[Paper Review] Chern-Simmons electrodynamics and torsion dark matter axions

Zhi‐Fu Gao, L. C. García de Andrade|arXiv (Cornell University)|Apr 21, 2024

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper investigates torsion-induced damping of primordial magnetic fields via dark photons in a Chern-Simons electrodynamics framework with axion-torsion coupling. It shows that axial torsion with a 0-component of 10⁸ MeV and dark photon mass near the axion mass leads to magnetic field damping to ~10⁻⁸ G at the QCD scale—consistent with current universe observations—while also enabling a dynamo mechanism under specific torsion chirality conditions.

ABSTRACT

In this paper, we delve into the influence of torsion axial pseudo vector on dark photons in an axion torsionic background, as investigated previously by Duncan et al[ Nucl Phys B 387:215 (1992)]. Notably, axial torsion, owing to its significantly greater mass compared to axions, gives rise to magnetic helicity in torsionful Chern-Simons (CS) electrodynamics, leading to the damping of magnetic fields. In QCD scale the damping from dark massive photons leads us to obtain a magnetic field of $10^{-8}$ Gauss, which is approximated the order of magnitude of magnetic fields at present universe. This result is obtained by considering that torsion has the value of the 1 MeV at the early universe, and can be improved to the higher value of $10^{-3}$ Gauss when the axial torsion 0-component is given by $10^{8}$ MeV and the mass of dark photon is approximated equal to the axion. The axion plays a crucial role in achieving CS dynamo action arising from axions. This study is useful in deepening our understanding of fundamental physics, from nuclear interactions to the nature of dark matter.

Motivation & Objective

• To investigate the influence of axial torsion on dark photons in a torsionful Chern-Simons electrodynamics framework.
• To determine how torsion and axion interactions affect magnetic field damping at QCD scales.
• To explore the feasibility of a dynamo mechanism driven by axial torsion and dark photon mass.
• To connect axion-torsion transmutation to observable primordial magnetic field strengths.

Proposed method

• Formulates a generalized action for Chern-Simons electrodynamics coupled to axions and dark photons, including kinetic and potential terms.
• Derives field equations via variation of the action with respect to the axion field and vector potential.
• Solves the magnetic wave equation under the ansatz B = B_seed × exp(γt) to analyze growth or decay of magnetic fields.
• Analyzes the characteristic equation for γ to determine dynamo onset or damping based on torsion chirality and mass parameters.
• Uses the QCD scale as a reference, assuming seed field B_seed ≈ 10¹⁷ G and evaluates damping to B_QCD ≈ 10⁻⁸ G.
• Considers the role of magnetic helicity density and the Beltrami-Maxwell condition in sustaining helical magnetic fields.

Experimental results

Research questions

• RQ1 How does axial torsion influence the damping of magnetic fields in Chern-Simons electrodynamics with dark photons?
• RQ2 Can a dynamo mechanism be triggered by axial torsion in the early universe, and under what conditions?
• RQ3 What is the resulting magnetic field strength at the QCD scale when the axial torsion 0-component reaches 10⁸ MeV and dark photon mass matches the axion mass?
• RQ4 How does axion-torsion transmutation affect the evolution of primordial magnetic fields?
• RQ5 What role does the sign of axial torsion (chirality) play in magnetic field amplification or decay?

Key findings

• At the QCD scale, magnetic field damping due to massive dark photons yields a final field strength of approximately 10⁻⁸ Gauss when axial torsion’s 0-component is 10⁸ MeV and dark photon mass matches the axion mass.
• The damping effect is significantly stronger than in torsion-free axionic electrodynamics, which predicts only 10⁻¹³ Gauss, indicating a crucial role for torsion.
• A dynamo mechanism can be initiated when axial torsion is on the order of 10⁵ GeV or 10⁻⁴ GeV, within the energy reach of the LHC.
• Magnetic field decay occurs for positive axial torsion, while amplification is possible for negative (left-chiral) axial torsion, depending on the sign of the γ solution branch.
• The initial axion boson mass is estimated at ~0.1 GeV when fitting the observed B_QCD ≈ 10⁻⁸ G using the relation B_QCD = B × 10⁻²φ₀.
• The model supports the possibility of axion-torsion transmutation and provides a mechanism for generating observable primordial magnetic fields through torsion-driven dynamo action.