  Recently, compact black hole X-ray binaries XTE J 1118+480 and A0620-00 have
been reported to be experiencing a fast orbital period decay, which is two
orders of magnitude higher than expected with gravitational wave radiation.
Magnetic braking of an Ap/Bp star has been suggested to account for the period
change when the surface magnetic field of the companion star $B_{\rm s}\ga
10^{4}$ G. However, our calculation indicates that anomalous magnetic braking
cannot significantly contribute to the large orbital period decay rates
observed in these two sources even if $B_{\rm s}\ga 10^{4}$ G. Observations
have provided evidence that circumbinary disks around two compact black hole
X-ray binaries may exist. Our analysis shows that, for some reasonable
parameters, tidal torque between the circumbinary disk and the binary can
efficiently extract the orbital angular momentum from the binary, and result in
a large orbital period change rate. Based on the circumbinary disk model, we
simulate the evolution of XTE J 1118+480 via a stellar evolution code. Our
computations are approximatively in agreement with the observed data (the
masses of two components, donor star radius, orbital period, and orbital period
derivative). The mass transfer rate and circumbinary disk mass are obviously
far greater than the inferred values from observations. Therefore, it seems
that the circumbinary disk is unlikely to be the main cause of the rapid
orbital decay observed in some compact black hole X-ray binaries.
