2009/05/27 by V. Dmitrašinović, V. Dmitrasinovic, T. Sato +2
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph
paper · pdf · doi:10.1140/epjc/s10052-009-1050-y
published as Eur.Phys.J.C62:383-397,2009 · 19 pages, 6 figures
openalex publication_date 2009/05/27 · arxiv created 2009/06/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We calculate the energies of three-quark states with definite permutation symmetry (i.e. of SU(6) multiplets) in the N=0,1,2 shells, confined by the Y-string three-quark potential. The exact Y-string potential consists of one, so-called three-string term, and three angle-dependent two-string terms. Due to this technical complication we treat the problem at three increasingly accurate levels of approximation: 1) the (approximate) three-string potential expanded to first order in trigonometric functions of hyper-spherical angles; 2) the (approximate) three-string potential to all orders in the power expansion in hyper-spherical harmonics, but without taking into account the transition(s) to two-string potentials; 3) the exact minimal-length string potential to all orders in power expansion in hyper-spherical harmonics, and taking into account the transition(s) to two-string potentials. We show the general trend of improvement %convergence of these approximations: The exact non-perturbative corrections to the total energy are of the order of one per cent, as compared with approximation 2), yet the exact energy differences between the [20,1+], [70,2+], [56,2+], [70,0+]-plets are shifted to 2:2:0.9, from the Bowler and Tynemouth separation rule 2:2:1, which is obeyed by approximation 2) at the one per cent level. The precise value of the energy separation of the first radial excitation ("Roper") [56′,0+]-plet from the [70,1-]-plet depends on the approximation, but does not become negative, i.e. the "Roper" remains heavier than the odd-parity [70,1-]-plet in all of our approximations.