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We report on a campaign on the bright black hole X-ray binary SwiftJ1727.8$-$1613 centered around five observations by the Imaging X-rayPolarimetry Explorer (IXPE). This is the first time it has been possible totrace the evolution of the X-ray polarization of a black hole X-ray binaryacross a hard to soft state transition. The 2--8 keV polarization degree slowlydecreased from $\sim$4\% to $\sim$3\% across the five observations, butremained in the North-South direction throughout. Using the Australia TelescopeCompact Array (ATCA), we measure the intrinsic 7.25 GHz radio polarization toalign in the same direction. Assuming the radio polarization aligns with thejet direction (which can be tested in the future with resolved jet images),this implies that the X-ray corona is extended in the disk plane, rather thanalong the jet axis, for the entire hard intermediate state. This in turnimplies that the long ($\gtrsim$10 ms) soft lags that we measure with theNeutron star Interior Composition ExploreR (NICER) are dominated by processesother than pure light-crossing delays. Moreover, we find that the evolution ofthe soft lag amplitude with spectral state differs from the common trend seenfor other sources, implying that Swift J1727.8$-$1613 is a member of a hithertounder-sampled sub-population.

Tracking the X-ray Polarization of the Black Hole Transient Swift J1727.8-1613 during a State Transition