A Program for SU(N) Color Structure Decomposition into Multiplet Bases Using Wigner 3j and 6j Coefficients

Abstract: The increased capacity of elementary particle accelerators raises the demand for the simulation data of the experiments. One of the bottlenecks in the simulations is the QCD color structure calculation, which is usually treated using non-orthogonal and overcomplete sets of bases. The computational cost could be decreased significantly if orthogonal bases, such as the multiplet bases, were used instead. However, no computation tool performing calculations using these bases is available yet. In this thesis, we present a Mathematica program as proof-of-principle demonstrating the color structure decomposition into the multiplet bases. For a given amplitude, the corresponding multiplet basis states can be created and the scalar product between the amplitude and each of the basis states can be evaluated whenever the required Wigner 6j coefficients are available. The program offers tools for visualization of the tensor expressions in the birdtrack notation as well as a syntax similar to how the tensor expressions would be defined on paper. The available functions and replacement rules allow performing operations on SU(Nc) tensor expressions including index contraction, tensor conjugation, and scalar product of tensors.