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This is a library Circulating Copy which may be borrowed for two weeks.

A remark of profound import for strong-interaction theory has been made by Dolen, Horn, and Schmid 1 in connection with finite-energy sum rules. They have observed that high-energy Regge behavior is consistent with low-energy resonance behavior only if extrapolation of the smooth Regge representation down to low energy gives a certain semilocal average over the resonance peaks. In other words what is usually called the "peripheral" approximation to a reaction amplitude must, without containing energy poles, in a rough sense represent the resonances. (The converse presumably is also true.) We refer to this startling notion as "Dolen-Horn-Schmid duality." Its implication for bootstrap theory is being pursued vigorously by many authors 2 ; our object here is to suggest relevance to what has been called the "Deck effect." 3 We argue that the Deck peripheral model for a reaction such as irN^piiN, explaining a peak in the final irp mass spectrum without explicit insertion therein of a resonance, fails to imply the absence of a resonance. On the contrary, Dolen-Horn-Schmid duality means that when peripheral models of this kind predict large cross sections at low subenergies (the term "subenergy" is used to mean energy of a subsystem), there ). The curve of Fig. 2 is 7% lower than the approximate calculation of Ash et al. (Ref. 2).probably are resonances present. Such reasoning leads to enormous simplification of multiperipheral calculations.The step needed to relate Dolen-Horn-Schmid to Deck is the extension of single peripheralism to double peripheralism. Deck's model for the above reaction, for example, is depicted in Fig. 1, corresponding to a double Regge-pole representation, 4 a representation supposed to have validity when both the TTN and irp final subenergies are large. 5 The highest trajectory for the righthand momentum transfer is the Pomeranchuk; the highest for the left-hand momentum transfer is not the 77, but the small mass of the physical pion enhances the Regge residue so that this trap ir N FIG. 1. Diagram representing the Deck doubly peripheral model for the reaction irN^irpN.An extension to multiperipheralism is made of the Dolen-Horn-Schmid duality argument relating Regge poles to low-energy resonances. The Deck model is thereby interpreted as predicting the existence of the A it rather than as undermining experimental evidence for this resonance. It is shown in general that Dolen-Horn-Schmid duality permits a vast simplification in the calculation of multiple-production processes.1078