Fixing the Pole in the Pyramid

TL;DR

This paper investigates the RG flow of couplings in the Pyramid Scheme, identifying a fixed line near strong coupling, and explores implications for dark matter candidates and phenomenology.

Contribution

It demonstrates the existence of a fixed line in the hidden sector couplings and analyzes the RG flow towards a confining supersymmetric gauge theory, with implications for dark matter.

Findings

Couplings flow to a fixed line near strong coupling edge.

Flow leads to a confining N_F=N_C=3 supersymmetric gauge theory.

A viable dark matter candidate exists with adjusted confinement scale.

Abstract

We revisit the problem of the hidden sector Landau pole in the Pyramid Scheme. There is a fixed line in the plane of hidden sector gauge coupling and a Yukawa coupling between the trianon fields. We postulate that the couplings flow to this line, at a point where the hidden sector gauge coupling is close to the strong coupling edge of its perturbative regime. Below the masses of the heavier trianons, the model quickly flows to a confining N_F=N_C=3 supersymmetric gauge theory, as required by phenomenological considerations. We study possible discrete R-symmetries, which guarantee, among other things, that the basin of attraction of the fixed line has full co-dimension in the space of R-allowed couplings. The Yukawa couplings required to get the fixed line violate the pyrma-baryon symmetries we invoked in previous work to find a dark matter candidate. Omitting one of them, we have a dark matter candidate, and an acceptable RG flow down from the unification scale, if the confinement scale of the hidden sector group is lowered from 5 to 2 TeV.