Although air shower observations at the surface of the earth have been developed in order to understand the origin of the ultra high energy cosmic rays, the observations have uncertainties in interpretation of the observed data from the present phenomenological nuclear collision models. Precision measurements of the very forward particle production in the collider experiments improve understanding of particle production processes in the nuclear collisions, and provide large influences on interpretation of the observed data and the origin of the cosmic rays. On the other hand, a large 10% single transverse-spin asymmetry in neutron production from transversely polarized proton collisions was found at the RHIC collider at BNL. It has provided a valuable input for understanding particle production processes in the polarized proton collisions. We will have a new collider experiment at RHIC which has a high resolution and a wide coverage of transverse momentum measurements in order to figure out elementary processes of the air shower generation.
Collins Function and the Single Transverse Spin Asymmetry