Cygnus X--1 is the first Galactic source confirmed to host an accreting black hole. It has been detected across the entire electromagnetic spectrum from radio to GeV $gamma$-rays. The sources radio through mid-infrared radiation is thought to originate from the relativistic jets. The observed high degree of linear polarisation in the MeV X-rays suggests that the relativistic jets dominate in this regime as well, whereas a hot accretion flow dominates the soft X-ray band. The origin of the GeV non-thermal emission is still debated, with both leptonic and hadronic scenarios deemed to be viable. In this work, we present results from a new semi-analytical, multi-zone jet model applied to the broad-band spectral energy distribution of Cygnus X--1 for both leptonic and hadronic scenarios. We try to break this degeneracy by fitting the first-ever high-quality, simultaneous multiwavelength data set obtained from the CHOCBOX campaign (Cygnus X--1 Hard state Observations of a Complete Binary Orbit in X-rays). Our model parameterises dynamical properties, such as the jet velocity profile, the magnetic field, and the energy density. Moreover, the model combines these dynamical properties with a self-consistent radiative transfer calculation including secondary cascades, both of leptonic and hadronic origin. We conclude that sensitive TeV $gamma$-ray telescopes like Cherenkov Telescope Array (CTA) will definitively answer the question of whether hadronic processes occur inside the relativistic jets of Cygnus X--1.
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