33 research outputs found
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
We consider the application of the DRA method to the case of several master
integrals in a given sector. We establish a connection between the homogeneous
part of dimensional recurrence and maximal unitarity cuts of the corresponding
integrals: a maximally cut master integral appears to be a solution of the
homogeneous part of the dimensional recurrence relation. This observation
allows us to make a necessary step of the DRA method, the construction of the
general solution of the homogeneous equation, which, in this case, is a coupled
system of difference equations.Comment: 17 pages, 2 figure
Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of
Wilson-loop vacuum expectation values and scattering amplitudes. In this paper,
we investigate this correspondence at the diagram level. We find that one-loop
triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple
one- and two- parametric integrals over a single propagator in configuration
space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a
four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of
the configuration-space propagator and loop Feynman diagrams, we derive Feynman
parameterizations of complicated planar and non-planar Feynman diagrams which
simplify their evaluation. For illustration, we compute numerically a four-loop
hexagon scalar Feynman diagram.Comment: 20 pages, many figures. Two references added. Published versio
Electroweak Physics
The results of high precision weak neutral current (WNC), Z-pole, and high
energy collider electroweak experiments have been the primary prediction and
test of electroweak unification. The electroweak program is briefly reviewed
from a historical perspective. Current changes, anomalies, and things to watch
are summarized, and the implications for the standard model and beyond
discussed.Comment: 12 pages, invited talk presented at the Conference on the
Intersections of Particle and Nuclear Physics (CIPANP 2003), New York, May
200
An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry
constrains multi-loop n-edged Wilson loops to be basically given in terms of
the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a
function of conformally invariant cross ratios. We identify a class of
kinematics for which the Wilson loop exhibits exact Regge factorisation and
which leave invariant the analytic form of the multi-loop n-edged Wilson loop.
In those kinematics, the analytic result for the Wilson loop is the same as in
general kinematics, although the computation is remarkably simplified with
respect to general kinematics. Using the simplest of those kinematics, we have
performed the first analytic computation of the two-loop six-edged Wilson loop
in general kinematics.Comment: 17 pages. Extended discussion on how the QMRK limit is taken. Version
accepted by JHEP. A text file containing the Mathematica code with the
analytic expression for the 6-point remainder function is include
On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations
An improved method is presented for the numerical evaluation of multi-loop
integrals in dimensional regularization. The technique is based on
Mellin-Barnes representations, which have been used earlier to develop
algorithms for the extraction of ultraviolet and infrared divergencies. The
coefficients of these singularities and the non-singular part can be integrated
numerically. However, the numerical integration often does not converge for
diagrams with massive propagators and physical branch cuts. In this work,
several steps are proposed which substantially improve the behavior of the
numerical integrals. The efficacy of the method is demonstrated by calculating
several two-loop examples, some of which have not been known before.Comment: 13 pp. LaTe
Eikonal methods applied to gravitational scattering amplitudes
We apply factorization and eikonal methods from gauge theories to scattering
amplitudes in gravity. We hypothesize that these amplitudes factor into an
IR-divergent soft function and an IR-finite hard function, with the former
given by the expectation value of a product of gravitational Wilson line
operators. Using this approach, we show that the IR-divergent part of the
n-graviton scattering amplitude is given by the exponential of the one-loop IR
divergence, as originally discovered by Weinberg, with no additional subleading
IR-divergent contributions in dimensional regularization.Comment: 16 pages, 3 figures; v2: title change and minor rewording (published
version); v3: typos corrected in eqs.(3.2),(4.1
Mellin–Barnes meets Method of Brackets: a novel approach to Mellin–Barnes representations of Feynman integrals
On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
We propose a first implementation of the integrand-reduction method for
two-loop scattering amplitudes. We show that the residues of the amplitudes on
multi-particle cuts are polynomials in the irreducible scalar products
involving the loop momenta, and that the reduction of the amplitudes in terms
of master integrals can be realized through polynomial fitting of the
integrand, without any apriori knowledge of the integral basis. We discuss how
the polynomial shapes of the residues determine the basis of master integrals
appearing in the final result. We present a four-dimensional constructive
algorithm that we apply to planar and non-planar contributions to the 4- and
5-point MHV amplitudes in N=4 SYM. The technique hereby discussed extends the
well-established analogous method holding for one-loop amplitudes, and can be
considered a preliminary study towards the systematic reduction at the
integrand-level of two-loop amplitudes in any gauge theory, suitable for their
automated semianalytic evaluation.Comment: 26 pages, 11 figure