Infrared Synchrotron Emission in the Soft State of GX 339-4 and the Mid-Infrared/X-ray Luminosity Plane of Black Hole X-ray Binaries

Progress in understanding the growth of accreting black holes remains hampered by a lack of sensitive coordinated multiwavelength observations. In particular, the mid-infrared (MIR) regime remains ill-explored except for jet-dominant states. Here, we present comprehensive follow-up of the black hole X-ray binary GX 339-4 during a disc-dominated state in its 2023/24 outburst as part of a multi-wavelength campaign coordinated around JWST/MIRI. The X-ray properties are fairly typical of soft accretion states, with a high-energy Comptonised tail. The source is significantly detected between 5-10$\mu$m, albeit at a faint flux level requiring MIR compact jet emission to be quenched by a factor of $\sim$300 or more relative to previous hard-state detections. The MIRI spectrum can be described as a simple power-law with slope $\alpha$ = +0.39$\pm$0.07 ($F_\nu$ $\propto$ $\nu^\alpha$), but surprisingly matches neither the radio/sub-mm nor the optical broadband slopes. Significant MIR stochastic variability is detected. Synchrotron radiation from the same medium responsible for high-energy Comptonisation can self-consistently account for the observed MIRI spectral-timing behaviour, offering new constraints on the physical conditions in the soft-state accretion disc atmosphere/corona. Alternative explanations, including a circumbinary disc or emission from a warm wind, fail to cleanly explain either the spectral properties or the variability. Multiwavelength timing cross-correlations show a puzzlingly long MIR lag relative to the optical, though at limited significance. We compile archival MIR and X-ray luminosities of transient black hole systems, including previously unreported detections of GX 339-4. These trace the evolution of the MIR-to-X-ray flux ratio with accretion state, and also reveal high MIR luminosities for GX 339-4 across all states. (abridged)