  In this paper, we focus on the scientific case of Cygnus OB2, a northern sky
young massive stellar cluster (YMSC) located towards the Cygnus X star-forming
complex. We consider a model that assumes cosmic ray acceleration occurring
only at the termination shock of the collective wind of the YMSC and address
the question of whether, and under what hypotheses, hadronic emission by the
accelerated particles can account for the observations of Cygnus OB2 obtained
by Fermi-LAT, HAWC and LHAASO. In order to do so, we carefully review the
available information on this source, also confronting different estimates of
the relevant parameters with ad hoc developed simulations. Once other model
parameters are fixed, the spectral and spatial properties of the emission are
found to be very sensitive to the unknown properties of the turbulent magnetic
field. Comparison with the data shows that our suggested scenario is
incompatible with Kolmogorov turbulence. Assuming Kraichnan or Bohm type
turbulence spectra, the model accounts well for the Very High Energy (VHE)
data, but fails to reproduce the centrally peaked morphology observed by
Fermi-LAT, suggesting that additional effects might be important for lower
energy $\gamma$-ray emission. We discuss how additional progress can be made
with a more detailed and extended knowledge of the spectral and morphological
properties of the emission.
