, a C++ library for Yukawa decomposition in [formula omitted] models

Abstract

We present in this paper the ▪ library, which calculates an analytic decomposition of the Yukawa interactions invariant under SO(2N) 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 acting on a vacuum state. These noncommutative operators and their products are simulated in ▪ 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 ▪ that are made to simplify the writing of spinors and their interactions specifically for SO(10) models. Program summaryProgram title: SOSpinCatalogue identifier: AEZM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEZM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 25623No. of bytes in distributed program, including test data, etc.: 200391Distribution format: tar.gzProgramming language: C++.Computer: PC, Apple.Operating system: UNIX (Linux, Mac OS X 11).RAM: >20 MB depending on the number of processes requiredClassification: 4.2, 11.1, 11.6.External routines: In order to make further simplifications on the expressions obtained the library calls the Symbolic Manipulation System FORM program [1].Nature of problem: The decomposition of an Yukawa interaction invariant under SO(2N) in terms of SU (N) fields.Solution method: 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 acting on a vacuum state.Running time: It depends on the input expressions, it can take a few seconds or more for very large representations (because of memory exhaustion).