  A tight correlation between the radio and X-ray emission in the hard state of
black hole X-ray binaries (BHXRBs) indicates an intrinsic disc-jet connection
in stellar black hole accretion systems, though the detailed physics processes
at work are still quite unclear. A hot accretion flow is suggested to match the
outer cold thin disc at a certain radius in the hard state, which may vary with
the accretion rate. In this work, we assume that the magnetic field generated
in the outer thin disc is advected inwards by the inner hot accretion flow,
which is substantially enhanced near the BH. Such a strong field threading the
horizon of a spinning BH is responsible for launching relativistic jets in
BHXRBs via the Blandford-Znajek mechanism. Thus, both the jet power and the
X-ray emission increase with the mass accretion rate, and we find that our
model calculations are able to reproduce the observed radio/X-ray correlation
quantitatively. For some individual BHXRBs, the slopes of the radio/X-ray
correlations become steeper when the sources are brighter. Our model
calculations show that this feature is due to the transition of the outer disc
with gas pressure dominated to radiation pressure dominated, which leads to
different accretion rate dependence of the field strength in the outer disc.
