Ground States for Light and Heavy Quark Hadrons

Abstract

According to DE Rujula et al. if the degenerate multiplet masses are known then it is not necessary to parametrize the interactions [1]. With degenerate multiplet masses calculated from the spinorial decomposition of the SU(2) × SU (2) part of the SU (6) × SU (6) symmetry, the ground states for 3, 4 and 5 quark hadrons are calculated in terms of the Cartan matrix integers nα which represent the symmetry breaking of the SU (3) × SU (3) part, which is known to be badly broken. The effective SU (3) symmetry is found to result from a color neutrality relation ∑nα = 0 for the ground state integer sequences nα=± 3, 0, ∓ 1, ∓ 2 which hold exactly for the J = ½, 1 multiplets and approximately for the J = 0 multiplets. A large number of mass relations within each multiplet follows from the integer sequence and include the GMO and other well-known relations. The number and accuracy of the mass relations and the ground states mass series supports symmetry breaking according to the Cartan matrix integers.