Dynamic disk-corona coupling during the state transition of Swift J1727.8-1613

State transitions during outbursts of black hole X-ray binaries exhibit complex, rapidly evolving disk-corona coupling. Understanding this dynamic phase is essential for deciphering accretion physics and the mechanisms that drive outbursts, yet it remains poorly understood due to the scarcity of high-quality/-cadence observations. Here, we present an analysis of observations by the Hard X-ray Modulation Telescope (HXMT) during the 2023 outburst of the newly discovered low-mass black hole X-ray binary Swift J1727.8-1613. Follow-up, high-cadence monitoring reveals pronounced variability in disk emission, attributable to fluctuations in the accretion rate. These disk fluctuations exhibit damped amplitudes and shortened flare periods. This evolving disk emission modulates the supply of soft seed photons to the corona, leading to a dynamically changing positive correlation between the photon index $\Gamma$ and the Comptonization luminosity $L_{\rm Comp}$. As the transition proceeds, the correlation shifts toward higher $\Gamma$ and a narrower range of $L_{\rm Comp}$. We further suggest that the damped disk variability arises from fluctuations generated at large disk radii and propagating inward, possibly linked to the thermal-viscous disk instability.