  The processes with single top quark production provide a prototype search for
the types of final state that are expected in many new physics scenarios. Some
distinctive features are considered for particle production in the top sector
in ultra-high energy domain which can be covered partly in the collisions of
cosmic ray particles with atmosphere. The single top quark production through
electroweak interaction is studied within the Standard Model and the Effective
Field Theory approach used for calculations of total partonic cross sections in
$s$-channel. These quantitative results can be important for both the future
collider experiments at center-of-mass energy frontier and the improvement of
the phenomenological models for development of the cosmic ray cascades in
ultra-high energy domain. Thus the study allows the better understanding of
heavy particle production and emphasizes the exciting interrelation between the
high-energy physics on accelerators and ultra-high energy cosmic ray
measurements.
