Eikonal Amplitude in the Gravireggeon Model at Superplanckian Energies
  The gravity effects in high-energy scattering, described by a four-dimensional eikonal amplitude related to gravireggeons induced by compact extra dimensions are studied. It is demonstrated that the real part of the eikonal (with a massless mode subtracted) dominates its imaginary part at both small and large impact parameters, in contrast to the usual case of hadronic high-energy behavior. The real part of the scattering amplitude exhibits an exponential falloff at large momentum transfer, similar to that of the imaginary part of the amplitude. 
A.V. Kisselev and V.A. Petrov (IHEP, Protvino)