Towards the minimal renormalizable supersymmetric E 6 model

Abstract

Abstract:We find an explicit renormalizable supersymmetric E 6 model with all the ingredients for being realistic. It consists of the Higgs sector 351 + 351 + 27 + 27, which breaks E 6 directly to the Standard Model gauge group. Three copies of 27 dimensional representations then describe the matter sector, while an extra 27 + 27 pair is needed to successfully split the Standard Model Higgs doublet from the heavy Higgs triplet. We perform the analysis of the vacuum structure and the Yukawa sector of this model, as well as compute contributions to proton decay. Also, we show why some other simpler E 6 models fail to be realistic at the renormalizable level.

A minimal supersymmetric E6 unified theory

“…In a minimal E 6 case with 27 + 27 + 351 ′ + 351 ′ , there are many more doublets which couple to fermions, yet the naive DT splitting fails (a completely different approach to DT splitting in E 6 can be found in [12]). We thus proposed in [11] to add another 27 + 27 pair. In this way, the Yukawa sector consisted of three Yukawa matrices: the matter fields (3 copies of 27 F ) have one coupling to the 351 ′ and a coupling to each of the two Higgs-like 27s.…”

“…The purpose of this paper is to find an E 6 theory with only two Yukawa matrices and thus a simpler Yukawa sector than the model in [11], while keeping the symmetry breaking sector as simple as possible. The idea is to add to the minimal breaking sector (instead of the extra 27 + 27 pair) another multiplet, which preferably has the following properties:…”

“…Five different appendices collect various definitions and technical results. All explicit computation in E 6 has been performed using methods from [21] and [11]; also, [22][23][24] might also prove useful to the reader.…”

“…The renormalizable E 6 SUSY GUT that we consider here is an alternative to the model in [11]. It is motivated by the fact that the minimal Higgs sector in a renormalizable SUSY E 6 model, which can break E 6 to the Standard Model, is 351 ′ +351 ′ +27+27.…”

“…Recently, two of us have tried to fill this gap by suggesting a possible minimal renormalizable supersymmetric E 6 model [11]. The Higgs sector is composed of pairs of fundamental 27 + 27 and the two-index symmetric 351 ′ + 351 ′ representations.…”