142 research outputs found
Laurent series expansion of a class of massive scalar one-loop integrals up to {\cal O}(\ep^2) in terms of multiple polylogarithms
In a recent paper we have presented results for a set of massive scalar
one-loop master integrals needed in the NNLO parton model description of the
hadroproduction of heavy flavors. The one--loop integrals were evaluated in
n=4-2\ep dimension and the results were presented in terms of a Laurent
series expansion up to {\cal O}(\ep^2). We found that some of the \ep^2
coefficients contain a new class of functions which we termed the
functions. The functions are defined in terms of one--dimensional integrals
involving products of logarithm and dilogarithm functions. In this paper we
derive a complete set of algebraic relations that allow one to convert the
functions of our previous approach to a sum of classical and multiple
polylogarithms. Using these results we are now able to present the \ep^2
coefficients of the one-loop master integrals in terms of classical and
multiple polylogarithms.Comment: 32 pages, Latex, references added, matches published versio
Higgs Production via Gluon-Induced Weak Boson Fusion
We present a calculation that allows for an estimation of the NNLO
contributions to the Higgs production in the weak boson fusion channel. A
possible deterioration of this important channel for the Higgs discoveries at
the LHC can be ruled out by this calculation due to the small remaining cross
section after the weak boson cuts.Comment: 4 pages, 3 figures. To appear in the proceedings of the 14th
International QCD Conference (QCD 08), Montpellier, France, 7-12 July 200
Gluon-Induced Weak Boson Fusion
The gluon-gluon induced terms for Higgs production through weak boson fusion
(WBF) are computed. Formally, these are of NNLO in the strong coupling
constant. This is the lowest order at which non-zero color exchange occurs
between the scattering quarks, leading to a color field and thus additional
hadronic activity between the outgoing jets. Using a minimal set of cuts, the
numerical impact of these terms is at the percent level with respect to the NLO
rate for weak boson fusion. Applying the so-called WBF cuts leads to an even
stronger suppression, so that we do not expect a significant deterioration of
the WFB signal by these color exchange effects.Comment: 9 pages, 8 figures (21 included ps- and eps-files
Multiple polylogarithm values at roots of unity
For any positive integer let be the group of the th roots of
unity. In this note we shall study the \Q-linear relations among values of
multiple polylogarithms evaluated at \mmu_N. We show that the standard
relations considered by Racinet do not provide all the possible relations in
the following cases: (i) level N=4, weight or 4, and (ii) ,
, and is a power of 2 or 3, or has at least two prime factors.
We further find some (presumably all) of the missing relations in (i) by using
the octahedral symmetry of . We also prove some
other results when or ( prime ) by using the motivic
fundamental group of .Comment: A shorter version is to appear in C. R. Acad. Sci. Paris, Ser.
FORM version 4.0
We present version 4.0 of the symbolic manipulation system FORM. The most
important new features are manipulation of rational polynomials and the
factorization of expressions. Many other new functions and commands are also
added; some of them are very general, while others are designed for building
specific high level packages, such as one for Groebner bases. New is also the
checkpoint facility, that allows for periodic backups during long calculations.
Lastly, FORM 4.0 has become available as open source under the GNU General
Public License version 3.Comment: 26 pages. Uses axodra
Status of jet cross sections to NNLO
I review the state-of-the-art for fully differential numerical NNLO programs.
Topics which are covered include the calculation of two-loop amplitudes,
multiple polylogarithms, cancellation of infra-red divergences at NNLO and the
efficient generation of the phase space. Numerical results for e+ e- --> 2 jets
are also discussed.Comment: 5 pages, to appear in the proceedings of the conference "Loops and
Legs", Eisenach, 200
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