The decay of resonance in the Lobachevsky velocity space is represented by an isosceles triangle inscribed in a horocycle. Near the decay triangles of scalar, strange mesons and Δ, N baryons, there are Heron’s triangles, for which are equal to integers: a) the length of the arc of the oricycle subtending the base, by the cotangent of half the angle at the vertex opposite the base; b) the hyperbolic cosines of the lengths of the lateral sides and the lengths of the bases.
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Abstract
The ends of the velocity vectors of the decay resonance particles are represented by material points of the velocity pace located inside a sphere of radius C (C is the speed of light, the points are assigned the rest masses of the decay particles). The Lorentz group defines in the velocity space the Lobachevsky geometry of curvature k = -1/ C2. A pair of material points of 2-part resonance decay can be connected by a straight line segment and an arc of zero curvature line, called an oricycle [7]. A
