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

The TOTEMexperiment at the LHC has performed the first measurement at \(\sqrt{s} = 13\,\mathrm{TeV}\) of the \(\rho \) parameter, the real to imaginary ratio of the nuclear elastic scatteringamplitude at \(t=0\), obtaining the following results: \(\rho = 0.09 \pm 0.01\) and \(\rho = 0.10 \pm 0.01\), depending on different physics assumptions and mathematical modelling. The unprecedented precision of the \(\rho \) measurement, combined with the TOTEMtotal cross-section measurements in an energy range larger than \(10\,\mathrm{TeV}\) (from 2.76 to \(13\,\mathrm{TeV}\)), has implied the exclusion of all the models classified and published by COMPETE. The \(\rho \) results obtained by TOTEMare compatible with the predictions, from other theoretical models both in the Regge-like framework and in the QCD framework, of a crossing-odd colourless 3-gluon compound state exchange in the t-channel of the proton–proton elastic scattering. On the contrary, if shown that the crossing-odd 3-gluon compound state t-channel exchange is not of importance for the description of elastic scattering, the \(\rho \) value determined by TOTEMwould 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 \(\sigma _{\mathrm{tot}} = (110.3 \pm 3.5)\,\mathrm{mb}\), completely independent from the previous TOTEMdetermination. Combining the two TOTEMresults yields \(\sigma _{\mathrm{tot}} = (110.5 \pm 2.4)\,\mathrm{mb}\).