  The detection of gamma-ray emission from accreting pulsars in X-ray binaries
(XRBs) has long been sought after. For some high-mass X-ray binaries (HMXBs),
marginal detections have recently been reported. Regardless of whether these
will be confirmed or not, future telescopes operating in the gamma-ray band
could offer the sensitivity needed to achieve solid detections and possibly
spectra. In view of future observational advances, we explored the expected
emission above 10 GeV from XRBs, based on the Cheng & Ruderman model, where
gamma-ray photons are produced by the decay of pion-0 originated by protons
accelerated in the magnetosphere of an accreting pulsar fed by an accretion
disc. We improved this model by considering, through Monte Carlo simulations,
the development of cascades inside of and outside the accretion disc, taking
into account pair and photon production processes that involve interaction with
nuclei, X-ray photons from the accretion disc, and the magnetic field. We
produced grids of solutions for different input parameter values of the X-ray
luminosity (L_x), magnetic field strength (B), and for different properties of
the region where acceleration occurs. We found that the gamma-ray luminosity
spans more than five orders of magnitude, with a maximum of ~1E35 erg/s. The
gamma-ray spectra show a large variety of shapes: some have most of the
emission below ~100 GeV, others are harder (emission up to 10-100 TeV). We
compared our results with Fermi/LAT and VERITAS detections and upper-limits of
two HMXBs: A0535+26 and GROJ1008-57. More consequential comparisons will be
possible when more sensitive instruments will be operational in the coming
years.
