The ALMA view of MP Mus (PDS 66): A protoplanetary disk with no visible gaps down to 4 au scales

Aims. We aim to characterize the protoplanetary disk around the nearby (d similar to 100 pc), young solar analog MP Mus (PDS 66) and to reveal any signs of planets or ongoing planet formation in the system. Methods. We present new ALMA observations of MP Mus at 0.89 mm, 1.3 mm, and 2.2 mm with angular resolutions of similar to 1 '', 0.05 '', and 0.25 '', respectively. These data probe the dust and gas in the disk with unprecedented detail and sensitivity. Results. The disk appears smooth down to the 4 au resolution of the 1.3 mm observations, in contrast with most disks observed at comparable spatial scales. The dust disk has a radius of 60 +/- 5 au, a dust mass of 0.14(-0.06)(+0.11) M-Jup, and a millimeter spectral index <2 in the inner 30 au, suggesting optically thick emission from grains with a high albedo in this region. Several molecular gas lines are also detected extending up to 130 +/- 15 au, similar to small grains traced by scattered light observations. Comparing the fluxes of different CO isotopologues with previous models yields a gas mass of 0.1-1 M-Jup, implying a gas-to-dust ratio of 1-10. We also measured a dynamical stellar mass of M-dyn = 1.30 +/- 0.08 M-circle dot and derived an age of 7-10 Myr. Conclusions. The survival of large grains in an evolved disk without gaps or rings is surprising, and it is possible that existing substructures remain undetected due to optically thick emission at 1.3 mm. Alternatively, small structures may still remain unresolved with the current observations. Based on simple scaling relations for gap-opening planets and gap widths, this lack of substructures places upper limits to the masses of planets in the disk as low as 2 M-circle plus-0.06 M-Jup at r > 40 au. The lack of millimeter emission at radii r > 60 au also suggests that the gap in scattered light between 30 and 80 au is likely not a gap in the disk density, but a shadow cast by a puffed-up inner disk.