  Compact, continuously launched jets in black hole X-ray binaries (BHXBs)
produce radio to optical-infrared synchrotron emission. In most BHXBs, an
infrared (IR) excess (above the disc component) is observed when the jet is
present in the hard spectral state. We investigate why some BHXBs have
prominent IR excesses and some do not, quantified by the amplitude of the IR
quenching or recovery over the transition from/to the hard state. We find that
the amplitude of the IR excess can be explained by inclination dependent
beaming of the jet synchrotron emission, and the projected area of the
accretion disc. Furthermore, we see no correlation between the expected and the
observed IR excess for Lorentz factor 1, which is strongly supportive of
relativistic beaming of the IR emission, confirming that the IR excess is
produced by synchrotron emission in a relativistic outflow. Using the amplitude
of the jet fade and recovery over state transitions and the known orbital
parameters, we constrain for the first time the bulk Lorentz factor range of
compact jets in several BHXBs (with all the well-constrained Lorentz factors
lying in the range of $\Gamma$ = 1.3 - 3.5). Under the assumption that the
Lorentz factor distribution of BHXB jets is a power-law, we find that
N($\Gamma$) $\propto \Gamma^{ -1.88^{+0.27}_{-0.34}}$. We also find that the
very high amplitude IR fade/recovery seen repeatedly in the BHXB GX 339-4
favors a low inclination angle ($< 15^\circ$) of the jet.
