorithms to deal with nested symbolic sums over
combinations of harmonic series, binomial coefficients and denominators. In
addition it treats Mellin transforms and the inverse Mellin transformation for
functions that are encountered in Feynman diagram calculations. Together with
results for the values of the higher harmonic series at infinity the presented
algorithms can be used for the symbolic evaluation of whole classes of
integrals that were thus far intractable. Also many of the sums that had to be
evaluated seem to involve new results. Most of the algorithms have been
programmed in the language of FORM. The resulting set of procedures is called
SUMMER.Comment: 31 pages LaTeX, for programs, see http://norma.nikhef.nl/~t68/summe

### Mathematics for structure functions

We show some of the mathematics that is being developed for the computation
of deep inelastic structure functions to three loops. These include harmonic
sums, harmonic polylogarithms and a class of difference equations that can be
solved with the use of harmonic sums.Comment: 6 pages LaTeX, uses axodraw.sty and npb.sty (included

### The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass

We consider the two-loop self-mass sunrise amplitude with two equal masses
$M$ and the external invariant equal to the square of the third mass $m$ in the
usual $d$-continuous dimensional regularization. We write a second order
differential equation for the amplitude in $x=m/M$ and show as solve it in
close analytic form. As a result, all the coefficients of the Laurent expansion
in $(d-4)$ of the amplitude are expressed in terms of harmonic polylogarithms
of argument $x$ and increasing weight. As a by product, we give the explicit
analytic expressions of the value of the amplitude at $x=1$, corresponding to
the on-mass-shell sunrise amplitude in the equal mass case, up to the $(d-4)^5$
term included.Comment: 11 pages, 2 figures. Added Eq. (5.20) and reference [4

### The reaction e+e- --> hh recomputed

We notice that the existing literature about the reaction e+e- --> hh suffers
from a mistake in the relative sign between the t-channel and u-channel graphs.
Correcting this lowers the crosssections by about an order of magnitude.Comment: 7 pages, 5 figure

### Hypergeometric representation of a four-loop vacuum bubble

In this article, we present a new analytic result for a certain
single-mass-scale four-loop vacuum (bubble) integral. We also discuss its
systematic \e-expansion in d=4-2\e as well as d=3-2\e dimensions, the
coefficients of which are expressible in terms of harmonic sums at infinity.Comment: 5 pages, to appear in the proceedings of the conference "Loops and
Legs", Eisenach, 200

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