First determination of the $ρ$ parameter at $\sqrt{s} = 13$ TeV -- probing the existence of a colourless three-gluon bound state

The TOTEM experiment at the LHC has performed the first measurement at $\sqrt{s} = 13$ TeV of the $ρ$ parameter, the real to imaginary ratio of the nuclear elastic scattering amplitude at $t=0$, obtaining the following results: $ρ= 0.09 \pm 0.01$ and $ρ= 0.10 \pm 0.01$, 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 10 TeV (from 2.76 to 13 TeV), 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 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. The very low-$|t|$ reach allowed also to determine the absolute normalisation using the Coulomb amplitude for the first time at the LHC and obtain a new total proton-proton cross-section measurement $σ_{tot} = 110.3 \pm 3.5$ mb, completely independent from the previous TOTEM determination. Combining the two TOTEM results yields $σ_{tot} = 110.5 \pm 2.4$ mb.