Toshiaki Kaneko

A geometric method of sector decomposition

We propose a new geometric method of IR factorization in sector decomposition. The problem is converted into a set of problems in convex geometry. The latter problems are solved using algorithms in combinatorial geometry. This method provides a deterministic algorithm and never falls into an infinite loop. The number of resulting sectors depends on the algorithm of triangulation. Our test implementation shows smaller number of sectors comparing with other existing methods with iterations.

A Feynman-graph generator for any order of coupling constants

A computer program has been developed which generates Feynman graphs automatically for scattering and decay processes in non-Abelian gauge theory of high-energy physics. A new acceleration method is presented for both generating and eliminating graphs. This method has been shown to work quite efficiently for any order of coupling constants in any kind of theoretical model. A utility program is also available for drawing generated graphs. These programs consist of the most basic parts of the GRACE system, which is now used to automatically calculate tree and one-loop processes.

Broken S3 symmetry in flavor physics

Abstract The S 3 symmetry is shown to be a very good approximate symmetry when it is broken in a specific way. This is true both in quark sector and in lepton sector. The way to break it is implied by the K–M mechanism applied not to the mixing matrix but to the mass matrices. In quark sector, we have an almost perfect fitting to the experimental data, and in lepton sector, we have a precision for the θ 13 .

Sector decomposition via computational geometry

A non-iterative method is presented for the factorization step of sector decomposition method, which separates infrared divergent part from loop integration. This method is based on a classification of asymptotic behavior of polynomials. The problem is converted to ones for convex body in Euclidean space. They are solved with algorithms developed in computational geometry. A test implementation shows that this method produces less number of decomposed sectors than usual iterative sector decompositions.

On the Structure of Space, Time and Field

A unified theory of gravity and other interactions is proposed. We are guided by the principle of equivalence of space-time and field and by Machs principle. Fundamental Lagranxad gian is assumed to describe the whole universe on the one hand and local physical phenomena on the other. A condensed scalar field determines both the structure of the universe and that of the group of grand unification: The Hubble constant and deacceleration parameter are related to the grand unification group. One remarkable feature of our theory is the dependence of the gravitational and the gauge coupling constants on the cosmological time.

A package of generating Feynman rules in GRACE system

A package of automatic derivation of Feynman rules form Lagrangian has been developed for GRACE system, an automatic system of perturbative calculation in quantum field theory.