Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED

In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli-Fierz model up to the order $O(α^5\logα^{-1})$, where $α$ denotes the finestructure constant, and prove rigorous bounds on the remainder term of the order $o(α^5\logα^{-1})$. As a consequence, we prove that the binding energy is not a real analytic function of $α$, and verify the existence of logarithmic corrections to the expansion of the ground state energy in powers of $α$, as conjectured in the recent literature.

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