In X-ray binaries, compact jets are known to commonly radiate at radio to infrared frequencies, whereas at optical to γ-ray
energies, the contribution of the jet is debated. The total luminosity, and hence power of the jet, is critically dependent
on the position of the break in its spectrum, between optically thick (self-absorbed) and optically thin synchrotron emission.
This break, or turnover, has been reported in just one black hole X-ray binary (BHXB) thus far, GX 339−4, and inferred via
spectral fitting in two others, A0620−00 and Cyg X−1. Here, we collect a wealth of multi-wavelength data from the outbursts
of BHXBs during hard X-ray states, in order to search for jet breaks as yet unidentified in their spectral energy distributions.
In particular, we report the direct detection of the jet break in the spectrum of V404 Cyg during its 1989 outburst, at νb
= (1.8 ± 0.3) × 1014 Hz (1.7 ± 0.2 μm). We increase the number of BHXBs with measured jet breaks from three to eight. Jet
breaks are found at frequencies spanning more than two orders of magnitude, from νb = (4.5 ± 0.8) × 1012 Hz for XTE J1118+480
during its 2005 outburst, to νb > 4.7 × 1014 Hz for V4641 Sgr in outburst. A positive correlation between jet break frequency
and luminosity is expected theoretically; νb∝L∼ 0.5ν, jet if other parameters are constant. With constraints on the jet break
in a total of 12 BHXBs including two quiescent systems, we find a large range of jet break frequencies at similar luminosities
and no obvious global relation (but such a relation cannot be ruled out for individual sources). We speculate that different
magnetic field strengths and/or different radii of the acceleration zone in the inner regions of the jet are likely to be
responsible for the observed scatter between sources. There is evidence that the high-energy cooling break in the jet spectrum
shifts from UV energies at LX ∼ 10−8LEdd (implying the jet may dominate the X-ray emission in quiescence) to X-ray energies
at ∼10−3LEdd. Finally, we find that the jet break luminosity scales as Lν, jet∝L0.56 ± 0.05X (very similar to the radio-X-ray
correlation), and radio-faint BHXBs have fainter jet breaks. In quiescence the jet break luminosity exceeds the X-ray luminosity.