Theory and application of chiral anomalies in quantum field theory



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In this thesis we investigate both the theoretical mechanism by which chiral anomalies arise in quantum field theories, as well as their implications for physical observables. In Chapter 1, we set the stage by providing a brief historical account of the so-called PCAC (partially conserved axial current) puzzle and the theoretical work which spawned from the observed anomalous decay of the π⁰ to two photons. Chapter 2 is dedicated to developing the necessary formalism and theoretical tools– namely the effects of symmetry transformations and their associated Noether currents. The path integral formalism is introduced and the U(1) [subscript A] anomaly is derived in detail by studying the noninvariance of the measure. In Chapter 3, we introduce the effective chiral Lagrangian of QCD to investigate the dynamics of the meson nonet. We apply our results from Chapter 2 in calculating the width Γ [subscript η′→γγ], and consequently the lifetime τ [subscript η′→γγ] to leading order. We report that our derived expressions yield numerical values of Γ [subscript η′→γγ] = (0.0037 ± 0.0003)MeV and τ [subscript η′→γγ] = (1.78 ± 0.03) × 10⁻¹⁹ s. Our results lie within 2σ of the experimental values reported by the Particle Data Group.



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