Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks
Abstract At the classical level, the SU(2/1) superalgebra offers a natural description of the elementary particles: leptons and quarks massless states, graded by their chirality, fit the smallest irreducible representations of SU(2/1). Our new proposition is to pair the left/right space-time chirali...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2020)167 |
| _version_ | 1819005970954584064 |
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| author | Jean Thierry-Mieg |
| author_facet | Jean Thierry-Mieg |
| author_sort | Jean Thierry-Mieg |
| collection | DOAJ |
| description | Abstract At the classical level, the SU(2/1) superalgebra offers a natural description of the elementary particles: leptons and quarks massless states, graded by their chirality, fit the smallest irreducible representations of SU(2/1). Our new proposition is to pair the left/right space-time chirality with the superalgebra chirality and to study the model at the one-loop quantum level. If, despite the fact that they are non-Hermitian, we use the odd matrices of SU(2/1) to minimally couple an oriented complex Higgs scalar field to the chiral Fermions, novel anomalies occur. They affect the scalar propagators and vertices. However, these undesired new terms cancel out, together with the Adler-Bell-Jackiw vector anomalies, because the quarks compensate the leptons. The unexpected and striking consequence is that the scalar propagator must be normalized using the anti-symmetric super-Killing metric and the scalar-vector vertex must use the symmetric d_aij structure constants of the superalgebra. Despite this extraordinary structure, the resulting Lagrangian is actually Hermitian. |
| first_indexed | 2024-12-21T00:01:15Z |
| format | Article |
| id | doaj.art-59d46afc5fd347beb43d3077c125bc1e |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T00:01:15Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-59d46afc5fd347beb43d3077c125bc1e2022-12-21T19:22:35ZengSpringerOpenJournal of High Energy Physics1029-84792020-10-0120201012610.1007/JHEP10(2020)167Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarksJean Thierry-Mieg0NCBI, National Library of Medicine, National Institute of HealthAbstract At the classical level, the SU(2/1) superalgebra offers a natural description of the elementary particles: leptons and quarks massless states, graded by their chirality, fit the smallest irreducible representations of SU(2/1). Our new proposition is to pair the left/right space-time chirality with the superalgebra chirality and to study the model at the one-loop quantum level. If, despite the fact that they are non-Hermitian, we use the odd matrices of SU(2/1) to minimally couple an oriented complex Higgs scalar field to the chiral Fermions, novel anomalies occur. They affect the scalar propagators and vertices. However, these undesired new terms cancel out, together with the Adler-Bell-Jackiw vector anomalies, because the quarks compensate the leptons. The unexpected and striking consequence is that the scalar propagator must be normalized using the anti-symmetric super-Killing metric and the scalar-vector vertex must use the symmetric d_aij structure constants of the superalgebra. Despite this extraordinary structure, the resulting Lagrangian is actually Hermitian.http://link.springer.com/article/10.1007/JHEP10(2020)167Anomalies in Field and String TheoriesGauge SymmetryBeyond Standard Model |
| spellingShingle | Jean Thierry-Mieg Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks Journal of High Energy Physics Anomalies in Field and String Theories Gauge Symmetry Beyond Standard Model |
| title | Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks |
| title_full | Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks |
| title_fullStr | Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks |
| title_full_unstemmed | Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks |
| title_short | Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks |
| title_sort | scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral su 2 1 model of leptons and quarks |
| topic | Anomalies in Field and String Theories Gauge Symmetry Beyond Standard Model |
| url | http://link.springer.com/article/10.1007/JHEP10(2020)167 |
| work_keys_str_mv | AT jeanthierrymieg scalaranomalycancellationrevealsthehiddensuperalgebraicstructureofthequantumchiralsu21modelofleptonsandquarks |