Phenomenology of the BFKL pomeron and Unitarity Corrections at low x

Abstract

The low $x$ limit of deep inelastic electron proton scattering is considered using methods of perturbative QCD. In the first part we investigate the phenomenological consequences of the resummation of leading logarithms in $1/x$ given by the BFKL pomeron. We apply the BFKL pomeron to the inclusive structure function $F_2$, to the diffractive production of vector mesons at large momentum transfer, to inclusive photon diffractive dissociation in DIS and to quark-antiquark production with large transverse momenta in DIS diffractive dissociation. For the last process we perform extensive numerical calculations based on the double logarithmic approximation. The BFKL pomeron is known to violate unitarity. In the second part the first next-to-leading corrections which have to be taken into account to restore unitarity of the scattering amplitude are investigated. A compact configuration space representation of the two to four gluon transition vertex is derived. Conformal symmetry of the vertex is proven and its relation to a conformal covariant three point function is established. The important role of the spectral function $χ_4$ of the four gluon state is pointed out. We relate this function to the twist expansion of the four gluon amplitude. Motivated by this relation we develop a method to perform the twist expansion of the amplitude. Based upon first results of our analysis we draw conclusions concerning the singularity structure of the function $χ_4$.