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The Perturbation Paradigm Stumbles

It didn't take long for the theory of strong interactions to run into problems. The essence of the difficulty lies in the very word "strong." The strength of an interaction can be calibrated by the magnitude of the dimensionless coupling constant applied at each vertex [wherever a virtual particle is created or annihilated] in a Feynman diagram such as Fig. 1. As explained earlier, each such vertex in has a strength of , which makes "higher order diagrams" rapidly insignificant -- great for calculating with a perturbation theory!

Unfortunately, the "strength" of a vertex in strong interactions is on the order of 1. This means that the single pion exchange diagram shown on the left in Fig. 3 or Fig. 4 is in principle no more likely than the incomprehensible mess on the right in Fig. 4, involving manifold exchanges of pions and other mesons, as well as creation and annihilation of baryon-antibaryon pairs.* Worse yet, this is only one example of the seemingly endless variety of possible diargams one must in principle consider in order to make an accurate calculation of "simple" nucleon-nucleon scattering!

  
Figure: Left: Feynman diagram for single pion exchange. Right: A far more complicated Feynman diagram that is in principle no less important!

Of course, it wasn't quite that bad. Handy "sum rules" were discovered that explained why single pion exchange usually got you pretty close to the right answer, but in principle one had to make an almost infinitely difficult calculation in order to get the sort of precise predictions that Perturbation Theorists had come to expect from their experiences with . Moreover, there were conceptual nightmares to sweat out -- if you look closely at Fig. 4, for instance, you will notice that a proton can emit a pion [OK, there are pions inside protons] which can turn into a proton-antiproton pair [OK, there are protons inside pions... Wait a minute!] and so on. Like many nightmares, this revealed an unexplored avenue of understanding: in the 1960's and 70's, Geoffrey Chew and his Theory group at Berkeley developed a non-perturbative theory of strong interactions that contained the "bootstrap principle:" every hadron is made up of combinations of all the other hadrons (and itself). Although I never could understand Chew's models, they represented a genuinely new paradigm that gained a good deal of purchase on the problem when suddenly the attention of the particle physics community was diverted by a revival of perturbation theory in the form of a quark model, about which I will say more later; since then Chew's approach has been sadly neglected, which I suspect is a great loss to physics. Still, if we can get answers more easily by "recycling an old paradigm," the outcome is inevitable.



Next: Weak Interactions Up: The Go-Betweens Previous: The Go-Betweens

Jess H. Brewer - Last modified: Mon Nov 23 14:54:21 PST 2015