PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.
-
Upload
willa-doris-oneal -
Category
Documents
-
view
219 -
download
0
Transcript of PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.
![Page 1: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/1.jpg)
PATTERNS IN THE NONSTRANGE BARYON SPECTRUM
P. González, J. Vijande, A. Valcarce, H. Garcilazo
![Page 2: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/2.jpg)
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.
![Page 3: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/3.jpg)
![Page 4: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/4.jpg)
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.
![Page 5: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/5.jpg)
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
![Page 6: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/6.jpg)
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
![Page 7: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/7.jpg)
SU(6) Breaking : Strange quark mass + Hyperfine (OGE) splitting
jijiji
HSij mm
cV
. .2
![Page 8: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/8.jpg)
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
![Page 9: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/9.jpg)
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.
![Page 10: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/10.jpg)
![Page 11: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/11.jpg)
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
![Page 12: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/12.jpg)
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)).
![Page 13: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/13.jpg)
Lattice QCD : Q-Q static potential
Unquenched (valence + sea quarks)(DeTar et al. PRD 59 (1999) 031501).
![Page 14: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/14.jpg)
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.
![Page 15: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/15.jpg)
Screened Potential Model
satijsatBhaduriij
satijijBhaduriij
rrrVrV
rrrVrV
if )()(
if )()(
![Page 16: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/16.jpg)
![Page 17: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/17.jpg)
![Page 18: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/18.jpg)
(N, Ground States : SU(4) x O(3)
4202020444 MMS
2 4 20 24 S
2 4 2 20 224 M
LP )(
![Page 19: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/19.jpg)
MeVEEi JJ 500400)()( ) 2
For J>5/2 :
![Page 20: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/20.jpg)
For J>5/2 :
...3,2,1 with 2
34for )()( ) ,,
nn
JJJNii
![Page 21: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/21.jpg)
![Page 22: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/22.jpg)
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
![Page 23: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/23.jpg)
![Page 24: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/24.jpg)
(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.
![Page 25: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/25.jpg)
![Page 26: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/26.jpg)
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
![Page 27: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/27.jpg)
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.
![Page 28: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/28.jpg)
THE END
![Page 29: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/29.jpg)
![Page 30: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/30.jpg)
![Page 31: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/31.jpg)
![Page 32: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/32.jpg)
(N, Ground States : SU(4) x O(3)
4202020444 MMS
2 4 20 24 S
2 4 2 20 224 M
LP )(
![Page 33: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/33.jpg)
![Page 34: PATTERNS IN THE NONSTRANGE BARYON SPECTRUM P. González, J. Vijande, A. Valcarce, H. Garcilazo.](https://reader035.fdocuments.us/reader035/viewer/2022062322/56649ee65503460f94bf650a/html5/thumbnails/34.jpg)
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