What is resonance?

Abstract

The concept of duality, discussed in the previous paper by Dr C. Schmid, refers to the notion that the analysis of an S matrix amplitude in terms of s channel resonances and its analysis in terms of t channel (and u channel) reggeon exchanges are not independent, but represent alternative descriptions, the former being the more appropriate in the low energy domain and the latter being the more appropriate in the low t (or low u ) domain for high energy interactions. Hence, at the time when this Discussion meeting was planned, it appeared necessary to attempt to clarify the notion of resonance , since there was then a good deal of discussion about how partial wave analyses of scattering data should be interpreted in terms of resonance states (Bransden, O’Donnell & Moorhouse 1965; Lovelace 1968; Donnachie 1968), and even whether such an interpretation was necessarily the case at all (Schmid 1968 a,b ; Collins, Johnson & Squires 1968; Alessandrini & Squires 1968; Alessandrini, Freund, Oehme & Squires 1968; Collins, Johnson & Ross 1968; Kreps & Logan 1969). However, in the actual use of duality in this meeting and in the model amplitudes which have been discussed thus far for the illustration of duality, there is really no controversy about the nature of resonance, since these models are still confined to the cases of resonances with zero width, characterized by poles on the real s axis, and there is essentially no ambiguity about the relation between resonances and poles in this limiting case. All the same, it still seems worthwhile to take a few moments to draw attention to a number of points about the description of resonance, which deserve to be more widely known.