arXiv subjects

Gregory W. Anderson

Publications and source records attributed to Gregory W. Anderson.

3 recordsLinked to original sources

arXiv2001

E_6 unification model building III. Clebsch-Gordan coefficients in E_6 tensor products of the 27 with higher dimensional representations

$E_6$ is an attractive group for unification model building. However, the complexity of a rank 6 group makes it non-trivial to write down the structure of higher dimensional operators in an $E_6$ theory in terms of the states labeled by quantum numbers of the Standard Model gauge group. In this paper, we show the results of our computation of the Clebsch-Gordan coefficients for the products of the {\bf 27} with irreducible representations of higher dimensionality: ${\bf 78}$, ${\bf 351}$, ${\bf 351^\prime}$, ${\bf \ol{351}}$, and ${\bf \ol{351^\prime}}$. Application of these results to $E_6$ model building involving higher dimensional operators is straightforward.

hep-ph↗

arXiv2000

E_6 unification model building II. Clebsch-Gordan coefficients of 78$\otimes$78

We have computed the Clebsch-Gordan coefficients for the product (000001) $\otimes$ (000001), where (000001) is the adjoint 78-dimensional representation of $E_6$. The results are presented for the dominant weights of the irreducible representations in this product. As a simple application we express the singlet operator in $ 27 \otimes 78 \otimes \bar{27}$ in terms of multiplets of the Standard Model gauge group.

hep-ph↗

arXiv1999

$E_6$ unification model building I: Clebsch-Gordan coefficients of $27\otimes \ol{27}$

In an effort to develop tools for grand unified model building for the Lie group $E_6$, in this paper we present the computation of the Clebsch-Gordan coefficients for the product (100000) $\otimes$ (000010), where (100000) is the fundamental 27-dimensional representation of $E_6$ and (000010) is its charged conjugate. The results are presented in terms of the dominant weight states of the irreducible representations in this product. These results are necessary for the group analysis of $E_6$ operators involving also higher representations, which is the next step in this project. In this paper we apply the results to the construction of the operator ${\bf 27}^3$.

hep-ph↗