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Forward physics measurements with the Compact Muon Solenoid (CMS) experiment, one of the two large multi-purpose experiments at the Large Hadron Collider (LHC) at CERN, cover a wide range of physics subjects. The forward calorimeters of CMS, HF and CASTOR, are used to collect data up to a pseudo-rapidity of 6.6. These detectors provide sensitivity to a large part of the total inelastic cross section, including diffractive events that produce particles only at forward rapidity, with the exception of very low mass diffraction. The results obtained with a centre-of-mass energy of 13 TeV are presented. The measurements are compared to model predictions and provide valuable input for tuning of Monte Carlo models used to describe high-energy hadronic interactions

Forward Physics with the CMS Experiment at LHC