On the Casimir operator dependences of QCD amplitudes

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In eikonal and quenched approximations at least, it is argued that the strong-coupling fermionic QCD amplitudes based on the newly discovered effective locality property, depart from a dependence on the sole quadratic Casimir operator, evaluated over the fundamental gauge group representation: A definite dependence on the cubic SU(3) Casimir operator takes place. This result, in contradistinction to perturbation theory, but also to a number of non-perturbative approaches such as the MIT bag, the stochastic vacuum models, and lattice simulations, accounts, instead, for the full algebraic content of the rank-2 Lie algebra.