PATTERNS IN THE NONSTRANGE BARYON SPECTRUM. P. González , J. Vijande, A. Valcarce, H. Garcilazo. INDEX i) The baryon spectrum: SU(3) and SU(6) x O(3). ii) The Quantum Number Assignment Problem. iii) Screened Potential Model for Nonstrange Baryons.
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P. González, J. Vijande, A. Valcarce, H. Garcilazo
i) The baryon spectrum: SU(3) and SU(6) x O(3).
ii) The Quantum Number Assignment Problem.
iii) Screened Potential Model for Nonstrange Baryons.
iv) SU(4) x O(3) : Spectral predictions up to 3 GeV.
The richness of the baryon spectrum tells us about the existence, properties and dynamics of the intrabaryon constituents.
How can we extract this physical content?
The knowledge of spectral patterns is of great help.
The Eightfold Way: SU(3)
The pattern of multiplets makes clear the existence of quarks with “triplet” quantum numbers and the regularities in the spectrum.
From the spectral regularities one can make predictions and obtain information on the dynamics (SU(3) breaking terms).
Strange quark mass splitting?
I prediction by Gell-Mann
Quarks with Spin : SU(6) i SU(3) x SU(2)
Quarks with Spin in a Potential : SU(6) x O(3)
The splitting Baryon Quantum Number Assignment, determined by QCD, requires in practice the use of dynamical models (NRQM,…).
Regarding the identification of resonances the experimental situation for nonstrange baryons is (though not very precise) more complete.
From a simple NRQM calculation we shall show that SU(4) x O(3) is a convenient classification scheme for non-strange baryons in order to identify regularities and make predictions.
NRQM for Baryons splitting
The Bhaduri Model
The Missing State Problem splitting
E > 1.9 GeV: many more predicted states than observed resonances.
The observed resonances seem to correspond to predicted
states with a significant coupling to pion-nucleon channels
(S. Capstick, W. Roberts PRD47, 1994 (1993)).
Lattice QCD : Q-Q static potential splitting
Unquenched(valence + sea quarks)
(DeTar et al. PRD 59 (1999) 031501).
String breaking splitting
The saturation of the potential is a consequence of the
opening of decay channels.
The decay effect can be effectively taken into account
through a saturation distance in the potential providing
a solution to the quantum number assignment.
Screened Potential Model splitting
Dynamical Nucleon Parity Series splitting
(N, splitting D) First Nonradial Excited States
Our dynamical model (absence of spin-orbit and tensor forces)
suggests the following rule satisfied by data at the level of the 3%
The first nonradial excitation of N, D (J) and the ground state of N, D (J+1)respectivelyare almost degenerate.
For radial as well as for higher excitations the results are much more dependent on the details of the potential.
Spectral Pattern Rules splitting
ForJ>5/2the pattern suggests the following dynamical regularities
THE END splitting
For splitting J>5/2the pattern suggests the following dynamical regularities