[Paper Review] Suppressed SUSY for the SU(5) Grand Unified Supergravity Theory

John A. Dixon|arXiv (Cornell University)|Jun 26, 2017

Cosmology and Gravitation Theories10 references3 citations

TL;DR

This paper proposes Suppressed SUSY as a replacement for spontaneous SUSY breaking in an SU(5) Grand Unified Supergravity theory, using an Exchange Transformation to alter field content while preserving local SUSY's constraints. It predicts a naturally zero cosmological constant and a mass spectrum with X/Y bosons and Higgs multiplets at Planck- and SuperPlanck-scale masses, respectively, using only three dimensionless parameters and the Planck mass.

ABSTRACT

This paper starts with the most basic SU(5) Grand Unified Theory, coupled to Supergravity. Then it builds a new theory, incorporating the ideas of Suppressed SUSY. Suppressed SUSY is an alternative to the spontaneous breaking of SUSY. It does not need an invisible sector or explicit soft breaking of SUSY. It varies the content of the supermultiplets while keeping the restrictive nature of SUSY. For the simple model and sector constructed here, Suppressed SUSY has only three dimensionless parameters, plus the Planck mass. At tree level, this predicts a set of 8 different new masses, along with a cosmological constant that is naturally zero. The X and Y vector bosons get Planck scale masses $2 \sqrt{10} g_5 M_{ m P}$. The five scalar multiplets that accompany the Higgs, and the Gravitino, all get colossally huge `SuperPlanck' scale masses of order $M_{ m SP} \approx 10^{17} M_{ m P}$ from a see-saw mechanism that arises from the theory. This new mass spectrum, the well-known $SU(5)$ weak angle problem, and the cosmological constant value, should serve as guides for further modifications for the new Action.

Motivation & Objective

• To resolve the unpredictive nature of SUSY GUTs coupled to supergravity by replacing spontaneous SUSY breaking with Suppressed SUSY.
• To eliminate the need for an invisible sector or explicit soft SUSY breaking, which underlie the MSSM’s over-parameterization.
• To construct a minimal model with only three dimensionless parameters and the Planck mass, achieving a naturally vanishing cosmological constant at tree level.
• To explore whether Suppressed SUSY can generate a viable mass spectrum, including heavy X/Y bosons and a stabilized Higgs mass via a see-saw mechanism.
• To re-evaluate nucleon decay and dark matter prospects by reclassifying superpartners as non-existent or extremely heavy, avoiding MSSM constraints.

Proposed method

• Applying an Exchange Transformation—a linear, invertible canonical transformation—to the Master Equation of local SUSY, interchanging sources and fields to redefine the quantized content of the theory.
• Rewriting the scalar potential in 'Counting Form' to reveal a superpotential structure that enables a see-saw mechanism for mass generation.
• Using a 'square root' mass-style superpotential to ensure the scalar potential's vacuum expectation value yields a vanishing cosmological constant at tree level.
• Deriving the mass spectrum via explicit Mathematica calculations of the Higgs and gauge sector mass matrices, dependent only on $ g_1, g_2, g_5 $, and $ M_P $.
• Applying the see-saw mechanism to the scalar multiplets and gravitino, generating SuperPlanck-scale masses of order $ M_{ m SP} o 10^{17} M_P $.
• Removing squarks, sleptons, gauginos, and Higgsinos from the spectrum, while retaining key Higgs and gauge multiplets to test consistency with electroweak symmetry breaking.

Experimental results

Research questions

• RQ1 Can Suppressed SUSY eliminate the need for spontaneous SUSY breaking and its associated fine-tuning and invisible sector problems in GUTs?
• RQ2 Does the Exchange Transformation preserve the restrictive structure of local SUSY while allowing a physically viable mass spectrum?
• RQ3 Can a naturally zero cosmological constant be achieved at tree level in an SU(5) GUT-supergravity model using Suppressed SUSY?
• RQ4 Can the see-saw mechanism in this framework generate a light Higgs boson mass while keeping other scalars and gauge bosons at SuperPlanck or Planck scales?
• RQ5 What are the implications for nucleon decay and dark matter if superpartners are suppressed rather than present at weak scale masses?

Key findings

• The X and Y vector bosons acquire Planck-scale masses of $ 2ar{10}g_5 M_P $, consistent with the SU(5) GUT prediction but stabilized by Suppressed SUSY.
• The five scalar multiplets (Higgs octet, triplet, H⁺, Higgs₂, Higgs₃) and the gravitino all obtain SuperPlanck-scale masses: $ M_{ m SP} o 10^{17} M_P $, with values ranging from 0.68 to 2.05 $ M_{ m SP} $.
• The cosmological constant is naturally zero at tree level due to a balance in the scalar potential, achieved via the superpotential's structure and the 'Counting Form' rewriting.
• The W and Z boson masses are consistent with observation only when the ratio $ r = g_2/g_1 o -2 - rac{2f^2}{9} + O(f^4) $, with $ g_5 f o M_W / M_P o 10^{-17} $, ensuring correct electroweak symmetry breaking.
• The lightest neutral scalar (Higgs) mass is fixed by the see-saw mechanism and determines $ g_1 $ in terms of $ f $ and $ g_5 $, leading to a consistent mass hierarchy.
• The gravitino is extremely massive (~1 Megatonne) and stable in this model, suggesting a potential role as a dark matter candidate if modified to allow decay at loop level.