Weak-interaction bootstrap

In two research notes from the mid-2000s, Alejandro Rivero reported that the Z boson decay width lies on the same curve (proportional to mass cubed) as the pion and several other mesons, and that the width is minimized for a value of the Weinberg angle which is realized at the GUT scale in grand unified theories.

It is unclear to me whether this is unusual. The width is not a fundamental property, and it could be that these observations can be completely explained in terms of the SM, or a GUT, respectively; I would have to check.

But if it is unusual... and if it is not to be dismissed as a coincidence... then it seems it might need a "bootstrap" explanation. The bootstrap philosophy, also known as S-matrix theory and as nuclear democracy, was an idea of the 1960s which sought to explain the behavior of hadrons, not through reductionism, but through an algebraic holism of "Regge trajectories" and scattering dualities. (In the mainstream histories, the bootstrap is regarded as having been superseded by QCD and the standard model, but as Ron Maimon has explained in recent years, the bootstrap also gave rise to string theory.)

This holistic approach, though hard to penetrate, seems appropriate for explaining relations between quantities that aren't fundamental. But the main problem is that the bootstrap was just about the strong force; there seems no opportunity for weak and electromagnetic forces to enter the synthesis.

So here I would like to unearth an unpublished preprint from 1975, “Instability of Collective Strong-Interaction Phenomena in Hadron Production as a Possible Origin of the Weak and Electromagnetic Interactions” by Richard C. Arnold, simply to quote its opening remarks:

Recent attempts, in the context of local field theories, to unify all interactions (strong, electromagnetic, and weak) have led to serious consideration of the possibility that all these interactions become indistinguishable at sufficiently small distances, or large momenta. If this were true, then methods applicable to strong interactions such as the self-consistent S-matrix approach ("bootstrap") should be equally well relevant for the other interactions, leading to the expectation that symmetries combining all interactions would be found, as in the strong-interaction dynamics alone. This phenomenon cannot be seen in a low energy ("old") bootstrap theory, since the weak and electromagnetic forces are negligible compared to the strong at low energies. However, a self-consistent S-matrix theory which relies on high-energy, high-multiplicity intermediate states should make manifest such an interplay between classes of interactions. 

I cannot judge the merits of Arnold's particular idea, of producing leptons and the electroweak interactions from "t-channel Regge poles". But if the peculiar properties of Z boson decay mentioned above are real and not a coincidence and not already explained by standard theory, here is a place to start looking...