Log-periodic oscillations of transverse momentum distributions

Large p_T transverse momentum distributions exhibit apparently a power-like behavior. We argue that, under closer inspection, this behavior is in fact decorated with some log-periodic oscillations. Assuming that this is genuine effect and not experimental artefact, it suggests that either the exponent of the power-like behavior is in reality complex number or that there is a scale parameter which exhibits specific log-eriodic oscillations. This problem is discussed using Tsallis distributions with scale parameter being a temperature T. At this stage we consider both possibilities on equal footing.