Fast X-ray/IR observations of the black hole transient Swift~J1753.5--0127: from an IR lead to a very long jet lag

We report on two epochs of simultaneous near-infrared (IR) and X-ray observations with a sub-second time resolution of the low mass X-ray binary black hole candidate Swift J1753.5--0127 during its long 2005--2016 outburst. Data were collected strictly simultaneously with VLT/ISAAC (K$_{S}$ band, 2.2 $\mu m$) and RXTE (2-15 keV) or \textit{XMM-Newton} (0.7-10 keV). A clear correlation between the X-ray and the IR variable emission is found during both epochs but with very different properties. In the first epoch, the near-IR variability leads the X-ray by $ \sim 130 \, ms$. This is the opposite of what is usually observed in similar systems. The correlation is more complex in the second epoch, with both anti-correlation and correlations at negative and positive lags. Frequency-resolved Fourier analysis allows us to identify two main components in the complex structure of the phase lags: the first component, characterised by a few seconds near-IR lag at low frequencies, is consistent with a combination of disc reprocessing and a magnetised hot flow; the second component is identified at high frequencies by a near-IR lag of $\approx$0.7 s. Given the similarities of this second component with the well-known constant optical/near-IR jet lag observed in other black hole transients, we tentatively interpret this feature as a signature of a longer-than-usual jet lag. We discuss the possible implications of measuring such a long jet lag in a radio-quiet black hole transient.