93 research outputs found
Reduction of one-massless-loop with scalar boxes in dimensions
All one-massless-loop Feynman diagrams could be written like a linear
combination of scalar boxes, triangles an bubbles in dimensions plus
rational terms. However, the four-point scalar integrals in dimensions
are free of infrared divergences. We are going to change the dimensions of the
scalar boxes and the using of this degree of freedom to simplify
the computation of coefficients of the decomposition.Comment: 17 page
Six-Photon Amplitudes in Scalar QED
The analytical result for the six-photon helicity amplitudes in scalar QED is
presented. To compute the loop, a recently developed method based on multiple
cuts is used. The amplitudes for QED and QED^{\caln=1} are also derived using
the supersymmetric decomposition linking the three theories.Comment: 15 pages, 13 figure
Double Parton Scattering Singularity in One-Loop Integrals
We present a detailed study of the double parton scattering (DPS)
singularity, which is a specific type of Landau singularity that can occur in
certain one-loop graphs in theories with massless particles. A simple formula
for the DPS singular part of a four-point diagram with arbitrary
internal/external particles is derived in terms of the transverse momentum
integral of a product of light cone wavefunctions with tree-level matrix
elements. This is used to reproduce and explain some results for DPS
singularities in box integrals that have been obtained using traditional loop
integration techniques. The formula can be straightforwardly generalised to
calculate the DPS singularity in loops with an arbitrary number of external
particles. We use the generalised version to explain why the specific MHV and
NMHV six-photon amplitudes often studied by the NLO multileg community are not
divergent at the DPS singular point, and point out that whilst all NMHV
amplitudes are always finite, certain MHV amplitudes do contain a DPS
divergence. It is shown that our framework for calculating DPS divergences in
loop diagrams is entirely consistent with the `two-parton GPD' framework of
Diehl and Schafer for calculating proton-proton DPS cross sections, but is
inconsistent with the `double PDF' framework of Snigirev.Comment: 29 pages, 8 figures. Minor corrections and clarifications added.
Version accepted for publication in JHE
Direct Extraction Of One Loop Rational Terms
We present a method for the direct extraction of rational contributions to
one-loop scattering amplitudes, missed by standard four-dimensional unitarity
techniques. We use generalised unitarity in D=4-2\e dimensions to write the
loop amplitudes in terms of products of massive tree amplitudes. We find that
the rational terms in 4-2\e dimensions can be determined from quadruple,
triple and double cuts without the need for independent pentagon contributions
using a massive integral basis. The additional mass-dependent integral
coefficients may then be extracted from the large mass limit which can be
performed analytically or numerically. We check the method by computing the
rational parts of all gluon helicity amplitudes with up to six external legs.
We also present a simple application to amplitudes with external massless
fermions.Comment: 35 pages, 6 figures. Major revisions: new analytic results for gluon
amplitudes and new section on treatment of massless fermions. References
added and typos corrected. Accepted for publication in JHE
Loop amplitudes in gauge theories: modern analytic approaches
This article reviews on-shell methods for analytic computation of loop
amplitudes, emphasizing techniques based on unitarity cuts. Unitarity
techniques are formulated generally but have been especially useful for
calculating one-loop amplitudes in massless theories such as Yang-Mills theory,
QCD, and QED.Comment: 34 pages. Invited review for a special issue of Journal of Physics A
devoted to "Scattering Amplitudes in Gauge Theories." v2: typesetting macro
error fixe
Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
SAMURAI is a tool for the automated numerical evaluation of one-loop
corrections to any scattering amplitudes within the dimensional-regularization
scheme. It is based on the decomposition of the integrand according to the
OPP-approach, extended to accommodate an implementation of the generalized
d-dimensional unitarity-cuts technique, and uses a polynomial interpolation
exploiting the Discrete Fourier Transform. SAMURAI can process integrands
written either as numerator of Feynman diagrams or as product of tree-level
amplitudes. We discuss some applications, among which the 6- and 8-photon
scattering in QED, and the 6-quark scattering in QCD. SAMURAI has been
implemented as a Fortran90 library, publicly available, and it could be a
useful module for the systematic evaluation of the virtual corrections oriented
towards automating next-to-leading order calculations relevant for the LHC
phenomenology.Comment: 35 pages, 7 figure
The Specificity of Environmental Influence: Socioeconomic Status Affects Early Vocabulary Development Via Maternal Speech
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