\(SU(2/1)\) gauge-Higgs unification

DOI10.1142/S0217751X16501025zbMATH Open1344.81121arXiv1012.3692MaRDI QIDQ2820139

Publication date: 14 September 2016

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Abstract: We discuss a question whether the observed Weinberg angle and Higgs mass are calculable in the formalism based on a construction in which the electroweak gauge group

S U (2) i m e s U (1)_{Y}

is embedded in the graded Lie group

S U (2 / 1)

. Here we follow original works of Ne'eman and Fairlie believing that bosonic fields take their values in the Lie superalgebra and fermionic fields take their values in its representation space. At the same time, our approach differs significantly. The main one is that while for them the gauge symmetry group is

S U (2 / 1)

, here we consider only symmetries generated by its even subgroup, i.e., symmetries of the standard electroweak model. The reason is that such formalism fixes the quartic Higgs coupling and at the same time removes the sign and statistics problems. The main result is that the presented model predicts values of the Weinberg angle and the Higgs mass correctly up to the two-loop level. Moreover, the model sets the unification scale coinciding with the electroweak scale and automatically describes the fermions correctly with the correct quark and lepton charges.

Full work available at URL: https://arxiv.org/abs/1012.3692

zbMATH Keywords

symmetry unification gauge Higgs

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Applications of Lie (super)algebras to physics, etc. (17B81) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)