  We propose a mechanism for the superhump modulations observed in optical
photometry of at least two black hole X-ray transients (SXTs). As in extreme
mass-ratio cataclysmic variables (CVs), superhumps are assumed to result from
the presence of the 3:1 orbital resonance in the accretion disc. This causes
the disc to become non-axisymmetric and precess. However the mechanism for
superhump luminosity variations in low mass X-ray binaries (LMXBs) must differ
from that in CVs, where it is attributed to a tidally-driven modulation of the
disc's viscous dissipation, varying on the beat between the orbital and disc
precession period. By contrast in LMXBs, tidal dissipation in the outer
accretion disc is negligible: the optical emission is overwhelming dominated by
reprocessing of intercepted central X-rays. Thus a different origin for the
superhump modulation is required. Recent observations and numerical simulations
indicate that in an extreme mass-ratio system the disc area changes on the
superhump period. We deduce that the superhumps observed in SXTs arise from a
modulation of the reprocessed flux by the changing area. Therefore, unlike the
situation in CVs, where the superhump amplitude is inclination-independent,
superhumps should be best seen in low-inclination LMXBs, whereas an orbital
modulation from the heated face of the secondary star should be more prominent
at high inclinations. Modulation at the disc precession period (10s of days)
may indicate disc asymmetries such as warping. We comment on the orbital period
determinations of LMXBs, and the possibility and significance of possible
permanent superhump LMXBs.
