First determination of the ${\rho }$ parameter at ${\sqrt{s} = 13}$ TeV: probing the existence of a colourless C-odd three-gluon compound state

The TOTEM experiment at the LHC has performed the first measurement at √s = 13 TeV of the ρ parameter, the real to imaginary ratio of the nuclear elastic scattering amplitude at t = 0, obtaining the following results: ρ = 0.09 ± 0.01 and ρ = 0.10 ± 0.01, depending on different physics assumptions and mathematical modelling. The unprecedented precision of the ρ measurement, combined with the TOTEM total cross-section measurements in an energy range larger than 10TeV (from 2.76 to 13TeV), has implied the exclusion of all the models classified and published by COMPETE. The ρ results obtained by TOTEM are compatible with the predictions, from alternative theoretical models both in the Regge-like framework and in the modern QCD framework, of a colourless 3-gluon bound state exchange in the t-channel of the proton-proton elastic scattering. On the contrary, if shown that the 3-gluon bound state t-channel exchange is not of importance for the description of elastic scattering, the ρ value determined by TOTEM would represent a first evidence of a slowing down of the total cross-section growth at higher energies.