On the ground state energy of the translation invariant Pauli-Fierz model

In this note, we determine the ground state energy of the translation invariant Pauli-Fierz model to subleading order $O(\alpha^3)$ with respect to powers of the finestructure constant $\alpha$, and prove rigorous error bounds of order $O(\alpha^{4})$. A main objective of our argument is its brevity.