From Bjorken Scaling to Scaling Violations

Giorgio Parisi

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arXiv · 2506.03383

From Bjorken Scaling to Scaling Violations

Giorgio Parisi

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Abstract

This paper traces the historical and conceptual journey from Bjorken scaling to the discovery of scaling violations in deep inelastic scattering, culminating in the development of Quantum Chromodynamics (QCD). Beginning with the challenges faced by early strong interaction theories in the 1950s, we explore the emergence of agnostic approaches such as the bootstrap philosophy and current algebra, which sought to describe hadronic phenomena without relying on specific field theories. The pivotal role of experimental results from SLAC in the late 1960s is highlighted, leading to Bjorken's proposal of scaling in deep inelastic scattering and Feynman's parton model. We then delve into the theoretical breakthroughs of the 1970s, including Wilson's operator product expansion and the renormalization group, which provided the framework for understanding scaling violations. The discovery of asymptotic freedom in non-Abelian gauge theories by Gross, Wilczek, and Politzer marked a turning point, establishing QCD as the theory of strong interactions. Finally, we discuss the formulation of the Altarelli-Parisi equations, which elegantly describe the evolution of parton distribution functions and scaling violations, and their profound impact on the study of hard processes in particle physics. This paper not only recounts the key developments but also reflects on the interplay between theory and experiment that drove the field forward.

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Giorgio Parisi. 2025-06-03. From Bjorken Scaling to Scaling Violations. https://arxiv.org/abs/2506.03383

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