Using C++ to Calculate $\mathsf{SO(10)}$ Tensor Couplings

Abstract

\noindent Model building in $\mathsf{SO(10)}$, which is the leading grand unification framework, often involves large Higgs representations and their couplings. Explicit calculations of such couplings is a multi-step process that involves laborious calculations that are time-consuming and error-prone, an issue which only grows as the complexity of the coupling increases. Therefore, there exists an opportunity to leverage the abilities of computer software in order to algorithmically perform these calculations on-demand. This paper outlines the details of such a software, implemented in C++ using in-built libraries. The software is capable of accepting invariant couplings involving an arbitrary number of $\mathsf{SO(10)}$ Higgs tensors, each having up to 5 indices. The output is then produced in \LaTeX, so that it is universally readable and sufficiently expressive. Through the use of this software, $\mathsf{SO(10)}$ coupling analysis can be performed in a way that minimizes calculation time, eliminates errors, and allows for experimentation with couplings that have not been computed before in the literature. Furthermore, this software can be expanded in the future to account for similar Higgs-Spinor coupling analysis, or extended to include further $\mathsf{SO(N)}$ invariant couplings.