Thermodynamic Geometric Stability of Quarkonia states

TL;DR

This paper analyzes the thermodynamic geometric properties of non-abelian quarkonium states using exact calculations from one-loop strong coupling, revealing intrinsic geometric structures and stability features across different regimes.

Contribution

It provides the first exact thermodynamic geometric analysis of strongly coupled quarkonia without approximations, covering various regimes and including the effects of soft gluons and resummation.

Findings

Existence of well-defined, non-degenerate Riemannian manifolds for quarkonia.

Thermodynamic stability persists across different physical regimes.

Strong coupling from Sudhakov form factor exhibits consistent thermodynamic properties.

Abstract

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 Columbic, rising and Regge rotating regimes. Without any approximation, we have obtained the non-linear 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, non-degenerate, 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 Sudhakov form factor possesses exact local and global thermodynamic properties of the underlying mesons, kaons and $D_s$ particles.