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

TL;DR

This paper reports the first measurement of the rho parameter at 13 TeV by the TOTEM experiment, providing insights into proton-proton elastic scattering and potential evidence for a three-gluon bound state or a slowdown in cross-section growth.

Contribution

It presents the first 13 TeV measurement of the rho parameter and total cross-section, testing models including a three-gluon bound state and refining elastic scattering understanding.

Findings

Measured rho parameter as 0.09 and 0.10 with high precision.

Excluded all models from the COMPETE classification based on measurements.

Determined the total cross-section as 110.3 mb, independent of previous results.

Abstract

The TOTEM experiment at the LHC has performed the first measurement at $\sqrt{s} = 13$ TeV of the $\rho$ parameter, the real to imaginary ratio of the nuclear elastic scattering amplitude 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 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 $\rho$ 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 $\rho$ 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 $\sigma_{tot} = 110.3 \pm 3.5$ mb, completely independent from the previous TOTEM determination. Combining the two TOTEM results yields $\sigma_{tot} = 110.5 \pm 2.4$ mb.