SU(3) systematization of baryons: Theoretical methods and mixing with the antidecuplet

Abstract

We take a fresh look at the SU(3) systematization of all known baryons with mass less than 2000 MeV. We describe well-known and new theoretical tools used in grouping elementary particles into unitary multiplets and present the emerging picture of the unitary multiplets and their mixing. The issue of multiplet mixing is discussed in detail with an emphasis on the mixing with the antidecuplet. While SU(3) does not strongly require that the antidecuplet mixes with any established octet or decuplet, it is still possible to mix the antidecuplet with a J P = 1/2 + octet. However, the mixing parameters cannot be reliably determined this way. Instead, one should consider decays of the antidecuplet members.

Theory of baryon resonances at largeNc

“…For the octet, the center is defined as M 8 = (2m N + 2m Ξ + 3m Σ + m Λ )/8, and for the decuplet it is M 10 = (4m ∆ + 3m Σ * + 2m Ξ * + m Ω )/10 ≈ m Σ * . We take the phenomenological values for M 8 , M 10 from the paper by Guzey and Polyakov [22] who have analyzed baryon multiplets up to 2 GeV.…”

“…(57) gives a small χ 2 = 15 MeV. It should be kept in mind, however, that not all members of all multiplets are well established [22], and those that are, have an experimental uncertainty in the masses. It means that the 'experimental' masses for the centers of multiplets are known at best to an accuracy of 20-40 MeV.…”

“…For this reason even the contents of lowest SU (3) multiplets is under discussion. We will follow analysis of paper [22] (see also [23]). …”

Dynamics of pentaquarks in constituent quark models: recent developments

“…The mixing of the antidecuplet with three octets with J P = 1/2 + has also recently been investigated phenomenologically in the chiral soliton model where it was assumed that the mixing is small [30]. It was found that this can reduce the size of the widths of the antidecuplet members without much affecting the masses.…”

Mixing and decays of the antidecuplet in context of approximate SU(3) symmetry

“…The success of this assumption was proven in [4,42]. This allows one to make definite predictions for the 10 → B + P transitions in terms of the antidecuplet and octet universal coupling constants.…”