Baryons from quarks in curved space and deconfinement

Abstract

Detailed account is given of the fact that the Cornell potential predicted by Lattice QCD and its exactly solvable trigonometric extension recently reported by us can be viewed as the respective approximate and exact counterparts on a curved space to an 1/r flat space potential. The "curved" potential describes a confinement phenomenon as it is of infinite depth and has only bound states. It furthermore has the remarkable property of preserving both the SO(4) and SO(2, 1) symmetries characterizing the ordinary 1/r potential. We first make the case that this particular geometric vision on confinement provides a remarkably adequate description of both nucleon and ∆ spectra and the proton mean square charge radius as well, and suggests an intriguing venue toward quark deconfinement as a shut-down of the curvature considered as temperature dependent. Next we observe that the SO(2, 1) symmetry of the "curved" potential allows to place it within the context of AdS 5 /CF T correspondence and to establish in this manner the algebraic link of the latter to QCD potentiology. "...there will be no contradiction in our mind if we assume that some natural forces are governed by one special geometry, while other forces by another."N. I. Lobachevsky

Dynamically generated resonances from the vector octet-baryon octet interaction

“…Since the spin dependence only comes from the ǫ ǫ ′ factor and there is no dependence on the spin of the baryons, the interaction for vector-baryon states with 1/2 − and 3/2 − is the same and then one should associate each peak with the existence of two degenerate states. The spin degeneration also appears in some quarks models [44].…”

Dynamically generated resonances from the vector octet-baryon decuplet interaction

“…Since the spin dependence only comes from the ǫ • ǫ ′ factor and there is no dependence on the spin of the baryons, the interaction for vector-baryon states with 1/2 − , 3/2 − and 5/2 − is the same and thus we get three degenerate states for each of the resonances found. The spin degeneracy also appears in some quark models [47].…”