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Low mass X-ray binaries (LMXBs) show evidence of a global correlation ofdebated origin between X-ray and optical luminosity. We study for the firsttime this correlation in two transient LMXBs, the black hole V404 Cyg and theneutron star Cen X-4, over 6 orders of magnitude in X-ray luminosity, fromoutburst to quiescence. After subtracting the contribution from the companionstar, the Cen X-4 data can be described by a single power law correlation ofthe form $L_{opt}\propto\,L_{X}^{0.44}$, consistent with disk reprocessing. Wefind a similar correlation slope for V404 Cyg in quiescence (0.46) and asteeper one (0.56) in the outburst hard state of 1989. However, V404 Cyg isabout $160-280$ times optically brighter, at a given $3-9$ keV X-rayluminosity, compared to Cen X-4. This ratio is a factor of 10 smaller inquiescence, where the normalization of the V404 Cyg correlation also changes.We show that once the bolometric X-ray emission is considered and the knownmain differences between V404 Cyg and Cen X-4 are taken into account (a largercompact object mass, accretion disk size, and the presence of a strong jetcontribution in the hard state for the black hole system) the two systems lieon the same correlation. In V404 Cyg, the jet dominates spectrally atoptical-infrared frequencies during the hard state, but makes a negligiblecontribution in quiescence, which may account for the change in its correlationslope and normalization. These results provide a benchmark to compare with datafrom the 2015 outburst of V404 Cyg and, potentially, other transient LMXBs aswell.

On the Optical -- X-ray correlation from outburst to quiescence in Low Mass X-ray Binaries: the representative cases of V404 Cyg and Cen X-4