We compute exact thermodynamic geometric properties of the non-Abelian quarkonium bound states from the consideration of one-loop strong coupling. From the general statistical principle, the intrinsic geometric nature of strongly coupled QCD is analyzed for the Colombic, rising and Regge rotating regimes. Without any approximation, we have obtained the nonlinear mass effect for the Bloch–Nordsieck rotating strongly coupled quarkonia. For a range of physical parameters, we show in each cases that there exists a well-defined, nondegenerate, curved, intrinsic Riemannian manifold. As the gluons become softer and softer, we find in the limit of the Bloch–Nordsieck resummation that the strong coupling obtained from the Sudakov form factor possesses exact local and global thermodynamic properties of the underlying mesons, kayons and Ds particles.
Two-loop Sudakov form factor in ABJM
