SU(2/1) gauge-Higgs unification

TL;DR

This paper presents a gauge-Higgs unification model based on the graded Lie group SU(2/1), which accurately predicts the Weinberg angle and Higgs mass at two-loop level, unifies fermions, and sets the unification scale at the electroweak scale.

Contribution

The model uniquely uses only the even subgroup of SU(2/1), fixing the Higgs quartic coupling and resolving sign and statistics issues, leading to correct electroweak predictions.

Findings

Predicts Weinberg angle and Higgs mass accurately at two-loop level

Sets unification scale at the electroweak scale

Automatically incorporates correct fermion charges

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 $SU(2)\times U(1)_{Y}$ is embedded in the graded Lie group $SU(2/1)$. 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 $SU(2/1)$, 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.