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We consider a vectorial, asymptotically free gauge theory and analyze the effect of higher-loop corrections to the beta function on the evolution of the theory from the ultraviolet to the infrared.
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Here a “hard” fermion mass is a mass that would remain in the hypothetical limit in which one turned off the SU( N N ) interactions. If these masses are dynamically generated, then they are actually soft on the higher scale where they arise, as discussed in N. D. Christensen and R. Shrock, Phys. Rev. Lett. 94
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