Neutron to proton mass difference, parton distribution functions and baryon resonances from dynamics on the Lie group u(3)

Abstract

We present a hamiltonian structure on the Lie group u(3) to describe the baryon spectrum. The ground state is identified with the proton. From this single fit we calculate approximately the relative neutron to proton mass shift to within half a percentage of the experimental value. From the same fit we calculate the nucleon and delta resonance spectrum with correct grouping and no missing resonances. For specific spin eigenfunctions we calculate the delta to nucleon mass ratio to within one percent. Finally we derive parton distribution functions that compare well with those for the proton valence quarks. The distributions are generated by projecting the proton state to space via the exterior derivative on u(3). We predict scarce neutral flavour singlets which should be visible in neutron diffraction dissociation experiments or in invariant mass spectra of protons and negative pions in B-decays and in photoproduction on neutrons. The presence of such singlet states distinguishes experimentally the present model from the standard model as does the prediction of the neutron to proton mass splitting. Conceptually the Hamiltonian may describe an effective phenomenology or more radically describe interior dynamics implying quarks and gluons as projections from u(3) which we then call allospace.