The strong coupling constant: Its theoretical derivation from a geometric approach to hadron structure

Since more than a decade, a 'bi-scale', unified approach to strong and gravitational interactions has been proposed, that uses the geometrical methods of general relativity, and yielded results similar to 'strong gravity' theory's. The authors fix their attention, in this note, on hadron structure, and show that also the strong interaction strength αS, ordinarly called the '(pertubative) coupling-constant square', can be evaluated within their theory, and found to decrease (increase) as the distances 'r' decreases (increases). This yields both the confinement of the hadron constituents (for large values of r), and their asymptotic freedom (for small values of r inside the hadron): in qualitative agreement with the experimental evidence. Their approach lead, on a purely theoretical ground, to a dependence of δS on r which had been previously found only on phenomenological and heuristical grounds. The authors expect the above agreement to be also quantitative, on the basis of a few checks performed in this paper, and of further works about calculating meson mass-spectra