5 - From cuts to poles

Summary

As we pointed out in the preceding chapter, there are several important differences between the behaviour of the perturbative QCD Pomeron which is the solution of the BFKL equation and that of the ‘soft’ Pomeron predicted by Regge theory and identified in total hadronic cross-sections and differential cross-sections at small tranverse momenta. Although one might have hoped that a purely perturbative analysis of QCD would yield results which were in qualitative agreement with the behaviour of the ‘soft’ Pomeron, it is not surprising that the results are in fact very different. Perturbative QCD theory can only be applied reliably to Green functions in which all the momenta and their scalar products are sufficiently large. In the subsequent two chapters we shall be discussing experimental situations in which such criteria are obeyed. However, total hadronic cross-sections or differential cross-sections with low momentum transfer do not obey these criteria and we must therefore expect that non-perturbative features of QCD will play a crucial role in describing such phenomena. Unfortunately a complete analysis of the non-perturbative behaviour of QCD is outside our present grasp. Nevertheless, we can investigate the ‘meeting points’ of perturbative and non-perturbative QCD in order to obtain some idea of how non-perturbative effects are likely to affect the Pomeron and to what extent we may expect to be able to reproduce the behaviour of hadronic cross-sections in QCD.