First determination of the $${\rho }$$ parameter at $${\sqrt{s} = 13}$$ TeV: probing the existence of a colourless C-odd three-gluon compound state
Authors: Antchev G. , Aspell P. , Atanassov I. , Avati V. , Baechler J. , Barrera C. Baldenegro , Berardi V. , Berretti M. , Bossini E. , Bottigli U. , Bozzo M. , Bruce R. , Burkhardt H. , Cafagna F. S. , Catanesi M. G. , Csanád M. , Csörgő T. , Deile M. , De Leonardis F. , D’Orazio A. , Doubek M. , Druzhkin D. , Eggert K. , Eremin V. , Ferro F. , Fiergolski A. , Garcia F. , Morales H. Garcia , Georgiev V. , Giani S. , Grzanka L. , Hammerbauer J. , Heino J. , Helander P. , Isidori T. , Ivanchenko V. , Janda M. , Karev A. , Kašpar J. , Kopal J. , Kundrát V. , Lami S. , Latino G. , Lauhakangas R. , Linhart R. , Lindsey C. , Lokajíček M. V. , Losurdo L. , Lo Vetere M. , Rodríguez F. Lucas , Macrí M. , Malawski M. , Mereghetti A. , Minafra N. , Minutoli S. , Mirarchi D. , Naaranoja T. , Nemes F. , Niewiadomski H. , Novák T. , Oliveri E. , Oljemark F. , Oriunno M. , Österberg K. , Palazzi P. , Passaro V. , Peroutka Z. , Procházka J. , Quinto M. , Radermacher E. , Radicioni E. , Ravotti F. , Redaelli S. , Robutti E. , Royon C. , Ruggiero G. , Saarikko H. , Salvachua B. , Scribano A. , Siroky J. , Smajek J. , Snoeys W. , Stefanovitch R. , Sziklai J. , Taylor C. , Tcherniaev E. , Turini N. , Vacek V. , Valentino G. , Welti J. , Wenninger J. , Williams J. , Wyszkowski P. , Zich J. , Zielinski K. 
Published: September 2019

Abstract
The TOTEM experiment at the LHC has performed the first measurement at $$\sqrt{s} = 13\,\mathrm{TeV}$$s=13TeV of the $$\rho $$ρ parameter, the real to imaginary ratio of the nuclear elastic scattering amplitude at $$t=0$$t=0, obtaining the following results: $$\rho = 0.09 \pm 0.01$$ρ=0.09±0.01 and $$\rho = 0.10 \pm 0.01$$ρ=0.10±0.01, depending on different physics assumptions and mathematical modelling. The unprecedented precision of the $$\rho $$ρ measurement, combined with the TOTEM total cross-section measurements in an energy range larger than $$10\,\mathrm{TeV}$$10TeV (from 2.76 to $$13\,\mathrm{TeV}$$13TeV), has implied the exclusion of all the models classified and published by COMPETE. The $$\rho $$ρ results obtained by TOTEM are 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 $$\rho $$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 $$\sigma _{\mathrm{tot}} = (110.3 \pm 3.5)\,\mathrm{mb}$$σtot=(110.3±3.5)mb, completely independent from the previous TOTEM determination. Combining the two TOTEM results yields $$\sigma _{\mathrm{tot}} = (110.5 \pm 2.4)\,\mathrm{mb}$$σtot=(110.5±2.4)mb.