High-redshift quasars host galaxies: is there a stellar mass crisis?

We investigate the evolutionary properties of a sample of quasars at 5<z<6.4 using the semi-analytical hierarchical model GAMETE/QSOdust. We find that the observed properties of these quasars are well reproduced by a common formation scenario in which stars form according to a standard IMF, via quiescent star formation and efficient merger-driven bursts, while the central BH grows via gas accretion and BH-BH mergers. Eventually, a strong AGN driven wind starts to clear up the ISM of dust and gas, damping the star formation and un-obscuring the line of sight toward the QSO. In this scenario, all the QSOs hosts have final stellar masses in the range $(4-6)\times 10^{11} M_{sun}$, a factor 3-30 larger than the upper limits allowed by the observations. We discuss alternative scenarios to alleviate this apparent tension: the most likely explanation resides in the large uncertainties that still affect dynamical mass measurements in these high-z galaxies. In addition, during the transition between the starburst-dominated and the active QSO phase, we predict that about 40% of the progenitor galaxies can be classified as Sub Millimeter Galaxies, although their number rapidly decreases with redshift.