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 γ-rays. The source's 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 γ-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.Comment: 16 pages, 4 figures, accepted for publication in MNRA