Forward physics with the LHCf experiment: a LHC contribution to cosmic-ray physics

LHCf is a small detector installed at LHC accelerator to measure neutral particle flow in the forward direction of proton - proton (p - p) and proton - nucleus (p - A) interactions. Thanks to the optimal performance that has characterized the last years' running of the LHC collider, several measurements have been taken since 2009 in different running conditions. After data taking for p - p interactions at root s = 900 GeV, 2.76 TeV and 7 TeV and proton - Lead nucleus (p - Pb) at root s(NN) = 5.02 TeV (energy of a couple of projectile and target nucleons in their center of mass reference frame), LHCf is now going to complete its physics program with the 13 TeV p - p run foreseen in 2015. The complete set of results will become a reference data set of forward physics for the calibration and tuning of the hadronic interaction models currently used for the simulation of the atmospheric showers induced by very high energy cosmic rays. For this reason we think that LHCf is giving an important contribution for the study of cosmic rays at the highest energies. In this paper the experiment, the published results and the current status are reviewed.