4,774 research outputs found
Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
We show that scattering amplitudes in planar N = 4 Super Yang-Mills in
multi-Regge kinematics can naturally be expressed in terms of single-valued
iterated integrals on the moduli space of Riemann spheres with marked points.
As a consequence, scattering amplitudes in this limit can be expressed as
convolutions that can easily be computed using Stokes' theorem. We apply this
framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove
that at L loops all MHV amplitudes are determined by amplitudes with up to L +
4 external legs. We also investigate non-MHV amplitudes, and we show that they
can be obtained by convoluting the MHV results with a certain helicity flip
kernel. We classify all leading singularities that appear at LLA in the Regge
limit for arbitrary helicity configurations and any number of external legs.
Finally, we use our new framework to obtain explicit analytic results at LLA
for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to
eight external legs and four loops.Comment: 104 pages, six awesome figures and ancillary files containing the
results in Mathematica forma
Gluon fusion contribution to W+W- + jet production
We describe the computation of the process that contributes
to the production of two -bosons and a jet at the CERN Large Hadron Collider
(LHC). While formally of next-to-next-to-leading order (NNLO) in QCD, this
process can be evaluated separately from the bulk of NNLO QCD corrections
because it is finite and gauge-invariant. It is also enhanced by the large
gluon flux and by selection cuts employed in the Higgs boson searches in the
decay channel , as was first pointed out by Binoth {\it et al.}
in the context of production. For cuts employed by the ATLAS
collaboration, we find that the gluon fusion contribution to
enhances the background by about ten percent and can lead to moderate
distortions of kinematic distributions which are instrumental for the ongoing
Higgs boson searches at the LHC. We also release a public code to compute the
NLO QCD corrections to this process, in the form of an add-on to the package
{\tt MCFM}.Comment: 13 pages, 4 figures, 3 table
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
We provide an analytic formula for the (rescaled) one-loop scalar hexagon
integral with all external legs massless, in terms of classical
polylogarithms. We show that this integral is closely connected to two
integrals appearing in one- and two-loop amplitudes in planar
super-Yang-Mills theory, and . The derivative of
with respect to one of the conformal invariants yields
, while another first-order differential operator applied to
yields . We also introduce some kinematic
variables that rationalize the arguments of the polylogarithms, making it easy
to verify the latter differential equation. We also give a further example of a
six-dimensional integral relevant for amplitudes in
super-Yang-Mills.Comment: 18 pages, 2 figure
The One-Loop One-Mass Hexagon Integral in D=6 Dimensions
We evaluate analytically the one-loop one-mass hexagon in six dimensions. The
result is given in terms of standard polylogarithms of uniform transcendental
weight three.Comment: 9 page
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