Double-Logarithmic contribution to Pomeron and application to the photon-photon scattering

by Boris Ermolaev (Ioffe Physico-Technical Institute)


Pomeron was introduced in 1958 in the framework of phe- nomenological Regge theory. It is supposed to govern the high-energy asymp- totics of various hadronic processes and control dependence of the total cross section on the energy. There are phenomenological and QCD based Pomerons in the literature. The best-known QCD contribution to Pomeron comes from the BFKL equation which resums Leading Logarithmic (LL) contributions, i.e. the single-logarithmic contributions multiplied by the overall factor s (or 1/x for the inclusive processes). The high-energy asymptotics of this resum- mation is known as the BFKL Pomeron.

In contrast, a contribution to Pomeron obtained in the Double-Logarithmic Approximation (DLA) does not involve such factor. By this reason it looks negligibly small and as a result such DL contributions were ignored by the HEP society.

Using the γ ∗ γ ∗ -scattering amplitude Aγ γ as an example, we demonstrate

that the DL contribution to Pomeron is of the same value as the BFKL con-

tribution. We also show that the higher accuracy of calculation the lower

is the Pomeron intercept. We fix the applicability region for Pomeron (for

example, the asymptotics of Aγγ can be used at x < 10−6 Q21Q2, with Q21,2 being the photon virtualities). The use of Pomerons outside its proper appli- cability region leads to misconceptions such as introducing phenomenological ”hard” Pomerons for both unpolarized and spin-dependent processes.