Can supersymmetry breaking lead to electroweak symmetry breaking via formation of scalar bound states?

TL;DR

This paper explores the idea that supersymmetry breaking, specifically large A_t terms, can induce electroweak symmetry breaking through the formation of scalar bound states, potentially altering Higgs mass predictions.

Contribution

It introduces a novel mechanism where supersymmetry breaking triggers Higgs-like bound states, challenging traditional relations between gauge and Higgs self-couplings.

Findings

Calculated critical A_t for symmetry breaking using Bethe-Salpeter equation.

Developed an approximation for the complex kernel of the BS equation.

Outlined a pathway for a realistic model with bound state and Higgs mixing.

Abstract

The recent discovery of the putative 125-GeV Higgs boson has motivated a number of attempts to reconcile its relatively large mass with the predictions of the minimal supersymmetric standard model (MSSM). Some approaches invoked large trilinear supersymmetry-breaking terms A_t between stops and one of the elementary Higgs fields. We consider the possibility that electroweak symmetry breaking may be triggered by supersymmetry breaking with a large A_t, large enough to generate a composite field with the same quantum numbers as the Higgs boson and with a non-vanishing vacuum expectation value. In the resulting vacuum, the usual relation between the gauge couplings and the Higgs self-coupling does not apply, and there is no reason to expect the same upper bound on the mass of the lightest Higgs boson. In a simple model where the bound state is assumed to have no mixing with the other fields, we calculate the critical coupling A_t necessary for symmetry breaking using the lowest-order Bethe-Salpeter (BS) equation. Study of the BS equation is complicated by the structure of its lowest-order kernel, which is a crossed box graph, but we find an accurate approximation to its solution. In a realistic model, the mixing of the bound state with the fundamental Higgs boson creates a symmetry-breaking seesaw. We outline the steps toward a realistic model.