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PATTERNS IN THE NONSTRANGE BARYON SPECTRUM
P. González, J. Vijande, A. Valcarce, H. Garcilazo
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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. iv) SU(4) x O(3) Spectral predictions
up to 3 GeV. v) Conclusions.
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What is the physical content of the baryon
spectrum? 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).
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SU(3 ) Quarks (3 x 3 x 3 10 8 8 1)
Baryons
I prediction by Gell-Mann
Strange quark mass splitting?
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Quarks with Spin SU(6) i SU(3) x SU(2)
Quarks with Spin in a Potential SU(6) x O(3)
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SU(6) Breaking Strange quark mass Hyperfine
(OGE) splitting
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The Baryon Quantum Number Assignment Problem

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The 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.
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NRQM for Baryons

• Lattice QCD Q-Q static potential
• (G. Bali, Phys. Rep. 343 (2001)
  1)
• Quenched approximation (valence quarks)

The Bhaduri Model
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The Missing State Problem E gt 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)).
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Lattice QCD Q-Q static potential Unquenched
(valence sea quarks) (DeTar et al. PRD 59
(1999) 031501).
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String breaking
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.
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Screened Potential Model
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(N, D) Ground States SU(4) x O(3)
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For Jgt5/2
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For Jgt5/2
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Dynamical Nucleon Parity Series
For Jgt5/2

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(N, 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 (J1) respectively are
almost degenerate.
For radial as well as for higher excitations the
results are much more dependent on the details of
the potential.
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Spectral Pattern Rules
For Jgt5/2 the pattern suggests the following
dynamical regularities
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• Conclusions
• The use of a NRQM containing a minimal screened
  dynamics provides an unambiguous assignment of
  quantum numbers to nonstrange baryon resonances,
  i. e. a spectral pattern.
• ii) The ground and first non-radial excited
  states of Ns and Ds are classified according to
  SU(4) x O(3) multiplets with hyperfine splittings
  inside them.
• iii) The spectral pattern makes clear energy
  step regularities, N-D degeneracies and N parity
  doublets.
• Ground and first non-radial excited states for
  Ns and Ds, in the experimentally quite
  uncertain energy region between 2 and 3 GeV, are
  predicted.

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THE END
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(N, D) Ground States SU(4) x O(3)
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For Jgt5/2 the pattern suggests the following
dynamical regularities