[Paper Review] Some Composite Hadrons and Leptons which induce Supersymmetry Breaking in the Supersymmetric Standard Model: Cybersusy III

John A. Dixon|ArXiv.org|Aug 16, 2008

Biofield Effects and Biophysics4 references6 citations

TL;DR

This paper proposes a composite model of supersymmetry breaking in the Supersymmetric Standard Model (SSM) via BRS cohomology constraints, introducing leptonic and hadronic dotspinor pseudosupermultiplets that generate mass matrices for superpartners. The key result is that solutions to the constraint equations—particularly from the special term $ d_{3,{ m special}} $—yield physical particles like charged leptons and baryons with $ Q = -1 $, linking their structure to supersymmetry breaking through cybersusy.

ABSTRACT

This is the third paper in a series of four papers which introduce cybersusy, which is a new mechanism for supersymmetry breaking in the supersymmetric standard model (SSM). In this paper we display some solutions to the constraint equations of BRS cohomology in the SSM. In particular we discuss the leptonic dotspinor pseudosupermultiplets that were used in Cybersusy I to calculate leptonic supersymmetry breaking in the supersymmetric standard model. We also introduce examples of hadronic dotspinor pseudosupermultiplets that will induce baryonic supersymmetry breaking in the SSM for the baryons with charge Q=-1, and related supersymmetry partner baryons. Some interesting relationships between the peculiar structure of the SSM, the existence of solutions for the BRS constraints, and supersymmetry breaking using cybersusy are noted.

Motivation & Objective

• To derive and solve the BRS cohomology constraint equations for composite chiral dotted pseudosuperfields in the Supersymmetric Standard Model (SSM).
• To construct explicit examples of leptonic and hadronic dotspinor pseudosupermultiplets that induce supersymmetry breaking.
• To demonstrate how solutions to the constraint equations correspond to physical particles, such as leptons and baryons with charge $ Q = -1 $.
• To establish a connection between the peculiar structure of the SSM and the emergence of supersymmetry-breaking states via cybersusy.

Proposed method

• The paper uses the BRS cohomology framework to derive the nilpotent operator $ \delta $, arising from the BRS-ZJ identity after auxiliary field integration in the Wess-Zumino model.
• It introduces fundamental chiral dotted pseudosuperfields $ \hat{\phi}^{i}_{\dot{\alpha}} $ and scalar pseudosuperfields $ \hat{A}^{i} $ as building blocks for composite structures.
• The constraint equations for simple composite chiral dotted pseudosuperfields $ \hat{\omega}_{\dot{\alpha}_1\cdots\dot{\alpha}_n} $ are derived and solved within the SSM framework.
• The generic $ d_3 $ operator is decomposed into $ d_{3,{\rm special}} $ and $ d_{3,{\rm remaining}} $, with only the former contributing to the physical solutions.
• The special term $ d_{3,{\rm special}} = \overline{C}_{\dot{\alpha}} \left\{ g\epsilon_{ij}H^iK^j \overline{\psi}_{J\dot{\alpha}}^{\dagger} + \cdots \right\} $ is identified as the source of physical particle solutions.
• The method relies on the superpotential structure and gauge symmetry breaking to generate mass matrices for superpartners via the cohomology solutions.

Experimental results

Research questions

• RQ1 How do composite dotspinor pseudosupermultiplets in the SSM satisfy the BRS cohomology constraints necessary for supersymmetry breaking?
• RQ2 What role does the special term $ d_{3,{\rm special}} $ play in generating physical leptons and baryons with $ Q = -1 $?
• RQ3 Why do the solutions to the constraint equations correspond to known particles like charged leptons and baryons, despite not being generators of the standard $ SU(3)\times SU(2)\times U(1) $ symmetries?
• RQ4 How does the left-right asymmetry in the SSM superpotential enable the formation of bound-state-like solutions in the cohomology space?
• RQ5 What is the significance of the $ \epsilon_{ij}H^iK^j $ contraction in generating the $ J $-field's supersymmetry-breaking contribution?

Key findings

• The special term $ d_{3,{\rm special}} $, containing $ g\epsilon_{ij}H^iK^j \overline{\psi}_{J\dot{\alpha}}^{\dagger} $, is the primary source of solutions to the BRS cohomology constraints in the SSM.
• Solutions to the constraint equations yield physical leptons and baryons with charge $ Q = -1 $, indicating that these particles emerge as composite states from the cohomology structure.
• The leptonic and hadronic dotspinor pseudosupermultiplets are constructed from the superpotential via contractions with fields like $ H^i, K^i, L^{pi}, Q^{cpi}, P^q, R^q, T_c^q, B_c^q $.
• The remaining terms $ d_{3,{\rm remaining}} $, involving $ \psi_{Kj\dot{\alpha}}^{\dagger} $ and $ \psi_{Hi\dot{\alpha}}^{\dagger} $, do not contribute to the current solutions and are likely relevant to gauged sectors such as weak bosons and mesons.
• The solutions are not associated with the standard global symmetries of the SSM, suggesting they represent more subtle, bound-state-like structures in the cohomology space.
• The model establishes a mechanism—cybersusy—wherein supersymmetry breaking arises from composite structures in the SSM, with mass matrices derived from the cohomology solutions.