We have not understood well the fundamental properties of high-energy
cosmic rays, such as the accurate spectrum, origins, chemical compsitions.
To get such information, we have to observe the extensive air showers
which are induced by the collisions of cosmic rays with nuclei in the air,
and compare the results with numerical simulations. In fact, the energies
of the first contact of the cosmic rays with atomospheric nuclei are much
higher than the highest energy achieved in the experiment, and could reach
10^{20} eV. However, theoretical descriptions which are employed in the
numerical simulations are not based on the modern picture of QCD, which
affects the incomplete determinations of the properties of cosmic rays.
Our objective is (A) to establish theoretical description of the high
energy reactions of cosmic rays and atomospheric nuclei based on the
modern picture of high energy scattering in QCD (e.g. "Color Glass
Condensate"), and (B) to construct a new simulation code for the
extensive air showers. We expect we will be able to provide keys
to the unsolved problems in astrophysics and particle physics.
At the same time, we are able to clarify the range (upper limit)
of validity of the current theoretical description in hadron physics.

example of simulation study Cosmic ray spectrum
Kazunori Itakura, KEK (representative)
Yasushi Nara, Akita International University
Katsuaki Kasahara, Waseda University
Shunzo Kumano, KEK
Koichi Saito, Tokyo University of Science
Masanori Hirai, Tokyo University of Science
Hirotsugu Fujii, University of Tokyo
Naoki Hotta, Utsunomiya University
Dr. Kazunori Itakura, representative of the project
e-mail: kazunori.itakura@kek.jp
KEK Theory Center, Institute of Particle and Nuclear Studies,
High Energy Accelerator Research Organization (KEK)