[Paper Review] Generalized bumblebee models and Lorentz-violating electrodynamics

Michael Seifert|arXiv (Cornell University)|Sep 17, 2009

Noncommutative and Quantum Gravity Theories4 citations

TL;DR

This paper investigates generalized bumblebee models—Lorentz-violating vector field theories where perturbations of a dynamical vector field with a non-zero vacuum expectation value behave as a photon field. Unlike standard electrodynamics, the 'bumblebee photon' propagates at a direction-dependent speed differing from conventional matter and gravity, leading to observable effects such as photon decay and modified kinematics, with bounds derived from resonator experiments, accelerator physics, and cosmic ray observations.

ABSTRACT

The breaking of Lorentz symmetry via a dynamical mechanism, with a tensor field which takes on a non-zero expectation value in vacuum, has been a subject of significant research activity in recent years. In certain models of this type, the perturbations of the "Lorentz-violating field" about this background may be identified with known forces. I present the results of applying this interpretation to the "generalized bumblebee models" found in a prior work. In this model, the perturbations of a Lorentz-violating vector field can be interpreted as a photon field. However, the speed of propagation of this "bumblebee photon" is direction-dependent and differs from the limiting speed of conventional matter, leading to measurable physical effects. Bounds on the parameters of this theory can then be derived from resonator experiments, accelerator physics, and cosmic ray observations.

Motivation & Objective

• To investigate the physical consequences of generalized bumblebee models, where a dynamical vector field breaks Lorentz symmetry via a non-zero vacuum expectation value.
• To explore whether perturbations of this vector field can be interpreted as a photon field with a direction-dependent speed of propagation.
• To derive observable signatures of such a theory, including modified photon kinematics and decay rates.
• To place experimental bounds on the parameters of the underlying Lorentz-violating vector field using resonator experiments, accelerator data, and cosmic ray observations.
• To establish consistency with general relativity and the Standard Model Extension by ensuring decoupling of the Lorentz-violating field from gravity at linearized levels.

Proposed method

• Constructs generalized bumblebee models by promoting Lorentz-violating coefficients in the SME to dynamical vector fields, ensuring geometric consistency with curved spacetime and Bianchi identities.
• Derives linearized equations of motion for the vector field perturbations, showing they match those of linearized Einstein-Maxwell theory under specific conditions.
• Identifies the perturbations of the Lorentz-violating vector field as a 'bumblebee photon' with a dispersion relation dependent on propagation direction.
• Computes the matrix element for photon decay into electron-positron pairs using the modified dispersion relation and interaction Lagrangian, estimating the decay rate via phase space integration.
• Estimates the photon decay rate as Γ ∼ (α/2)βℬ²Eγ√(1−E_d0²/Eγ²), where β and ℬ parameterize Lorentz violation, and α is the fine structure constant.
• Uses order-of-magnitude estimates and phase space volume calculations to derive the scaling behavior of the decay rate, consistent with exact results in isotropic limits.

Experimental results

Research questions

• RQ1 Can perturbations of a dynamical Lorentz-violating vector field in generalized bumblebee models be consistently interpreted as a photon field with a direction-dependent speed of propagation?
• RQ2 What are the observable consequences of such a 'bumblebee photon' theory, particularly in terms of photon decay and modified kinematics?
• RQ3 How do resonator experiments, accelerator physics, and cosmic ray observations constrain the parameters of the underlying Lorentz-violating vector field?
• RQ4 Does the decoupling of the Lorentz-violating field from gravity at linearized levels preserve consistency with general relativity and the SME framework?
• RQ5 What is the order-of-magnitude estimate for the photon decay rate in this theory, and how does it scale with photon energy and Lorentz-violating parameters?

Key findings

• The perturbations of the Lorentz-violating vector field in generalized bumblebee models can be interpreted as a photon field with a direction-dependent speed of propagation, differing from the speed of conventional matter and gravity.
• The theory predicts that the 'bumblebee photon' can decay into electron-positron pairs, with a decay rate estimated as Γ ∼ (α/2)βℬ²Eγ√(1−E_d0²/Eγ²), where β and ℬ quantify Lorentz violation.
• The photon decay rate scales linearly with photon energy Eγ and quadratically with the Lorentz-violating parameter ℬ, indicating potentially measurable effects at high energies.
• The order-of-magnitude estimate for the decay rate is consistent with exact results derived in the spatially isotropic limit by Hohensee et al. (2009).
• Bounds on the Lorentz-violating parameters β and ℬ can be derived from resonator experiments, accelerator data, and cosmic ray observations, which constrain the magnitude of deviations from standard electrodynamics.
• The model maintains consistency with general relativity at linearized levels due to the decoupling of the Lorentz-violating field from the metric, ensuring geometric consistency with Bianchi identities.