Soft interaction at high energy andN= 4 SYM

Abstract

In this paper we show that the N=4 SYM total cross section violates the Froissart theorem, and in the huge range of energy this cross section is proportional to s1/3. The graviton reggeization will change this increase to the normal logarithmic behavior σ ln2s. However, we demonstrated that this happens at ultra high energy, much higher than the LHC energy. In the region of accessible energy we need to assume that there is a different source for the total cross section, with the value of the cross section about 40 mb. With this assumption we successfully describe σtot,σel and σdiff for the accessible range of energy from the fixed target Fermilab to the Tevatron energies. It turns out that the N=4 SYM mechanism can be responsible only for a small part of the inelastic cross section for this energy region (about 2 mb). However, at the LHC energy the N=4 SYM theory can describe the multiparticle production with σin ≈ 30 mb. The second surprise is the fact that the total cross section and the diffraction cross section can increase considerably from the Tevatron to the LHC energy. The bad description of Bel gives the strong argument that the non N=4 SYM background should depend on energy. We believe that we have a dilemma: to find a new mechanism for the inelastic production in the framework of N=4 SYM other than the reggeized graviton interaction, or to accept that N=4 SYM is irrelevant to any experimental data that has been measured before the LHC era.