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.

iv) SU(4) x O(3) : Spectral predictions up to 3 GeV.

v) Conclusions.

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.

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).

How can we extract this physical content?The knowledge of spectral patterns is of great help.

SU(3 ) : Quarks (3 x 3 x 3 = 10 + 8 + 8 + 1) Baryons

prediction by Gell-Mann Strange quark mass splitting?

2

1PJ

2

3PJ

Quarks with Spin : SU(6) i SU(3) x SU(2)

20707056666 8 10 56 24

2

1,

2

1zS 2

3,

2

1,

2

1,

2

3zS

Quarks with Spin in a Potential : SU(6) x O(3)

)0 ,56(),( PLN

SU(6) Breaking : Strange quark mass + Hyperfine (OGE) splitting

jijiji

HSij mm

cV

. .2

The Baryon Quantum Number Assignment Problem

PJ L

2

5

2

5

2

3

2

3

2

1

2

1

4,3,2,1

4,3,2,1

3,2,1

3,2,1,0

2,1

2,1,0

??:),,,,,(

)0 ,10 8( )0 ,56(:),,,,,(*

42

N

N

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.

NRQM for Baryons

Lattice QCD : Q-Q static potential (G. Bali, Phys. Rep. 343 (2001) 1)

Quenched approximation (valence quarks)

The Bhaduri Model

) (2

1)(

rrrVst

The Missing State ProblemE > 1.9 GeV: many more predicted states than observed resonances.

The observed resonances seem to correspond to predictedstates with a significant coupling to pion-nucleon

channels(S. Capstick, W. Roberts PRD47, 1994 (1993)).

Lattice QCD : Q-Q static potential

Unquenched (valence + sea quarks)(DeTar et al. PRD 59 (1999) 031501).

String breaking

The saturation of the potential is a consequence of theopening of decay channels.

The decay effect can be effectively taken into account through a saturation distance in the potential providinga solution to the quantum number assignment.

Screened Potential Model

satijsatBhaduriij

satijijBhaduriij

rrrVrV

rrrVrV

if )()(

if )()(

(N, Ground States : SU(4) x O(3)

4202020444 MMS

2 4 20 24 S

2 4 2 20 224 M

LP )(

MeVEEi JJ 500400)()( ) 2

For J>5/2 :

For J>5/2 :

...3,2,1 with 2

34for )()( ) ,,

nn

JJJNii

Dynamical Nucleon Parity Series

For J>5/2 :

...3,2,1 with 2

14for )()( )

nn

JJNJNiii

)AttractionBigger (

1

Repulsion)(Bigger

1 1

parity parity

S

LK

PositiveNegative

(N, 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%

2

5J The first nonradial excitation of N, (J) and the ground

state of N, (J+1) respectively are almost degenerate.

For radial as well as for higher excitations the results are much more dependent on the details of the potential.

For J>5/2 the pattern suggests the following dynamical regularities

MeVEEi JJ 500400)()( ) 2

...3,2,1 with 2

34for )()( ) ,,

nn

JJJNii

...3,2,1 with 2

14for )()( )

nn

JJNJNiii

1* ),( ),( iv) JJ NN

Spectral Pattern Rules

Conclusions

i) 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 N’s and ’sare classified according to SU(4) x O(3) multiplets with hyperfine splittings inside them.

iii) The spectral pattern makes clear energy step regularities, N- degeneracies and N parity doublets.

iv) Ground and first non-radial excited states for N’s and ’s, in the experimentally quite uncertain energy region between 2 and 3 GeV, are predicted.

THE END

(N, Ground States : SU(4) x O(3)

4202020444 MMS

2 4 20 24 S

2 4 2 20 224 M

LP )(

For J>5/2 the pattern suggests the following dynamical regularities

...3,2,1 with 2

34for )()( ) ,,

nn

JJJNii

...3,2,1 with 2

14for )()( )

nn

JJNJNiii

MeVEEi JJ 500400)()( ) 2