The stationary points and structure of high-energy scattering amplitude

The ISR and the 7 TeV LHC data indicate that the differential cross-section of elastic proton-proton scattering remains almost energy-independent at the transferred momentum t≈−0.21GeV2 at the level of ≈7.5  mb/GeV2. This property of dσ/dt (the “first” stationary point) appears due to the correlated growth of the total cross-section and the local slope parameter and can be expressed as a relation between the latter quantities. We anticipate that this property will be true up to 13 TeV. This enables us to normalize the preliminary TOTEM data for dσ/dt at 13 TeV and 0.05<|t|<3.4GeV2 and predict the values of dσ/dt at this energy. These data give an evidence of the second stationary point at t≈−2.3GeV2 at the level of ≈33  nb/GeV2. The energy evolution of dσ/dt looks as if the high energy elastic scattering amplitude is a sum of two similar terms. We argue that the existence of the two stationary points and the two-component structure of the high energy elastic scattering amplitude are general properties for all elastic processes.