The Lagrangian of the Standard Model of particle physics consists of four sectors: the Yang-Mills, the Higgs, the Dirac, and the Yukawa sector. In this talk we study the Dirac-Yang-Mills (DYM) sector in isolation in the Riemannian setting. Variation of the Lagrangian leads to a system of partial differential equations, called the DYM equations, and whose solutions are referred to as DYM pairs. Our goal is to study spherically symmetric DYM pairs on with structure group SU(2), on Riemannian manifolds of dimension 3. In particular, we will systematically obtain the most general spherically symmetric ansatz, which turns the DYM equations into a system of non-autonomous ODEs. We will then construct several different families of solutions to this system, leading to new examples Dirac-Yang-Mills pairs (most notably also on closed manifolds). This is joint work with Adam Lindström.