[Paper Review] Coupling of fermionic fields with mass dimensions one to the O'Raifeartaigh model

Kai E. Wunderle, Rainer Dick|arXiv (Cornell University)|Aug 23, 2012

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper proposes a supersymmetric extension of the O'Raifeartaigh model by coupling fermionic fields with mass dimension one, showing that such coupling can restore supersymmetry at the cost of breaking Lorentz invariance. The model yields two distinct solutions: one with spontaneous supersymmetry breaking like the original O’Raifeartaigh model, and another where supersymmetry is restored via non-vanishing fermionic expectation values, leading to a viable candidate for supersymmetric dark matter with experimentally accessible signatures.

ABSTRACT

The objective of this article is to discuss the coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model to study supersymmetry breaking for fermionic fields with mass dimension one. We find that the coupled model has two distinct solutions. The first solution represents a local minimum of the superpotential which spontaneously breaks supersymmetry in perfect analogy to the O'Raifeartaigh model. The second solution is more intriguing as it corresponds to a global minimum of the superpotential. In this case the coupling to the fermionic sector restores supersymmetry. However, this is achieved at the cost of breaking Lorentz invariance. Finally, the mass matrices for the multiplets of the coupled model are presented. It turns out that it contains two bosonic triplets and one fermionic doublet which are mass multiplets. In addition it contains a massless fermionic doublet as well as one fermionic triplet which is not a mass multiplet but rather an interaction multiplet that contains component fields of different mass dimension. These results show that the presented model for fermionic fields with mass dimension one is a viable candidate for supersymmetric dark matter that could be accessible to experiments in the near future.

Motivation & Objective

• To extend the O’Raifeartaigh model by incorporating fermionic fields with mass dimension one, generalizing ELKO spinors within a supersymmetric framework.
• To investigate how coupling these exotic fermions affects supersymmetry breaking and Lorentz invariance in a supersymmetric model.
• To determine whether the coupled system supports mass multiplets and identifies potential dark matter candidates.
• To explore the viability of mass-dimension-one fermions as a hidden-sector dark matter candidate with detectable couplings to the Higgs sector.
• To analyze the structure of mass matrices and multiplet content in the coupled model, especially the emergence of interaction multiplets with mixed mass dimension fields.

Proposed method

• Construction of a superpotential that couples a chiral superfield with non-vanishing vacuum expectation value to a spinor superfield with mass dimension one.
• Minimization of the superpotential to determine vacuum expectation values of component fields, identifying two distinct solutions: trivial and non-trivial.
• Derivation of equations of motion for auxiliary and fermionic fields, including contributions from the coupling strength to the F-terms and fermionic sector.
• Expansion of component fields around their vacuum expectation values to compute mass matrices and analyze multiplet structures.
• Assessment of Lorentz invariance by examining whether non-vanishing fermionic expectation values introduce preferred directions in spacetime.
• Consistency check by reducing the coupling strength to zero, confirming that the model reduces to the original O’Raifeartaigh and fermionic field models.

Experimental results

Research questions

• RQ1 Can fermionic fields with mass dimension one be consistently coupled to the O’Raifeartaigh model while preserving supersymmetry?
• RQ2 Does the coupling between mass-dimension-one fermions and the O’Raifeartaigh model lead to a restoration of supersymmetry, and if so, under what conditions?
• RQ3 What is the impact of the coupling on Lorentz invariance, and does the model break this symmetry when supersymmetry is restored?
• RQ4 How do the mass matrices and multiplet structures in the coupled model differ from those in the original O’Raifeartaigh model?
• RQ5 Can the resulting model support a viable, experimentally accessible candidate for supersymmetric dark matter?

Key findings

• The coupled model admits two distinct vacuum solutions: one with spontaneous supersymmetry breaking, identical to the original O’Raifeartaigh model, and another where supersymmetry is restored via non-vanishing expectation values of fermionic fields.
• Supersymmetry restoration occurs at the cost of breaking Lorentz invariance, as the non-vanishing fermionic expectation values introduce a preferred spacetime direction.
• The mass matrices reveal two bosonic triplets and one fermionic doublet that form mass multiplets, along with a massless fermionic doublet and a fermionic triplet that is not a mass multiplet due to component fields of different mass dimensions.
• The bosonic mass terms become dependent on both the coupling strength and the fermionic mass scale, unlike in the original O’Raifeartaigh model, which relied on an arbitrary scale parameter.
• The fermionic triplet in the O’Raifeartaigh model is replaced by a fermionic doublet that depends on the coupling strength and fermionic mass scale, and a new interaction multiplet emerges with mixed mass dimension fields.
• The model provides a viable candidate for supersymmetric dark matter that couples dominantly to the Higgs field, potentially allowing experimental detection via deviations in Higgs branching ratios at the LHC.