27 - A connection between the strong and weak interactions

Summary

In the mid-1950s, my colleague Marvin L. Goldberger had acquired a leading position in the burgeoning field of dispersion relations (i.e., the study and exploitation of analyticity properties of scattering amplitudes). To speak of scattering in that era was to speak of strong or perhaps electromagnetic reactions, not weak ones. The weak interactions were, of course, of great and growing interest; but the focus was mainly on decay of weakly unstable particles, rather than on weak scattering reactions. Even for the simplest kind of scattering process (e.g., forward pion–nucleon scattering) there is a continuous physical variable, the energy. It is a well-posed question, therefore, to ask if the amplitude function can be continued into the complex energy plane, to ask what singularities one encounters there, and so forth.

It turned out that these inquiries and others that grew out of them were illuminating and fruitful. In fact, they were among the dominant themes of particle physics throughout much of the 1960s. On the other hand, consider a simple one-body-to-two-body decay reaction (e.g., π → μ + v decay). Here there is no continuous physical variable, no spectrum, just a fixed number for the amplitude – thus, seemingly, no role for analyticity thinking. Maybe this judgment is, in fact, correct. But let us not get ahead of our story; we return to Goldberger. While he was conducting his dispersion-relation pyrotechnics, I was busy pursuing various interests in weak-interaction physics. However, he managed, all the while, to keep a somewhat avuncular eye on my doings, and I tried to keep up with his.