Chern-Simmons electrodynamics and torsion dark matter axions

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.