Mass renormalization in non-relativistic quantum electrodynamics with spin 1/2

The effective mass m_eff of the Pauli-Fierz Hamiltonian with ultraviolet cutoff Λ and the bare mass m in non-relativistic quantum electrodynamics (QED) with spin 1/2 is investigated. Analytic properties of m_eff in coupling constant e are shown. Let us set m_eff/m = 1 +a₁(Λ/m)e² + a₂(Λ/m)e ⁴ + script O sign (e⁶). The explicit form of constant a₂(Λ/m) depending on Λ/m is given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants c₁ and c₂ such that equation presented In particular though it is known that a₁(Λ/m) diverge log(Λ/m) as Λ → ∞, a₂2(Λ/m) does not diverge as ±[log(Λ/m)]² but -(Λ/m)².