Axion-photon-mixing dark matter conversion mediated by torsion mass constrained by the Barbero-Immirzi parameter

In the Standard Model\,(SM) of particle physics, photon-torsion mixing is extended to include the Einstein-Cartan portal to dark-photon-axion-torsion mixing beyond the Standard Model\,(BSM), mediated by torsion. The Barbero-Immirzi(BI) parameter, of the order of $10^{-31}$, is more stringent than those obtained by Aliberti and Lambiase using matter-antimatter asymmetry. This paper presents the coupling of the SM with dark matter\,(DM) axions, both mediated by torsion. We discuss tordions, the quanta of torsion, and the damping of propagating torsion. It is shown that with both kinds of vectorial torsion masses, equations from Einstein-Cartan-Holst gravity can be derived, which reduce to axionic photon equations where torsion appears only through its mass spectrum. Photon-axion conversions and axion mixing are found to depend on the BI parameter. This study demonstrates that when the spin-0 torsion mass is finite and Proca electrodynamics is not ghost-free, dark axion masses align with spin-0 torsion masses via axion-driven torsion and photon-torsion mixing. Our results provide innovative insights into Proca gravity models and the role of torsion in photon-axion conversion and dark matter dynamics, thereby offering a solid foundation for future research and new theoretical frameworks in quantum gravity.