  In this paper we develop a fully microscopic theory of the polarizability of
excitons in transition metal dichalcogenides. We apply our method to the
description of the excitation $2$p dark states. These states are not observable
in absorption experiments but can be excited in a pump-probe experiment. As an
example we consider $2$p dark states in WSe\textsubscript{2}. We find a good
agreement between recent experimental measurements and our theoretical
calculations.
