230 research outputs found
Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic
polylogarithms up to w = 8 at an absolute accuracy of
or better. Using algebraic and argument relations the numerical representation
can be limited to the range . We provide replacement
files to map all harmonic polylogarithms to a basis and the usual range of
arguments to the above interval analytically. We also
briefly comment on a numerical implementation of real valued cyclotomic
harmonic polylogarithms.Comment: 19 pages LATEX, 3 Figures, ancillary dat
PolyLogTools - Polylogs for the masses
We review recent developments in the study of multiple polylogarithms,
including the Hopf algebra of the multiple polylogarithms and the symbol map,
as well as the construction of single valued multiple polylogarithms and
discuss an algorithm for finding fibration bases. We document how these
algorithms are implemented in the Mathematica package PolyLogTools and show how
it can be used to study the coproduct structure of polylogarithmic expressions
and how to compute iterated parametric integrals over polylogarithmic
expressions that show up in Feynman integal computations at low loop orders.Comment: Package URL: https://gitlab.com/pltteam/pl
HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
We present the Mathematica package HypExp which allows to expand
hypergeometric functions around integer parameters to arbitrary
order. At this, we apply two methods, the first one being based on an integral
representation, the second one on the nested sums approach. The expansion works
for both symbolic argument and unit argument. We also implemented new
classes of integrals that appear in the first method and that are, in part, yet
unknown to Mathematica.Comment: 33 pages, latex, 2 figures, the package can be downloaded from
http://krone.physik.unizh.ch/~maitreda/HypExp/, minor changes, works now
under Window
Heavy quark form factors in the large limit
Heavy quark form factors are calculated at to all
orders in at the first order in . The
terms in the recent results [arXiv:1611.07535] for the vector form factors are
confirmed, and terms for higher are predicted.Comment: v2: the section on inversion relations extended; v3: 3 refs added,
discussion of the hypergeometric function expansion extended; v4: eq. (22)
and fig. 5 correcte
Extension of HPL to complex arguments
In this paper we describe the extension of the Mathematica package HPL to
treat harmonic polylogarithms of complex arguments. The harmonic polylogarithms
have been introduced by Remiddi and Vermaseren and have many applications in
high energy particle physics.Comment: 42 pages, references added, the package can be downloaded at
http://krone.physik.unizh.ch/~maitreda/HPL
Bootstrapping pentagon functions
In PRL 116 (2016) no.6, 062001, the space of planar pentagon functions that
describes all two-loop on-shell five-particle scattering amplitudes was
introduced. In the present paper we present a natural extension of this space
to non-planar pentagon functions. This provides the basis for our pentagon
bootstrap program. We classify the relevant functions up to weight four, which
is relevant for two-loop scattering amplitudes. We constrain the first entry of
the symbol of the functions using information on branch cuts. Drawing on an
analogy from the planar case, we introduce a conjectural second-entry condition
on the symbol. We then show that the information on the function space, when
complemented with some additional insights, can be used to efficiently
bootstrap individual Feynman integrals. The extra information is read off of
Mellin-Barnes representations of the integrals, either by evaluating simple
asymptotic limits, or by taking discontinuities in the kinematic variables. We
use this method to evaluate the symbols of two non-trivial non-planar
five-particle integrals, up to and including the finite part.Comment: 24 pages + 3 pages of appendices, 2 figures, 3 tables, 4 ancillary
files, added references and corrected typos, published versio
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