Flavor structure of E6 GUT models

TL;DR

This paper explores how specific vacuum expectation values in E6 GUT models with SU(2) family symmetry influence CP violation and quark mixing, linking theoretical predictions to experimental measurements of V_{ub}.

Contribution

It demonstrates that the cancellation leading to V_{ub} rom O(  4) in certain E6 models depends on the adjoint Higgs VEV not breaking U(1)_{B-L}, connecting GUT symmetry breaking to observable CP violation.

Findings

V_{ub} rom O(  4) is explained by a specific Higgs VEV alignment.

The Higgs VEV direction affects the solution to the doublet-triplet splitting problem.

Experimental measurement of V_{ub} can reveal the Higgs VEV structure in E6 models.

Abstract

It has been pointed out that in E6 grand unified theory with SU(2) family symmetry, the spontaneous CP violation can solve the supersymmetric CP problem. The scenario predicts V_{ub} \sim O(\lambda^4) rather than O(\lambda^3) which is naively expected value, because of a cancellation at the leading order. Since the experimental value of V_{ub} is O(\lambda^4), it must be important to consider the reason and the conditions for the cancellation. In this paper, we give a simple reason for the cancellation and show that in some E6 models such a cancellation requires that the vacuum expectation value (VEV) of the adjoint Higgs does not break U(1)_{B-L}. Note that this direction of the VEV plays an important role in solving the doublet-triplet splitting problem by Dimopoulos-Wilczek mechanism. In this E6 models, the experiments may measure the direction of the adjoint Higgs VEV by measuring the size of V_{ub} \sim O(\lambda^4).