Automatic generation of orthogonal multiplet bases in $\mathrm{SU}(N_c)$ color space

Abstract

We present a software that automatically generates a multiplet color basis for general $2\to n$ processes in quantum chromodynamics (QCD). The construction process is guided by the decomposition of the corresponding $\mathrm{SU}(N_c)$ representation into a direct sum of irreducible representations. The projectors of these irreducible multiplet states are then used to construct a minimal, linearly independent basis. The software achieves highest efficiency through a combination of the Z3 satisfiability modulo theories solver and the symbolic manipulation program FORM. The resulting color basis enables the analytical execution of involved QCD calculations that require color decomposition.