We examine the behavior of the connected /i-point function in a zero-dimensional scalar theory (.£ --jm 2 (f> 2 -jX<}> 4 ). The problematic n\(-Jx) n behavior for large n, previously found for tree graphs in scalar field theory, is again obtained in saddle-point approximation in this model. However, a similar behavior, n\[f(X)] n , persists in the full theory, where f~~Jx for A. -* 0,/-X~l /4 for X^> 1. This behavior can be traced to the existence of zeros in the complex J plane of the generating functional Z(7), which in turn is controlled by the asymptotic behavior in |/| of Z(J) calculated in saddle-point approximation. The application of these results to field theory is discussed.PACS numbers: ll.10.Jj, 11.15.Tk Several recent calculations have focused on the behavior of rt-point amplitudes in field theories with bosons when n is large. In a Euclidean-based calculation for the production of n Higgs bosons (or Ws) in the presence of the (constrained) instanton, Ringwald l and later Espinosa 2 showed that this amplitude grows like n\, so that unitarity is naively violated at a finite energy. In two subsequent studies of ordinary X 4 (Ref. 5) at tree level (i.e., the WKB approximation) gave the same result. In Ref. 4 the tree graphs for qq^> n Higgs bosons were analyzed, and the amplitude (for n-E/mn) was seen to grow like {Jx/mn) n n\, implying a cross section in apparent violation of s-wave unitarity when n -4K/X. The same problem was encountered in a supersymmetric two-Higgs-boson version of scalar field theory, which does not have the same triviality question associated with it. It was also noted in Ref. 4 that there is no obvious connection between these tree-level results and the standard asymptotic nature of perturbation expansions 6,7 in field theory. The latter are concerned with the behavior of the expansion coefficients at high order in perturbation theory of a Green's function with a fixed number of legs. Our present concern is the pathological behavior at tree level of an amplitude with many external legs. The failure of tree-level perturbativity for n-~l/X raises the question of how (or perhaps whether) the theory corrects itself in a nonperturbative manner. A glance at the tree diagrams in Ref. 4 shows the finalstate rescattering of pairs of scalars allows -n 2 new loop diagrams for each tree diagram, each one contributing a factor of X/\6K 2 .Even if these do a random walk in phase, there may be a contribution of 0(Xn/\6x 2 ) relative to the tree graphs. 8 Clearly, nonperturbative effects may play a significant role in taming the amplitude. 9 Thus, it is important to study a situation where the tree approximation may be compared with the complete theory in order to see where the problem originates.This paper constitutes such an initial, modest attempt.The model we propose to examine is a standard first simplification for t...
Using backward ?dV dispersion relations (BDR) and sum rules derived from BDR we obtain the spin-flip f ONN and a combination of the flip and nonflip gNN coupling constants, and fit certain backward ?rN data. Our results have implications in the one-boson-exchange theory of the nucleon-nucleon force and in theories of elementary particles which assume universal coupling to the stress tensor.
The small limits of discrepancy between experimental and theoretical values of (g -Z),,, are shown to eliminate any chance of seeing single excited e*'s or p*'s in colliding-beam or inelastic electro-or muoproduction experiments. On the other hand, visible I* tracks in very-high-energy (E > lox9 eV) cosmic-ray events are possible for m;-1 TeV. The results presuppose a new dynamics, disjoint from QED, underlying the 1 * excitations.
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