GRACE is an automatic calculation system that provides theoretical predictions of scattering cross sections of elementary particles and event generators for highenergy physics experiments.

Infrared diverges occur in the higher order corrections in QCD, accompanied by massless particles in the scattering processes. These infrared divergent parts are separated in d-dimensional space-time, and numerical calculation is applied to the finite parts. Sector decomposition methods are used for this separation. Since these methods divide the integration domain into several sectors, the integration must be performed in individual sectors; therefore, it is desirable to decrease the number of resulting sectors.

We have proposed a new method for sector decomposition. It is shown that this problem can be transformed to a problem in convex geometry, which can be solved using algorithms developed in computational geometry. We have also demonstrated that procedures of sector decomposition can be considered as a classification of asymptotic behaviors of integrands around singularities; the number of resulting sectors depends on the method of triangulation. Our test implementation shows the smallest number of sectors among the existing methods.

Since FY2007, this research project has been supported in part by the project of Hayama Center for Advanced Studies at the Graduate University for Advanced Studies. In addition, it has been conducted as part of a collaboration among Japanese, French, Dutch, and Russian groups for more than 10 years.

(from 2009 KEK annual report)