Effects of Dimension-5 Operators in $E_6$ Grand Unified Theories

Abstract

The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate the group theoretic nature of them for the well known E(6) model. Considering the breaking chains $E_6\mapsto H=SO(10)\times U_{V^{\prime }}(1)\mapsto SU(5)\times U_V(1)\times U_{V^{\prime }}(1)\mapsto SU(3)\times SU(2)\times U_Z(1)\times U_V(1)\times U_{V^{\prime }}(1)$ and $E_6\mapsto H=SO(10)\times U_{V^{\prime }}(1)\mapsto SU(4)\times S{U}_L(2)\times S{U}_R(2)\times U_{V^{\prime }}(1)\mapsto SU(3)\times S{U}_L(2)\times S{U}_R(2)\times U_S(1)\times U_{V^{\prime }}(1)$, we derive and give all of the Clebsch-Gordan coefficients ${\Phi }_{s,z}^{(r)}$ associated with $E_6$ breaking to the standard model. Some applications of the results are discussed shortly.

8 pages, latex, minor changes, accepted for the publication in MPLA

References in corpus (4)

• Non-universal gaugino masses from non-singlet F-terms in non-minimal unified models
• Grand unification and enhanced quantum gravitational effects
• Supersymmetry Breaking Scalar Masses and Trilinear Soft Terms From High-Dimensional Operators in E_6 SUSY GUT
• Realistic Standard Model Fermion Mass Relations in Generalized Minimal Supergravity (GmSUGRA)

Cited by in corpus (2)

• Flavour anomalies and dark matter assisted unification in $SO(10)$ GUT
• Gauge coupling unification with extra Higgs doublets