{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:24:53Z","timestamp":1760235893996,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T00:00:00Z","timestamp":1633305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002724","name":"American University of Sharjah","doi-asserted-by":"publisher","award":["AS1805"],"award-info":[{"award-number":["AS1805"]}],"id":[{"id":"10.13039\/501100002724","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2013Spinor coupling analysis, or extended to include further SO(N) invariant couplings.<\/jats:p>","DOI":"10.3390\/sym13101871","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1871","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Using C++ to Calculate SO(10) Tensor Couplings"],"prefix":"10.3390","volume":"13","author":[{"given":"Azadan","family":"Bhagwagar","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4047-2489","authenticated-orcid":false,"given":"Raza M.","family":"Syed","sequence":"additional","affiliation":[{"name":"Department of Physics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1103\/PhysRevLett.19.1264","article-title":"A Model of Leptons","volume":"19","author":"Weinberg","year":"1967","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/0029-5582(61)90469-2","article-title":"Partial Symmetries of Weak Interactions","volume":"22","author":"Glashow","year":"1961","journal-title":"Nucl. Phys."},{"key":"ref_3","first-page":"367","article-title":"Weak and Electromagnetic Interactions","volume":"680519","author":"Salam","year":"1968","journal-title":"Conf. Proc. C"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1103\/PhysRevLett.30.1343","article-title":"Ultraviolet Behavior of Nonabelian Gauge Theories","volume":"30","author":"Gross","year":"1973","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1103\/PhysRevLett.30.1346","article-title":"Reliable Perturbative Results for Strong Interactions?","volume":"30","author":"Politzer","year":"1973","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1063\/1.2947450","article-title":"The State of the Art\u2014Gauge Theories","volume":"23","author":"Georgi","year":"1975","journal-title":"AIP Conf. Proc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0003-4916(75)90211-0","article-title":"Unified Interactions of Leptons and Hadrons","volume":"93","author":"Fritzsch","year":"1975","journal-title":"Ann. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/S0370-2693(01)00392-6","article-title":"Analysis of couplings with large tensor representations in SO(2N) and proton decay","volume":"506","author":"Nath","year":"2001","journal-title":"Phys. Lett. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/S0550-3213(01)00493-X","article-title":"Complete cubic and quartic couplings of 16 and bar-16 in SO(10) unification","volume":"618","author":"Nath","year":"2001","journal-title":"Nucl. Phys. B"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Syed, R.M. (2004, January 16\u201322). Analysis of SO(2N) couplings of spinor and tensor representations in SU(N) times U(1) invariant forms. Proceedings of the 10th International Symposium on Particles, Strings and Cosmology (PASCOS 2004), Part II: Themes in Unification\u2014The Pran Nath Festschrift, Northeastern University, Boston, MA, USA.","DOI":"10.1142\/9789812701756_0086"},{"key":"ref_11","unstructured":"Syed, R.M. (2005). Couplings in SO(10) Grand Unification. [Ph.D. Thesis, Northeastern University]."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"047","DOI":"10.1007\/JHEP01(2021)047","article-title":"Corrections to Yukawa couplings from higher dimensional operators in a natural SUSY SO(10) and HL-LHC implications","volume":"01","author":"Aboubrahim","year":"2021","journal-title":"J. High Energy Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"002","DOI":"10.1007\/JHEP06(2021)002","article-title":"Yukawa coupling unification in an SO(10) model consistent with Fermilab (g \u2212 2)\u03bc result","volume":"06","author":"Aboubrahim","year":"2021","journal-title":"J. High Energy Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"055005","DOI":"10.1103\/PhysRevD.93.055005","article-title":"An Analysis of B \u2212 L = \u22122 Operators from Matter-Higgs Interactions in a Class of Supersymmetric SO(10) Models","volume":"93","author":"Nath","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"075002","DOI":"10.1103\/PhysRevD.85.075002","article-title":"Variety of SO(10) GUTs with Natural Doublet-Triplet Splitting via the Missing Partner Mechanism","volume":"85","author":"Babu","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"095011","DOI":"10.1103\/PhysRevD.72.095011","article-title":"A Unified framework for symmetry breaking in SO(10)","volume":"72","author":"Babu","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"075004","DOI":"10.1103\/PhysRevD.74.075004","article-title":"Fermion Mass Generation in SO(10) with a Unified Higgs