De Sitter Special Relativity as a Possible Reason for Conformal Symmetry and Confinement in QCD

TL;DR

This paper proposes a novel approach to understanding conformal symmetry and confinement in QCD by modeling hadrons within a de Sitter space-time framework, leading to predictions consistent with observed meson spectra and form factors.

Contribution

It introduces a de Sitter $dS_4$ geometric model for hadrons, linking conformal symmetry and confinement to the geometry of internal space-time and deriving a new potential for meson modeling.

Findings

Model predicts meson spectra consistent with experimental data.

Derived potential relates QCD parameters to fundamental constants.

Fair agreement with pion form factor measurements.

Abstract

Conformal symmetry and color confinement in the infrared regime of QCD are interpreted by means of a conjectured deSitter $dS_4$ geometry of the internal space-time of hadrons, an assumption inspired by the hypothesis on deSitter special relativity. Within such a scenario, the interactions involving the virtual gluon and constituent quark degrees of freedom of hadrons are deduced from the Green functions of Laplace operators on the $dS_4$ geodesics. Then the conformal symmetry of QCD emerges as a direct consequence of the conformal symmetry of the $dS_4$ space-time, while the color confinement, understood as colorlessness of hadrons, appears as a consequence of the inevitable charge neutrality of the unique closed space-like manifold, the three dimensional hyper-sphere $S^3$, on whose geodesics the hadron's constituents are conjectured to reside when near rest frame. Mesons are now modelled as quarkish color-anticolor dipoles, whose free quantum motions on the aforementioned $S^3$ geodesic are perturbed by a potential generated by a gluon--anti-gluon color dipole. The potential predicted presents itself as the color charge analogue to the "curved" Coulomb potential, i.e. to the electric potential that defines a consistent electrostatic theory on a hyper-spherical surface. The advantage of this method is that it allows to establish a direct relationship of the potential parameters to the fundamental constants of QCD. We apply the model to the description of the spectra of the $a_1$ and $f_1$ mesons, and the pion electric charge form factor, finding fair agreement with data.