  The gyraton model describes a gravitational field of an object moving with
the velocity of light which has finite energy and spin distributed during some
finite time interval $L$. A gyraton may be considered as a classical toy model
for a quantum wave packet of high-energy particles with spin. In this paper we
study a head-on collision of two gyratons and black hole formation in this
process. The goal of this study is to understand the role of the gravitational
spin-spin interaction in the process of mini-black-hole formation in particle
collisions. To simplify the problem we consider several gyraton models with
special profiles of the energy and spin density distribution. For these models
we study the apparent horizon (AH) formation on the future edge of a spacetime
region before interaction. We demonstrate that the AH forms only if the energy
duration and the spin are smaller than some critical values, while the length
of the spin distribution should be at least of the order of the system
gravitational radius. We also study gravitational spin-spin interaction in the
head-on collision of two gyratons under the assumption that the values of
gyraton spins are small. We demonstrate that the metric in the interaction
region for such gyratons depends on the relative helicities of incoming
gyratons, and the collision of gyratons with oppositely directed spins allows
the AH formation in a larger parameter region than in the collision of the
gyratons with the same direction of spins. Some applications of the obtained
results to the mini-black-hole production at the Large Hadron Collider in TeV
gravity scenarios are briefly discussed.

General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory