Polarization measurements of the microquasar Cygnus X-1 exist at gamma-ray, X-ray, UV, optical and radio frequencies. The gamma-ray emission has been shown to be highly linearly polarized. Here, we present new infrared polarimetric data of Cygnus X-1 taken with the 10.4-m Gran Telescopio Canarias and the 4.2-m William Herschel Telescope. We show that the broadband, radio to gamma-ray flux spectrum and polarization spectrum in the hard state are largely consistent with a simple phenomenological model of a strongly polarized synchrotron jet, an unpolarized Comptonized corona and a moderately polarized interstellar dust component. In this model, the origin of the gamma-ray, X-ray and some of the infrared polarization is the optically thin synchrotron power law from the inner regions of the jet. The model requires the magnetic field in this region to be highly ordered and perpendicular to the axis of the resolved radio jet. This differs to studies of some other X-ray binaries, in which the magnetic field is turbulent, variable and aligned with the jet axis. The model is able to explain the approximate polarization strength and position angle at all wavelengths including the detected X-ray (3 - 5 keV) polarization, except the observed position angle of the gamma-ray polarization, which differs to the model by ~ 60 degrees. Past numerical modelling has shown that a curved synchrotron spectrum can produce a shift in position angle by ~ 60 degrees, which may account for this.
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