Latest results for Proton-proton Cross Section Measurements with the TOTEM experiment at LHC

The precise knowledge of the proton-proton cross section is extremely important to model the development, in the atmosphere, of the showers induced by the interaction of ultra high energy cosmic rays.The TOTEM (TOTal cross section, Elastic scattering and diffraction dissociation Measurement at the LHC) experiment, located at the interaction point 5 of the LHC, has measured the total, elastic and inelastic proton-proton cross-sections, using a luminosity independent method, based on the optical theorem, in a center-of-mass energy range from 2.76 to 13 TeV. The elastic scattering was investigated in a wide range of the squared four-momentum transfer |t| allowing the study of Coulomb-nuclear interference region down to |t| ~8 x 10$^{-4}$ GeV$^{2}$. This made possible the first measurement of the $\rho$ parameter at $\sqrt{s}$ = 13 TeV, $\rho$ being the ratio between the real and the imaginary part of the nuclear elastic scattering amplitude at $t$ = 0. This measurement, combined with the total cross-section results, led to the exclusion of all the models classified and published by the COMPETE Collaboration. The results obtained by TOTEM are indeed compatible with predictions of a colorless 3-gluon bound state exchange in the t-channel of proton-proton elastic scattering, as postulated by alternative theoretical models both in the Regge-like framework and in the modern QCD framework.In this contribution the latest TOTEM will be given, along with the actual experiment status and the future physics program for the LHC run 3.