Abstract
Model building in 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 software, implemented in C++ using in-built libraries. The software is capable of accepting invariant couplings involving an arbitrary number of SO(10) Higgs tensors, each having up to five indices. The output is then produced in LaTeX, so that it is universally readable and sufficiently expressive. Through the use of this software, 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 SO(N) invariant couplings.
Highlights
The standard model of particle physics, including the strong and electroweak interactions comprising the group SU(3)C × SU(2)L × U(1)Y, is highly successful [1,2,3,4,5]
The program evaluates tensor couplings from input to their final normalized form. It is executed through various functions of the Product Resolver class, which stores all the intermediate terms during the calculation. It is based on the algorithm developed in Appendix B.4
This paper proposes a novel C++ software that can compute SO(10) Higgs couplings automatically in terms of SU(5) invariants, based on the algorithm developed in Appendix B.4
Summary
The standard model of particle physics, including the strong and electroweak interactions comprising the group SU(3)C × SU(2)L × U(1)Y, is highly successful [1,2,3,4,5]. The aim of grand unified theories is three-fold: (1) To accomplish these unifications; (2) to provide an understanding of the three generations of quarks and leptons; (3) to provide an explanation of the hierarchy of their masses and of other properties. Grand unified models based on the gauge group SO(10) [6,7] have the most desirable features They provide a framework for the unification of electroweak and strong interactions. They allow for all the quarks and leptons of one generation to reside in a single 16–plet irreducible spinor representation. SO(10) models solve—in a relatively natural way—the doublettriplet splitting problem without fine tuning. They possess gauge interactions that conserve parity. Supersymmetric SO(10) models have the additional feature that they manage to unify the gauge couplings, and solve the hierarchy problem
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