For muoniated radical spectroscopy studies, benzene has long been the classic prototype system. However most of these studies have been at higher temperatures, often in the liquid phase, whereas calculations of hyperfine coupling are generally made at zero temperature, deep in the solid phase. It is therefore desirable to obtain reference ALC data for benzene extending to as low a temperature as possible, to allow accurate comparison to be made with DFT computations of the full hyperfine tensor including the effects of zero point motion. HiFi will be therefore be used to study the ALC spectrum of solid benzene over as wide a range of temperature as possible and spectral anomalies suggested by previous reports will also be investigated further, in particular a low temperature spectral feature that is suggested to be a signature of quantum diffusion of muonium round the ring.