[Paper Review] Cosmological Supersymmetry Breaking and the Power of the Pentagon: A Model of Low Energy Particle Physics

T. Banks|ArXiv.org|Oct 12, 2005

Cosmology and Gravitation Theories10 references19 citations

TL;DR

This paper proposes the 'Pentagon' model, a low-energy effective theory implementing Cosmological Supersymmetry Breaking (CSB) via a strongly coupled gauge sector with singlet fields S and T. It achieves natural electroweak symmetry breaking, predicts tanβ ≈ 1, and generates a TeV-scale axion-like particle that may resolve the strong CP problem—though experimental constraints require fine-tuning of the gauge scale to ~3 TeV to avoid exclusion.

ABSTRACT

I present a low energy Lagrangian implementing the idea of Cosmological SUSY breaking (CSB). The model predicts ${ m tan}β\sim 1$, and incorporates a new mechanism for breaking of $SU(2) imes U(1)$. The Higgs mass is determined by new physics and can evade the bounds of the MSSM. The model resolves the CP and flavor problems of SUSY. The up quark mass is non-vanishing. An axion-like particle, with TeV scale decay constant, appears inevitably. Such a particle is experimentally ruled out if it has conventional QCD axion couplings. The problem {\it may} be avoided by adding dimension 5 operators, which explicitly break the axial symmetry, but this probably introduces a strong CP problem.

Motivation & Objective

• To construct a viable low-energy effective field theory implementing Cosmological Supersymmetry Breaking (CSB) without relying on R-symmetry breaking.
• To resolve the strong CP problem and flavor/CP problems in supersymmetric models through a new mechanism involving a strongly coupled gauge sector.
• To generate a TeV-scale axion-like particle that could solve the strong CP problem, while avoiding experimental exclusion via explicit symmetry breaking via dimension-5 operators.
• To explore the dual interpretation of the model as either dynamical SUSY breaking (DSB) or CSB, and assess their phenomenological consequences.
• To investigate anthropic constraints on the cosmological constant in the model, linking its observed value to the stability of stars and galaxies.

Proposed method

• Introduces a strongly coupled gauge theory G with matter fields transforming under SM quantum numbers, coupled to a singlet chiral superfield G and two R-charge-2 singlets S and T.
• Implements CSB via a non-perturbative superpotential term involving the cosmological constant λ, generating an effective potential with a minimum at G ~ M, breaking SUSY dynamically.
• Uses the inverse Kähler metric K^{GḠ} generated by the strong dynamics of G to mediate SUSY breaking to the visible sector.
• Tunes the superpotential with a constant term to set the low-energy cosmological constant to the observed value λ, ensuring metastability of the de Sitter vacuum.
• Analyzes the Higgs sector by including F-terms and D-terms, showing that the Higgs mass is stabilized via a combination of F-term and D-term contributions, with tanβ ≈ 1 enforced by D-term minimization.
• Considers the emergence of a pseudo-Nambu-Goldstone boson (PNGB) from the axial symmetry, which acts as a QCD axion; its mass is raised via dimension-5 operators to avoid experimental exclusion.

Experimental results

Research questions

• RQ1 Can a low-energy effective theory realize Cosmological Supersymmetry Breaking (CSB) without R-symmetry breaking or elementary R-charge-2 fields?
• RQ2 How can the strong CP problem be solved without introducing a conventional QCD axion or massless up quarks?
• RQ3 What is the role of the PNGB in the Pentagon model, and can its mass be raised sufficiently to evade experimental bounds while remaining a viable solution to the strong CP problem?
• RQ4 How does the interplay between the gauge scale M, the cosmological constant λ, and the electroweak scale v = 250 GeV constrain the model phenomenologically?
• RQ5 Can anthropic reasoning explain the observed value of the cosmological constant in this model, given its impact on nuclear and stellar physics?

Key findings

• The model realizes Cosmological SUSY Breaking via a strongly coupled gauge sector G with R-symmetry preserved at the fundamental level, avoiding the need for elementary R-charge-2 fields.
• The Higgs sector achieves tanβ ≈ 1 due to the minimization of D-terms and F-terms, with the electroweak scale stabilized at v = 250 GeV via fine-tuning of order 1% when Λ₅ = 3 TeV.
• A TeV-scale axion-like particle emerges as a PNGB from the axial symmetry, which could solve the strong CP problem if its couplings are modified via dimension-5 operators.
• The axion mass can be raised to ~1 TeV via explicit breaking from dimension-5 operators, avoiding experimental exclusion, though this requires tuning the gauge scale to ~3 TeV.
• The model predicts that the cosmological constant λ must be tuned to ~10⁻¹²⁰ in Planck units, and anthropic constraints from stellar and galactic stability may bound it within a few orders of magnitude of the observed value.
• The model exhibits a dual interpretation: as a CSB model with metastable SUSY-breaking vacua, or as a DSB model with a low-scale axion, with the key difference being the origin of the axion mass.