Generalizing Minimal Supergravity

TL;DR

This paper derives general gauge coupling and gaugino mass relations at the GUT scale in supersymmetric GUTs, providing a framework to test these theories at future colliders through the index k.

Contribution

It introduces a universal approach to gauge coupling and gaugino mass relations in GUTs, enabling experimental tests of GUT models via the index k at colliders.

Findings

Derived all GUT-scale gauge coupling relations for SU(5) and SO(10).

Calculated gaugino mass relations and indices k for various models.

Proposed a new method to test GUTs at colliders using the index k.

Abstract

In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the generic gauge coupling relations at the GUT scale, and the general gaugino mass relations which are valid from the GUT scale to the electroweak scale at one loop. We define the index k for these relations, which can be calculated in GUTs and can be determined at the Large Hadron Collider and the future International Linear Collider. Thus, we give a concrete definition of the GUT scale in these theories, and suggest a new way to test general GUTs at future experiments. We also discuss five special scenarios with interesting possibilities. With our generic formulae, we present all the GUT-scale gauge coupling relations and all the gaugino mass relations in the SU(5) and SO(10) models, and calculate the corresponding indices k. Especially, the index k is 5/3 in the traditional SU(5) and SO(10) models that have been studied extensively so far. Furthermore, we discuss the field theory realization of the U(1) flux effects on the SM gauge kinetic functions in F-theory GUTs, and calculate their indices k as well.