Charge specific baryon mass relations with deformed SUq(3) flavor symmetry

Abstract

The quantum group SUq(3) = Uq(su (3)) is taken as a baryon flavor symmetry. Accounting for electromagnetic contributions to baryons masses to zeroth order, new charge specific q-deformed octet and decuplet baryon mass formulas are obtained. These new mass relations have errors of only 0.02% and 0.08% respectively; a factor of 20 reduction compared to the standard Gell-Mann-Okubo mass formulas. A new relation between the octet and decuplet baryon masses that is accurate to 1.2% is derived. An explicit formula for the Cabibbo angle, taken to be π 14 , in terms of the deformation parameter q and spin parity J P of the baryons is obtained.

Magnetic moments of octet baryons with deformed Uq(su(3)) flavor symmetry

“…In this paper we have investigated the effect of using a q-deformed flavor symmetry on the magnetic moments of octet baryons. Our work was motivated by the exceptionally accurate baryon mass sum rules that arise from deforming flavor symmetry [1][2][3]. Using the experimentally observed values for the magnetic moments of the proton, neutron and Λ baryons as input, we calculated the magnetic moments of the up, down, and strange quarks, and by extension those of the remaining octet baryons as functions of the deformation parameter q.…”

“…φ(Λ 0 ) A = q [2] q [3] q [−q −3 2 [2] q dus + q −1 [2] q uds + usd − q −1 2 dsu − q −1 2 sud + q −1 sdu].…”

“…Even though the magnetic moments of nucleons and other octet baryons as calculated within the non-relativistic quark model based on SU (3) flavor symmetry are in reasonable agreement with experimental values, a first principle derivation of nucleon magnetic moments is still lacking at present. Taken as a flavor symmetry, the quantum group U q (su(3)) gives rise to exceptionally accurate baryon mass formulas [1,2] that agree perfectly with the experimental data, especially when the electromagnetic contributions to mass are accounted for [3]. Given this exceptional accuracy of baryon mass formulas that result from a deformation of flavor symmetry, it is natural and worthwhile to likewise investigate the effect of such a deformation on the magnetic moments of baryons.…”

Quantum groups as fundamental symmetries

“…For suitable values of the deformation parameter q (taken to be a root of unity), the obtained mass formulas are accurate enough that mass differences within baryon multiples, due to electromagnetic mass contributions, can no longer be ignored. Accounting for these electromagnetic mass contribution by using the general QCD parametrization scheme of Morpurgo [26], Gresnigt [27] derived the following generalized mass formulas for the octet baryons:…”

“…Additionally, the use of a quantum group as a flavour symmetry suggest an explicit formula for the Cabibbo angle, taken to be π 14 , in terms of the deformation parameter q and spin parity J P of the baryons [22,27,28] θ C = −iJ P ln q.…”