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As well known, if $m$ denotes the bare mass and $\\mass$ the mass computed from the theory, to order $\\alpha$ one has $$\\frac{\\mass}{m} =1+\\frac{8\\alpha}{3\\pi} \\log(1+\\half (\\Lambda/m))+O(\\alpha^2)$$ which suggests that $\\mass/m=(\\Lambda/m)^{8\\alpha/3\\pi}$ for small $\\alpha$. 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