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  • Print publication year: 2010
  • Online publication date: December 2010

6 - Theorizations of scaling


The experimental confirmation of the approximate scaling from SLAC stimulated intensive theoretical activities for conceptualizing the observed short-distance behavior of hadron currents and for developing a self-consistent theory of strong interactions, starting from and constrained by the observed scaling. At first, the most prominent among these efforts was the parton model that was originated from Bjorken's thinking on deep inelastic scattering and Feynman's speculations on hadron–hadron collision, and made popular by Feynman's influential advocacy.

The assumption adopted by the parton model that the short-distance behavior of hadron currents should be described by free field theory, however, was immediately challenged once the scaling results were published. The theoretical framework the challengers used was the renormalized perturbation theory. Detailed studies of renormalization effects on the behavior of currents, by Adler and many others, reinforced the conviction about the limitations of formal manipulations in the PCAC and current algebra reasoning, which made these physical effects theoretically invisible, and discovered, first, the chiral anomaly and, then, the logarithmic violation of scaling. The theoretically rigorous argument for scaling violation was soon to be incorporated into the notion of broken scale invariance by Kenneth G. Wilson, Curtis Callan, and others, which was taken to be the foundation of such approaches as Wilson's operator product expansion and Callan's scaling law version of the renormalization group equation for conceptualizing the short-distance behavior of hadron currents, for giving a more detailed picture of these behaviors than current algebra could offer, and even for a general theory of strong interactions.