Odderon effects in the differential cross-sections at Tevatron and LHC energies

In the present paper, we extend the Froissaron-Maximal Odderon (FMO) approach at t different from 0. Our extended FMO approach gives an excellent description of the 3266 experimental points considered in a wide range of energies and momentum transferred. We show that the very interesting TOTEM results for proton–proton differential cross-section in the range 2.76–13 TeV, together with the Tevatron data for antiproton–proton at 1.8 and 1.96 TeV give further experimental evidence for the existence of the Odderon. One spectacular theoretical result is the fact that the difference in the dip-bump region between \({\bar{p}}p\) and pp differential cross-sections is diminishing with increasing energies and for very high energies (say 100 TeV), the difference between \({\bar{p}}p\) and pp in the dip-bump region is changing its sign: pp becomes bigger than \({\bar{p}}p\) at |t| about 1 GeV\(^2\). This is a typical Odderon effect. Another important – phenomenological – result of our approach is that the slope in pp scattering has a different behavior in t than the slope in \({\bar{p}}p\) scattering. This is also a clear Odderon effect.