[Paper Review] A Simple Model of Dynamical Supersymmetry Breaking with the Generation of Soft Mass(es)

Yifan Cheng, Yan-Min Dai+2 more|arXiv (Cornell University)|Jul 6, 2015

Black Holes and Theoretical Physics3 citations

TL;DR

This paper proposes a simple supersymmetric model based on a four-superfield interaction that dynamically breaks supersymmetry and simultaneously generates soft supersymmetry-breaking masses. The mechanism relies on a composite spin-one vector superfield and a D-term condensate of the superfield magnitude squared, leading to spontaneous supersymmetry breaking without external soft terms.

ABSTRACT

We introduce a simple model of dynamical supersymmetry breaking. It is like a supersymmetric version of a Nambu--Jona-Lasinio model with a spin one composite. The simplest version of the model as presented here has a single chiral superfield (multiplet) with a four-superfield interaction. The latter has the structure of the square of the superfield magnitude square. A vacuum condensate of the latter is illustrated to develop giving rise to supersymmetry breaking with a soft mass term for the superfield. We report also the effective theory picture with a real superfield composite, illustrating the matching effective potential analysis and the vacuum solution conditions for the components. The nature of its fermionic part as the Goldstone mode is presented. Phenomenological application to the supersymmetric standard model is plausible.

Motivation & Objective

• To construct a minimal model of dynamical supersymmetry breaking that generates soft masses without external supersymmetry-breaking sectors.
• To explore whether soft supersymmetry-breaking terms can arise naturally from strong four-superfield interactions in a supersymmetric extension of the Nambu–Jona-Lasinio model.
• To demonstrate that a single chiral supermultiplet with a dimension-six interaction can lead to both dynamical supersymmetry breaking and the generation of soft masses.
• To analyze the effective theory picture using a real superfield composite and match the effective potential to derive vacuum solutions.
• To assess the phenomenological viability of such a mechanism for the supersymmetric Standard Model, particularly in the context of dynamical Higgs and squark mass generation.

Proposed method

• Formulate a supersymmetric Nambu–Jona-Lasinio-type model with a four-superfield interaction of the form $ g^2 \int d^4\theta\, \Phi^\dagger_a \Phi^b \Phi^\dagger_a \Phi^b $, preserving gauge invariance and supersymmetry at the Lagrangian level.
• Introduce a D-term component ($ \theta^2 \bar{\theta}^2 $) in the interaction to allow for the generation of soft mass terms via condensation of $ \langle \Phi^\dagger \Phi \rangle_D $.
• Analyze the gap equation for the condensate $ \langle \Phi^\dagger \Phi \rangle_D $, showing that it leads to a non-vanishing soft mass term for the scalar components.
• Construct an effective theory using a composite real superfield $ U \sim \Phi^\dagger_a \Phi^a $, and match the effective potential to derive vacuum conditions for the component fields.
• Identify the fermionic component of the composite superfield as a Goldstone fermion (Goldstino), confirming the dynamical breaking of supersymmetry.
• Use a quenched planar approximation (analogous to the quenched QED limit) to handle the non-perturbative dynamics, ensuring qualitative reliability in the large-N limit.

Experimental results

Research questions

• RQ1 Can a simple supersymmetric model with only a single chiral supermultiplet dynamically break supersymmetry through a four-superfield interaction?
• RQ2 Does the D-term component of the superfield condensate $ \langle \Phi^\dagger \Phi \rangle_D $ generate a soft mass term for the scalar fields without explicit mass terms?
• RQ3 Can the composite vector superfield arising from the condensate be identified as a spin-one composite, and what is its role in the dynamics?
• RQ4 Is it possible to generate both soft supersymmetry-breaking masses and dynamical electroweak symmetry breaking within a single, minimal framework?
• RQ5 How does the effective potential analysis of the composite superfield $ U $ confirm the vacuum structure and the presence of a Goldstino mode?

Key findings

• The model exhibits spontaneous supersymmetry breaking via the condensation of the D-term component $ \langle \Phi^\dagger \Phi \rangle_D $, which generates a soft mass term for the scalar fields.
• The soft mass term arises dynamically from the four-superfield interaction without requiring any explicit soft-breaking terms or auxiliary sectors.
• The fermionic component of the composite superfield $ U $ is identified as a Goldstino, confirming the dynamical breaking of supersymmetry.
• The effective potential analysis of the composite real superfield $ U $ yields a non-trivial vacuum solution, consistent with the formation of the condensate.
• The model supports a spin-one composite vector superfield as a dynamical composite, suggesting a possible link to gauge boson compositeness.
• The mechanism is viable for phenomenological model building, as it allows for a fully dynamical generation of soft masses and potentially the Higgs sector within a minimal framework, avoiding the hierarchy problem.