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There are no starless massive proto-clusters in the first quadrant of the Galaxy

We search the lambda = 1.1 mm Bolocam Galactic Plane Survey for clumps containing sufficient mass to form ~10^4 M\odot star clusters. 18 candidate massive proto-clusters are identified in the first Galactic quadrant outside of the central kiloparsec. This sample is complete to clumps with mass M(clump) > 10^4 M_sun and radius r < 2.5 pc. The overall Galactic massive cluster formation rate is CFR(M_cluster > 10^4) ~ 5 Myr^-1, which is in agreement with the rates inferred from Galactic open clusters and M31 massive clusters. We find that all massive proto-clusters in the first quadrant are actively forming massive stars and place an upper limit of t_starless < 0.5 Myr on the lifetime of the starless phase of massive cluster formation. If massive clusters go through a starless phase with all of their mass in a single clump, the lifetime of this phase is very short.