The TOTEM experiment at LHC has performed total and differential elastic p-p cross-section measurements at different LHC energies. Since 2018 a first hint of the presence of the Odderon was found in TOTEM results. Now the discovery has been confirmed after a comparison with the p-bar-p data measured by the D0 collaboration at Fermilab.
The comparison of the two experiment results led to the first experimental observation of the exchange of the Odderon with a significance of 5.4σ.

The Odderon, first theorized in 1973, represents the C-odd counterpart of the Pomeron, the dominant Regge trajectory in the soft high energy diffractive interactions.
The Odderon emerges not only in the Regge framework, but also in QCD theory where it can be modelled as an exchange of a colourless C-odd gluonic compound.
States comprising two, three or more gluons are usually called “glueballs”, and their observation represents a key test of the QCD.
The talk will give a theoretical introduction to the Odderon in the context of both Regge and QCD frameworks, highlighting the best strategy to observe such enigmatic object at the LHC.

The TOTEM experiment and results will be described and a detailed report of the latest analysis, in collaboration with D0, will be given. The future measurements of TOTEM at a centre-of-mass energy of 14 TeV will be briefly commented as well.

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