Spectral functions of gauge theories with Banks-Zaks fixed points

We investigate spectral functions of matter-gauge theories that are asymptotically free in the ultraviolet and display a Banks-Zaks conformal fixed point infrared. Using perturbation theory, Callan-Symanzik resummations, UV-IR connecting renormalization group trajectories, we analytically determine gluon, quark, ghost propagators entire complex momentum plane. At weak coupling, find K\"all\'en-Lehmann representation is achieved for all fields, suitable ranges gauge-fixing parameters. strong proliferation conjugated branch cuts renders causal impossible. also derive relations scaling exponents presence or absence propagator nonanalyticities. Further results include fields up to five loop order, bounds on window, an algorithm running gauge coupling at higher loops. Implications our findings extensions other discussed.