Dimensional transmutation

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In particle physics, dimensional transmutation is a physical mechanism that transforms a dimensionless parameter into a dimensionful parameter.

In classical field theory such as gauge theory in four-dimensional spacetime, the coupling constant is a dimensionless constant. However, logarithmic divergences in one-loop diagrams imply that this "constant" actually depends on the typical energy scale of the processes under considerations. The "running" is determined by the beta-function and renormalization group.

Consequently, the strength of the interaction may be described by a dimensionful parameter, namely the energy scale where the interaction strength reaches the value 1. In the case of quantum chromodynamics, this energy scale is called the QCD scale and its value 150 MeV replaces the original dimensionless coupling constant.

This is a fancy way of saying that the conformal symmetry of the classical theory is anomalously broken, thereby setting up a mass scale. See conformal anomaly.