Testing a conjecture on quantum chromodynamics

Abstract

A Planck-scale model that includes quantum chromodynamics and goes beyond it, is tested against observations. The model is based on a single fundamental principle. Starting with Dirac’s proposal describing spin [Formula: see text] particles as tethered objects, quarks and elementary fermions are conjectured to be fluctuating rational tangles with unobservable tethers. Such tangles obey the free Dirac equation. Classifying rational tangles naturally yields the observed spectrum of elementary fermions, including the six quark types and their quantum numbers. Classifying tangle deformations naturally yields exactly three types of gauge interactions, three types of elementary gauge bosons, and the symmetry groups U(1), broken SU(2) and SU(3). The possible rational tangles for quarks, leptons, Higgs and gauge bosons allow only the observed Feynman diagrams. The complete Lagrangian of the standard model — without any modification and including the Lagrangian of quantum chromodynamics — arises in a natural manner. Over 90 experimental consequences and tests about quark and gluon behavior are deduced from the single fundamental principle. No consequence is in contrast with observations. The consequences of the strand conjecture include the complete quark model for hadrons, the correct sign of hadron quadrupole moments, color flux tubes, confinement, Regge behavior, running quark masses, correctly predicted hadron mass sequences, the lack of CP violation for the strong interaction, asymptotic freedom, and the appearance of glueballs. Two consequences differ from quantum chromodynamics. First, the geometry of the strand process for the strong interaction leads to an ab-initio estimate for the running strong coupling constant. Second, the tangle shapes lead to ab-initio lower and upper limits for the mass values of the quarks.