0.1-10 MeV observations of the black hole microquasar Cygnus X-1 have shown the presence of a spectral feature in the form of a power law in addition to the standard black body and Comptonization components observed by INTEGRAL. This so-called high-energy tail has recently been shown to be strong in its hard spectral state and interpreted as high-energy part of the emission from a compact jet. This result was, however, obtained from a data set dominated by hard state observations. In the soft state, only upper limits on the presence and hence the potential parameters of a high-energy tail could be derived. Using an extended data set we aim at obtaining better constraints on the properties of this spectral component in both states. We make use of data obtained from 15 years of observations with the INTEGRAL satellite. The data set is separated into the different states and we analyse stacked state-resolved spectra obtained from the X-ray monitors, the gamma-ray imager, and the gamma-ray spectrometer onboard. A high-energy component is detected in both states confirming its earlier detection in the hard state and its suspected presence in the soft state with INTEGRAL. We first characterize the high-energy tail components in the two states through a model-independent, phenomenological analysis. We then apply physical models based on hybrid Comptonization. The spectra are well modeled in all cases, with a similar goodness of the fits. While in the phenomenological approach the high-enery tail has similar indices in both states, the fits with the physical models seem to indicate different properties. We discuss the potential origins of the high-energy components in both states, and favor an interpretation where the part of the high-energy component is due to a compact jet in the hard state and hybrid Comptonization in either a magnetised or non-magnetised corona in the soft state.
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