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Recently published and preliminary results of the TOTEM experiment arepresented, emphasizing a recent discovery of a non-exponential behaviour of thedifferential cross-section of elastic proton-proton scattering, that TOTEMmeasured 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 systematicuncertainties remained below 1%, except for the t-independent contribution fromthe overall normalisation. This measurement allowed TOTEM to exclude a purelyexponential differential cross-section in the range of four-momentum transfersquared 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 LHCoptics, that used elastic scattering data measured by the world's largest andmost complex Roman Pot detector system, and discuss recent preliminary TOTEMdata on the Coulomb-Nuclear interference region with its physics implications.

Evidence for Non-Exponential Differential Cross-Section of pp Elastic Scattering at Low |t| and $\sqrt{s}$ = 8 TeV by TOTEM