  We aim to understand under which conditions a low mass planet can open a gap
in viscous dusty protoplanetary discs. For this purpose, we extend the theory
of dust radial drift to include the contribution from the tides of an embedded
planet and from the gas viscous forces. From this formalism, we derive i) a
grain size-dependent criterion for dust gap opening in discs, ii) an estimate
of the location of the outer edge of the dust gap and iii) an estimate of the
minimum Stokes number above which low-mass planets are able to carve gaps which
appear only in the dust disc. These analytical estimates are particularly
helpful to appraise the minimum mass of an hypothetical planet carving gaps in
discs observed at long wavelengths and high resolution. We validate the theory
against 3D SPH simulations of planet-disc interaction in a broad range of dusty
protoplanetary discs. We find a remarkable agreement between the theoretical
model and the numerical experiments.
