In Section 4, the EFT is recast in terms of a “diparticle” field, and Weinberg’s Z is shown to track the relative importance of the diparticle kinetic term. The relevant EFT contains two S-wave poles, in terms of which Weinberg’s relations are rewritten in Section 3. In Section 2, the short-range EFT relevant for a discussion of Weinberg’s compositeness criterion is presented and contrasted with the short-range EFT normally considered in the two-nucleon system. This paper is not intended as a comprehensive review of the literature on Weinberg’s compositeness, but instead, should be viewed as a reconstruction of some known results from the point of view of a single-minded effective field theorist. More generally, because an EFT includes all interactions allowed by symmetries, the choice of fields is to some extent arbitrary as far as observables, such as the location of S-matrix poles, go. If anything, it is for the latter that the auxiliary field has been more useful despite its intuitively higher “compositeness” coming from its extreme proximity to the scattering threshold. The naive interpretation that an “elementary” particle is one associated with an explicit degree of freedom is muddled by the fact that one can always introduce an auxiliary field for the deuteron and/or another for the virtual spin-singlet S-wave state. In the nuclear EFTs formulated since the 1990s, Steve’s criterion of compositeness is automatically satisfied. The notion of compositeness is tied to resolution: one effective field theorist’s “elementary” particle is most likely another’s “composite” particle. I believe Steve’s loss of interest in that paper is due to his later, much grander, idea of effective field theory (EFT), where, from the very beginning, experimental limitations on accessible energies are explicitly incorporated into theory construction. ) In this context, Steve’s result has been invoked as a criterion to decide which of the new states should be viewed as hadronic molecules. Yet, it has now 300+ citations (again, in inSpire) due to the explosion of interest in the new exotic hadronic states found since the X ( 3872 ) in 2003. When we were looking into the deuteron also in the 1990s, not once did Steve recommend to me. The only citation by Steve himself I could locate is, where the “compositeness” condition Z = 0 is not considered particularly “useful” in quantum field theories, except that “it fixes the coupling of the deuteron to the neutron and proton”. By 2007, this paper had been cited in only about 20 publications, according to inSpire. NLO NUCLEAR PLANT SERIESI do not know that this is for sure the case, but he might have been referring to his paper on the evidence that the deuteron is not an “elementary” particle, which followed a series of papers on “quasiparticles”. He has also told me-and is even on record in some YouTube video I can no longer find-that some of his papers in the 1960s were better forgotten. Steve was not a conceited man, and he realized some of his work was not golden-even though by other people’s standards, it could very well seem so.
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