Greybody factors emitted by a regular black hole in a non-minimally coupled Einstein-Yang-Mills theory

In this paper, we study the greybody factors (GFs) for fermions with different spins and bosons in the regular black hole (BH) predicted by a non-minimal Einstein-Yang-Mills (EYM) theory. We investigate the effect of magnetic charge on effective potentials and GFs. For this purpose, we consider the Dirac and Rarita-Schwinger, as well as Klein-Gordon equations. First, we study the Dirac equation in curved spacetime for massive and massless spin-1/2 fermions. We then separate the Dirac equation into sets of radial and angular equations. Using the analytical solution of the angular equation, the Schr\"{o}dinger-like wave equations with potentials are derived by decoupling the radial wave equations via the tortoise coordinate. We also consider the Rarita-Schwinger equation for massless spin-3/2 fermions and derive the one-dimensional Schr\"odinger wave equation with gauge-invariant effective potential. For bosons, we study the Klein-Gordon equation in the regular non-minimal EYM BH. Afterward, semi-analytic methods were used to calculate the fermionic and bosonic GFs. Finally, we discuss the graphical behavior of the obtained effective potentials and bounds on the GFs. According to graphs, the GF is highly influenced by the potential's shape, which is determined by the parameterization of the model. This is in line with quantum theory.