We study long-term radio/X-ray correlations in Cyg X-1. We find the persistent existence of a compact radio jet in its soft state. This represents a new phenomenon in black-hole binaries, in addition to compact jets in the hard state and episodic ejections of ballistic blobs in the intermediate state. While the radio emission in the hard state is strongly correlated with both the soft and hard X-rays, the radio flux in the soft state is not directly correlated with the flux of the dominant disk blackbody in soft X-rays, but instead it is lagged by about a hundred days. We interpret the lag as occurring in the process of advection of the magnetic flux from the donor through the accretion disk. On the other hand, the soft-state radio flux is very tightly correlated with the hard X-ray, 15--50 keV, flux without a measurable lag and at the same rms. This implies that the X-ray emitting disk corona and the soft-state jet are powered by the same process, probably magnetically.
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