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Recently, Dvali, Gomez, and Mukhanov have investigated a classical lambdaphi^4 model with external source and without mass and they have clarified thatthere are underlying renormalization group structure, including the phenomenonof the dimensional transmutation, at purely classical level. Especially whenthe coupling lambda is negative, the classical beta function shows the propertyof asymptotic freedom as in QCD. In this paper, we investigate the lambda phi^4model with mass, and clarify the role of the mass. The obtained classical betafunction is identical with that of the massless lambda phi^4 model up to thecorrections of the ratio of the IR cutoff to UV cutoff, and describes therenormalization flow same as the massless theory. We also found that thedynamically generated scale of massive theory is larger than that of masslesstheory, which could be due to the screening effect of the mass term.

Classical Dimensional Transmutation and Renormalization in Massive lambda phi^4 Model