This is the extensive followup report of a recent Letter in which the existence of self-organized criticality (SOC) in systems of interacting soft gluons is proposed, and its consequences for inelastic diffractive scattering processes are discussed. It is pointed out that color-singlet gluon clusters can be formed in hadrons as a consequence of SOC in systems of interacting soft gluons, and that the properties of such spatiotemporal complexities can be probed experimentally by examing inelastic diffractive scattering. Theoretical arguments and experimental evidence supporting the proposed picture are presented—together with the result of a systematic analysis of the existing data for inelastic diffractive scattering processes performed at different incident energies and/or by using different beam particles. It is shown in particular that the size and the lifetime distributions of such gluon clusters can be directly extracted from the data, and the obtained results exhibit universal power-law behaviors—in accordance with the expected SOC fingerprints. As further consequences of SOC in systems of interacting soft gluons, the t dependence and the ${(M}_x^2/s)$ dependence of the double differential cross sections for inelastic diffractive scattering off a proton target are discussed. Here t stands for four-momentum-transfer squared, $M_x$ for the missing mass, and $\sqrt{s}$ for the total c.m. system energy. It is shown that the space-time properties of the color-singlet gluon clusters due to SOC, discussed above, lead to simple analytical formulas for $d^2\sigma /dt{d(M}_x^2/s)$ and for $d\sigma /dt,$ and that the obtained results are in good agreement with the existing data. Further experiments are suggested.

• Received 10 May 1999

DOI:https://doi.org/10.1103/PhysRevD.61.094010