Soft Dipole Pomeron in Hadronic Elastic and in Deep Inelastic Scattering

Abstract

Abstracts. A brief review on the Dipole Pomeron model is given. The model not only describes data on hadron-hadron interactions, but also allows to describe data on the proton structure function with a Q 2 independent intercept. Moreover the chosen Dipole Pomeron has an intercept equal to one and does not violate unitarity limit on the total elastic cross-section.The Regge approach [1] is one of the most powerful method to investigate hadronic interactions at high energies. In spite of many unsolved problems, its actual application is slowed down because of lacking new experimental data. Now, the main efforts of the experimentalists and theoreticians are concentrated on the deep inelastic scattering (DIS) and related processes. Again the Regge method shows its effectiveness in a wide kinematical domain.It follows quite evidently from the observed growth of the hadronic total cross-sections and of the structure functions that the true Pomeron singularity is more complicated than that a simple j-pole. Even if a simple pole with an intercept larger than unity is used as an input, it should be unitarized in order to restore the Froissart-Martin bound [2], σ t (s) < C ln 2 s. Unfortunately a well defined strict procedure of unitarization is still absent, while approximate methods are used; as consequence, we do not know what is really the true Pomeron.The well known and quite popular example of a model with an input Pomeron violating the unitarity bound (because it has α P (0) ≈ 1.08 > 1)) is the Donnachie-Landshoff Pomeron (D-L) [3]. Moreover, and regrettably, in some papers this model is identified with the Regge theory and its inability to describe some experimental data is declared as a problem of Regge theory. However, and happily, the D-L Pomeron is not the only phenomenological possibility to describe the above mentioned growth of observed quantities. Another way to satisfy this property is to suppose that the Pomeron is harder than a simple pole at j = 1. The simplest realization of such an hypothesis is the Dipole Pomeron model [4].The Dipole Pomeron (DP) is a combination of the double and simple poles in the partial j-plane amplitudewith the trajectory α P (t) ≈ 1 + α ′ P t, linear at small t. The Dipole Pomeron is the unitarity limit for an isolated j-singularity with a unit intercept and with a linear trajectory at small t. IfThus in the present Dipole Pomeron model at s → ∞:The Dipole Pomeron in hadronic processes. At preasymptotic energies the contribution of other reggeons (f, ω etc...) should be added. If only pp andpp amplitudes are considered one can write(pp) (s, t) = P(s, t) + f (s, t) ± ω(s, t)with P(s, t) = i[g 1 (t) ln(−is/s 0 ) + g 2 (t)](−is/s 0 ) αP (t)−1 , s 0 = const,r(s, t) = η r g r (t)(−is/s 0 ) αr (t)−1 , r = f, ω, η f = i, η ω = 1.1 We do not consider here Odderon because it is out of the subject of talk.