The introduction of a high-κ/metal gate stack in metal-oxide-Semiconductor field-effect transistors can cause a significant degradation of the mobility, especially at weak inversion densities. This degradation is commonly ascribed to remote Coulomb scattering (RCS, i.e., charges trapped at the SiO$_2$/HfO$_2$ interface). However, very large densities of RCS charges are usually needed to reproduce the experimental data. In this work, we explore alternative scattering mechanisms by quantum calculations of the carrier mobilities. We consider, in particular, metal grain workfunction fluctuations and local dipoles at the SiO$_2$/HfO$_2$ interface. Similarly to RCS, both scattering mechanisms are found to reduce the carrier mobility significantly at low carrier densities. However, the mobility exhibits a different dependence on the thickness of high-κ layer, which provides a way to identify the dominant mechanism.