Black hole formation in the grazing collision of high-energy particles

We numerically investigate the formation of D-dimensional black holes in high-energy particle collisions with the impact parameter and evaluate the total cross section of black hole production. We find that the formation of an apparent horizon occurs when the distance between the colliding particles is less than 1.5 times the effective gravitational radius of each particle. Our numerical result indicates that although both the one-dimensional hoop and the $\left(D-3\right)$-dimensional volume corresponding to the typical scale of the system give a fairly good condition for horizon formation in the higher-dimensional gravity, the $\left(D-3\right)$-dimensional volume provides a better condition to judge the existence of the horizon.