Mass renormalization in nonrelativistic quantum electrodynamics

In nonrelativistic quantum electrodynamics the charge of an electron equals its bare value, whereas the self-energy and the mass must be renormalized. In our contribution we study perturbative mass renormalization, including second order in the fine structure constant α, in the case of a single, spinless electron. As is well known, if m denotes the bare mass and meff the mass computed from the theory, to order α one has meff m=1+ (8α3π) log (1+ 1 2 (Λ/m)) +O (α2) which suggests that meff m= (Λ/m)8α3π for small α. If correct, in order α2 the leading term should be 1 2 ((8α3π) log (Λ/m)) 2. To check this point we expand meff m to order α2. The result is √Λ/m as leading term, suggesting a more complicated dependence of meff on m.