In this paper we present a method to study the polarizability due to transitions between exciton states in transition metal dichalcogenides. We apply our method to the description of the excitation of
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
W
S
e
2
. We find a good agreement between recent experimental measurements and our theoretical calculations.