Sector","volume":"74","author":"Babu","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"022","DOI":"10.1088\/1126-6708\/2006\/02\/022","article-title":"Couplings of vector-spinor representation for SO(10) model building","volume":"02","author":"Nath","year":"2006","journal-title":"J. High Energy Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"015015","DOI":"10.1103\/PhysRevD.77.015015","article-title":"Suppression of Higgsino mediated proton decay by cancellations in GUTs and strings","volume":"77","author":"Nath","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"037701","DOI":"10.1103\/PhysRevD.81.037701","article-title":"Yukawa Couplings and Quark and Lepton Masses in an SO(10) Model with a Unified Higgs Sector","volume":"81","author":"Nath","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2348","DOI":"10.1103\/PhysRevD.32.2348","article-title":"Nucleon Decay in Supergravity Unified Theories","volume":"32","author":"Nath","year":"1985","journal-title":"Phys. Rev. D"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.physrep.2007.02.010","article-title":"Proton stability in grand unified theories, in strings and in branes","volume":"441","author":"Nath","year":"2007","journal-title":"Phys. Rept."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1103\/PhysRevD.21.1062","article-title":"SO(2n) Grand Unification in an SU(N) Basis","volume":"21","author":"Mohapatra","year":"1980","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/S0550-3213(00)00666-0","article-title":"Construction and analysis of anomaly free supersymmetric SO(2N)\/U(N) sigma models","volume":"594","author":"Nibbelink","year":"2001","journal-title":"Nucl. Phys. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1142\/S0217751X0502001X","article-title":"SO(10) a la Pati-Salam","volume":"20","author":"Aulakh","year":"2005","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.nuclphysb.2005.01.008","article-title":"SO(10) MSGUT: Spectra, couplings and threshold effects","volume":"711","author":"Aulakh","year":"2005","journal-title":"Nucl. Phys. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0370-1573(81)90092-2","article-title":"Group Theory for Unified Model Building","volume":"79","author":"Slansky","year":"1981","journal-title":"Phys. Rept."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4808","DOI":"10.1063\/1.533380","article-title":"E(6) unification model building. 1. Clebsch-Gordan coefficients of 27 x 27-bar","volume":"41","author":"Anderson","year":"2000","journal-title":"J. Math. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.1103\/PhysRevD.41.1620","article-title":"Symmetry breaking and mass spectra in supersymmetric SO(10) models","volume":"41","author":"He","year":"1990","journal-title":"Phys. Rev. D"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"033505","DOI":"10.1063\/1.1847709","article-title":"SO(10) group theory for the unified model building","volume":"46","author":"Fukuyama","year":"2005","journal-title":"J. Math. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.cpc.2016.01.010","article-title":"SOSpin, a C++ library for Yukawa decomposition in SO(2N) models","volume":"203","author":"Cardoso","year":"2016","journal-title":"Comput. Phys. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107490","DOI":"10.1016\/j.cpc.2020.107490","article-title":"LieART 2.0 \u2013 A Mathematica application for Lie Algebras and Representation Theory","volume":"257","author":"Feger","year":"2020","journal-title":"Comput. Phys. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1016\/j.cpc.2014.02.018","article-title":"SARAH 4: A tool for (not only SUSY) model builders","volume":"185","author":"Staub","year":"2014","journal-title":"Comput. Phys. Commun."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1016\/j.cpc.2011.03.025","article-title":"CleGo: A package for automated computation of Clebsch-Gordan coefficients in Tensor Product Representations for Lie Algebras A\u2013G","volume":"182","author":"Horst","year":"2011","journal-title":"Comput. Phys. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2250","DOI":"10.1016\/j.cpc.2014.04.012","article-title":"FeynRules 2.0\u2014A complete toolbox for tree-level phenomenology","volume":"185","author":"Alloul","year":"2014","journal-title":"Comput. Phys. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1017\/S0017089500006832","article-title":"On the classification of isotropic tensors","volume":"29","author":"Appleby","year":"1987","journal-title":"Glasg. Math. J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1871\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:09:22Z","timestamp":1760166562000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1871"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,4]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101871"],"URL":"https:\/\/doi.org\/10.3390\/sym13101871","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,10,4]]}}}