Analytic Properties of DPE Amplitudes or Collinear Factorisation for Central Exclusive Production

Analytic and crossing properties of amplitudes of the central exclusive production (CEP) are considered using the formalism of collinear Generalised Parton Distributions (GPDs). The analytic continuation from unphysical region is considered which leads to the finite expression. The natural interpretation of the emerging cuts corresponds to double spectral density in overlapping channel due to the instability of produced particle and inapplicability of Steinmann relations. The relations of CEP amplitudes to the exclusive decay rates are discussed. The direct calculation in physical region results in violation of factorisation similar to the discussed recently for pion transition and electromagnetic form-factors. The similarity between Feynman mechanism for form-factor and Durham model is pointed out.