Chern-Simmons electrodynamics and torsion dark matter axions

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.