Evidence for Non-Exponential Differential Cross-Section of pp Elastic   Scattering at Low |t| and $\sqrt{s}$ = 8 TeV by TOTEM
  Recently published and preliminary results of the TOTEM experiment are presented, emphasizing a recent discovery of a non-exponential behaviour of the differential cross-section of elastic proton-proton scattering, that TOTEM measured with an unprecedented precision at the centre-of-mass energy $\sqrt{s}$ = 8 TeV based on a high-statistics data sample obtained with the $\beta_* = 90$ m optics of CERN LHC. Both the statistical and systematic uncertainties remained below 1%, except for the t-independent contribution from the overall normalisation. This measurement allowed TOTEM to exclude a purely exponential differential cross-section in the range of four-momentum transfer squared 0.027 < |t| < 0.2 GeV$^2$ with a significance greater than 7 $\sigma$. In this context we also highlight the innovative TOTEM recalibration of LHC optics, that used elastic scattering data measured by the world's largest and most complex Roman Pot detector system, and discuss recent preliminary TOTEM data on the Coulomb-Nuclear interference region with its physics implications. 
T. Cs\"org\H{o} (for the TOTEM Collaboration)
hep-ex hep-ph