Chiral perturbation theory

The development of chiral perturbation theory was a significant step in the study of the strong interactions. It produces rigorous results about the low energy behavior of QCD, vwhich have as much validity as perturbative results at high energy. Moreover, chiral perturbation theory provides one of the best examples of an effective field theory, and so was also important in the development of EFT methods.

My early interest in chiral methods came mainly from the weak interaction. As we tried to calculate more completely we were led to include loop diagrams. As soon as one does that, it becomes a full field theory of the form called effective field theory. Weinberg’s early work was influential, as were Gasser and Leutwyler’s seminal papers. Soon the interest was not just of making specific predictions, but also in understanding effective field theory. It was great fun participating in the exploration of this new area and the applications to the Standard Model.

One of the early successes was on the understanding of the physics underlying chiral Lagrangians, also explored by Ecker Pich and de Refael. The low energy amplitudes respond to nearby singularities, and the chiral coefficients reflect these properties of the underlying theory (QCD). Gradually we became more sophisticated about this insight, including unitarity effects through the Omnes function, understanding the connections to dispersion relations and doing a better job at matching the effective field theory. Overall, we have come to a reasonable understanding of how effective field theory works in the strong interactions and we have reasonable control over the low energy limit of the theory.

Lately, I have found myself in the unexpected role of explaining how cutoffs can be incorporated in the effective theory and understanding the effects of doing so. Most work is done with dimensional regularization. However, Wilson’s original lessons about EFTs were with cutoffs separating the EFT from the full high energy theory, and we still tend to think in this manner. However, thinking this way while using dimensional regularization can lead to problems because loop diagrams can include effects which come from energies beyond which the EFT is no longer valid. See my recent polemic on this subject. Cutoffs can also be used as a regularization scheme. Various applications where this is important include baryon chiral perturbation theory, chiral extrapolations and the nuclear interaction. This is not always warmly received, but nevertheless I feel that these insights are sometimes important in chiral perturbation theory.

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Research and teaching pages for John Donoghue