SOSpin, a C++ library for Yukawa decomposition in SO(2N) models

TL;DR

SOSpin is a C++ library that automates the analytic decomposition of Yukawa interactions in SO(2N) models into SU(N) basis, using oscillator formalism and efficient data structures.

Contribution

The paper introduces SOSpin, a novel C++ library that performs Yukawa decomposition in SO(2N) models with improved performance and flexibility, including higher-dimensional operators.

Findings

Successfully decomposes Yukawa interactions for N=2 and 5.

Handles higher-dimensional operators in SO(4).

Provides tools for simplifying spinors in SO(10) models.

Abstract

We present in this paper the SOSpin library, which calculates an analytic decomposition of the Yukawa interactions invariant under any SO(2N) group in terms of an SU(N) basis. We make use of the oscillator expansion formalism, where the SO(2N) spinor representations are expressed in terms of creation and annihilation operators of a Grassmann algebra. These noncommutative operators and their products are simulated in SOSpin through the implementation of doubly-linked-list data structures. These data structures were determinant to achieve a higher performance in the simplification of large products of creation and annihilation operators. We illustrate the use of our library with complete examples of how to decompose Yukawa terms invariant under SO(2N) in terms of SU(N) degrees of freedom for N=2 and 5. We further demonstrate, with an example for SO(4), that higher dimensional field-operator terms can also be processed with our library. Finally, we describe the functions available in SOSpin that are made to simplify the writing of spinors and their interactions specifically for SO(10) models.