Classical dimensional transmutation and renormalization in massive λϕ4 model

Recently, Dvali, Gomez, and Mukhanov have investigated a classical λϕ4 model with external source and without mass and they have clarified that there are underlying renormalization group structure, including the phenomenon of the dimensional transmutation, at purely classical level. Especially when the coupling λ is negative, the classical beta function shows the property of asymptotic freedom as in QCD. In this Letter, we investigate the λϕ4 model with mass, and clarify the role of the mass. The obtained classical beta function is identical with that of the massless λϕ4 model up to the corrections of the ratio of the IR cutoff to UV cutoff, and describes the renormalization flow same as the massless theory. We also found that the dynamically generated scale of massive theory is larger than that of massless theory, which could be due to the screening effect of the mass term.