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Abstract

Statistical DualityAs mentioned in Chapter 9 the Regge model predicts only the energy (s) dependence of the differential cross section of these reactions; the dependence on momentum transfer (t) (contained in the residue of the Regge pole) is left undetermined. Moreover, even this prediction is based on a relationship between spin and mass, which is an extrapolation involving complex angular momentum, analyticity and crossing symmetry. Some information about the t dependence of cross sections can be obtained from finite energy sum rules and duality: The amplitude for a given process is supposed to be "saturated" by resonances in the direct (s) channel, in the sense that the integral (in s) over the (imaginary part) of the resonance scattering amplitude is numerically equal ("dual") to the sum over all Regge amplitudes. The t dependence is contained in the (unknown) Regge residues of the left hand side of this equation.The statistical mesonic-cloud model, which leads to the conjecture of superfluidity of hadronic matter, provides another relationship between the s and t channels. Indeed one can show 259 that, under certain plausible assumptions, by integrating the differential cross section as given by the mesonic-cloud model over all physical t values, one gets an average, s dependent, cross section, which has the smooth power dependence characteristic for Regge behavior. This is reminiscent of finite energy sum rules Analogies in Physics and Life 367 and duality and because cross sections rather than amplitudes were involved, I called this relationship statistical duality. 259 In this sense the s dependence of cross sections, a prediction, which had been considered until then characteristic for Regge theory, can also be considered as a consequence of the mesonic-cloud model. This result is consistent with the fact that, as mentioned in chapter 12, resonances can in some sense be viewed as a consequence of the superfluid properties of hadronic matter and which were also derived from the mesonic-cloud model. In this context one should mention that within the above approach elastic scattering (Pomeron exchange) is due to phonon exchange. Finally another consequence of this model is that at large t the differential cross section cannot decrease with t faster than a power and therefore the observed exponential behavior of the differential cross section at small t, which is a consequence of the Bose-Einstein statistics, has to change, at a certain t, into a power. This could explain the break in t observed in the differential cross sections of certain reactions. It also follows that asymptotically the s and t dependences of the cross sections are of the same form, i.e. at large s a power-like decrease of cross sections with s, is matched at large t, by a power-like decrease of cross sections with t. L I S T O F P U B L I C A T I O N S BY RICHARD M. WEINER SELECTED LIST OF ARTICLES IN SCIENTIFIC JOURNALSInfluence of Argon on the vapour spectra of I, with I. Agarbiceanu, C. Ghiţa and V.Ţopa, Comunicarile Academ...