7 research outputs found
Subleading Regge limit from a soft anomalous dimension
Wilson lines capture important features of scattering amplitudes, for example
soft effects relevant for infrared divergences, and the Regge limit. Beyond the
leading power approximation, corrections to the eikonal picture have to be
taken into account. In this paper, we study such corrections in a model of
massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit,
where the mass is generated through a Higgs mechanism. Using known three-loop
analytic expressions for the scattering amplitude, we find that the first power
suppressed term has a very simple form, equal to a single power law. We propose
that its exponent is governed by the anomalous dimension of a Wilson loop with
a scalar inserted at the cusp, and we provide perturbative evidence for this
proposal. We also analyze other limits of the amplitude and conjecture an exact
formula for a total cross-section at high energies.Comment: 19 pages, several appendices, many figure
Feynman integral reduction using Gröbner bases
Abstract We investigate the reduction of Feynman integrals to master integrals using Gröbner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of integrals to master integrals can then be solved once and for all by computing the Gröbner basis of the left ideal formed by the IBP relations. We demonstrate this explicitly for several examples. We introduce so-called first-order normal-form IBP relations which we obtain by reducing the shift operators in Y modulo the Gröbner basis of the left ideal of IBP relations. For more complicated cases, where the Gröbner basis is computationally expensive, we develop an ansatz based on linear algebra over a function field to obtain the normal-form IBP relations