Light meson masses from baryon interaction states?

Abstract

We examine interaction states between baryons in U(3) configurations. Such interaction states may represent the meson mass spectrum above the pion triplet. Our configuration space is the Lie group U(3) with a Hamiltonian structure for baryons as stationary states. Mesonic states come about via an interaction potential. The Hamiltonian can be diagonalized by a Rayleigh-Ritz method resulting in matrix element integrals that can be solved analytically for the toroidal degrees of freedom by expanding on a suitable set of base functions. We compare calculated eigenvalues for indefinite parity states to observed unflavoured meson masses.

On quarks and the origin of QCD: Partons and baryons from intrinsic states

“…(43) Like for the neutral states R n in (41) also the Hamiltonian in ( 1) for (43) can be diagonalized with a Rayleigh-Ritz method [19,32] where the integrals needed for the Hamiltonian matrix elements can be found analytically and the eigenvalues therefore be found with high accuracy. The eigenvalues for these cases are given in table 2 (see Supplementary Material Supp5-3Dsinglets-Mathcad.mcd and Supp5a-3Dsinglets-Mathcad.pdf (SM5)).…”

“…with non-negative integers 0 ≤ p < r and 0 < q. For R n the set is complete and yields the very accurate neutron-to-electron mass ratio [9,32] (see Supplementary Material Supp4-3DneutralN-Mathcad.mcd and Supp4a-3DneutralN-Mathcad.pdf (SM4))…”

Neutron charge radius from intrinsic quark flavour generation

“…This is possible because the potential in (19) only depends on the eigenvalues e iθj of u [32] through the three dynamical eigenangles θ j ([aθ i , p j ] = −i δ ij ),…”

“…We want to ascribe curvatures with physical dimensions to these orbits. For that we use the length scale a in (19). We determine the length scale from the classical electron radius r e [17,18] by taking [24] πa = r e .…”

“…The torus embeds in the laboratory space two out of three dimensions of the Abelian part of U (3). The two dimensions are excited by flavour generators Tu, T d (26) with integral curves [13] of the vector fields (blue and green, respectively) excited by the momentum form applied to the intrinsic neutron wave function as a ground state of (19). and this interpretation is still alive in [14] which yields r 2 n = −0.119 fm 2 as a center value within the interval (−0.13…”