Theoretical μ_l profile obtained for the control region in Fig. 1. The grey shaded region indicates the model uncertainty. The position of Sgr A^* (8.2kpc and 0 mas/yr) is marked by the yellow star. The orange, green, and purple horizontal lines indicate the μ_l values at which the clouds are detected (μ_l differing from that of the control field at the 3σ level), with their uncertainties shown as shaded regions. The corresponding estimated distance ranges of the clouds are shown as vertical shaded regions.