Quark-model baryon-baryon interactions and their applications to few-body systems
Decays in a Hybrid Baryon Model
description
Transcript of Decays in a Hybrid Baryon Model
![Page 1: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/1.jpg)
*(1440)N Decays in a Hybrid Baryon Model
K. Khosonthongkee†, N. Supanam and Y. Yan
School of Physics, Suranaree University of Technology,Nakhon Ratchasima, Thailand
18th International IUPAP Conference on Few-BodyProblems in Physics (FB18)
Santos, São Paulo, Brazil August 24, 2006
![Page 2: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/2.jpg)
Outline
• Introduction• The Hybrid Baryon Model• Interaction Operator• The transition amplitude for N*(1440)
decay• Preliminary Results• Conclusions
![Page 3: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/3.jpg)
Introduction
Strong Interaction
Atom
Nucleus
electron
Nucleon
fundamental theoryof strong interaction
QCD
Low energy
???
Model
![Page 4: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/4.jpg)
Baryon excitation states
Nucleon internal structure
understanding
J= 3/2, I = 3/2, P=+1
J= 1/2, I = 1/2, P=+1
J= 1/2, I = 1/2, P=+1
∆(1232)
N*(1440) Intrinsic excitation of Nucleon at energy around 500 Mev
N, Nucleon(939)
N*(1440), Roper Resonance
![Page 5: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/5.jpg)
Simple Model for N*(1440)
N*(1440) is three-quark with the first radial excitation
N*(1440) too low mass to be radial excitation
problems of the models
Various quarks models
Met difficulties to explain its mass and electromagnetic couplings
![Page 6: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/6.jpg)
qqq G
N*(1440)
Hybrid
Bag Model
TE (transverse electric)
TM (transverse magnetic)
low mass
3 quarks and a TE gluon
TE mode is lowest eigenmode
N*(1440)
q3G
The Hybrid Baryon Model
![Page 7: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/7.jpg)
*(1440)N N
Wave functions
Interaction Operator
*(1440)NN
*(1440)N N
![Page 8: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/8.jpg)
Nucleon wave function
spatial spin-flavor colorN N N N
harmonic oscillator potentialqqq
2
3212
2
212N
6
2
2
1exp
22
1exp
pppa
ppaNN
kjikjiijk
TJSJ J
qqq
ZZ
,,321
Flavor
,2
1
)3()2()1(Spin
,2
11,0
)3()2()1(
6
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
''
![Page 9: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/9.jpg)
Pion wave function
spatial spin-flavor colorπ π π π
harmonic oscillator potentialqq
3
121
Flavor
,1
)2()1(
Spin
0,0
)2()1(2
212
3
1
2
1
2
1
2
1
2
1
8
1exp
lll
t
ppbN
z
![Page 10: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/10.jpg)
N*(1440) wave function
spatial spin-flavor-colorN*(1440) N*(1440) N*(1440)
harmonic oscillator potential
q3G spatialN*(1440)
2
43212
2
3212
2
212*
Spatial*N
12
3
2
1exp
6
2
2
1exp
22
1exp
pRpppc
pppa
ppaNN
![Page 11: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/11.jpg)
spin-flavor-colorN
2 4g g*(1440) A N N+B
2 1S :total spin of 3 quarksS
GN g 2
12
GN Sg
2
14
flavor wave function
color wave function
spin wave function
G gluon
S totally symmetric
mix symmetric
mix antisymmetric
![Page 12: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/12.jpg)
color
Flavor
,2
1
)3(
0
)2()1(
color
Flavor
,2
1
)3(
1
)2()1(
Spin
,2
1
m1,m1,43211
,2
3
)3(
1
)2()1(4
8
1
2
1
2
1
2
1
8
1
2
1
2
1
2
1
e)3(2
1
2
1
2
1
2
1
''
''
''
'2s
123
g
g
pRpppYN
Z
Z
Z
l
T
T
S
m
m
g
![Page 13: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/13.jpg)
color
Flavor
,2
1
)3()2()1(
Spin
,2
1
m1,m1,4321,1
,2
1
)3(
1
)2()1(
color
Flavor
,2
1
)3()2()1(
Spin
,2
1
m1,m1,4321,1
,2
1
)3()2()1(2
8
1
2
1
2
1
2
1
e)3(2
1
2
1
2
1
8
1
2
1
2
1
2
1
e)3(2
1
2
1
2
11
2
1
''12
''
'2s
12312
''12
12
''
'2s
12312
12
g
pRpppY
g
pRpppYN
Z
Z
l
Z
Z
l
TJ
S
m
mJ
TJ
J
S
m
mJ
Jg
![Page 14: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/14.jpg)
Interaction Operator *(1440)N N
*(1440)NN
Nonreletivistic approximation
kppAgV jiFijijij
2
11 1
2int AgL
k
jp
ip
![Page 15: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/15.jpg)
The Transition Amplitude for Decay *(1440)N
kppAgV jiFijijij
2
11 1
)1440*(
9
1)1440*( NN
iiNN OpdT
†
78936251 VppppppO †
*(1440)NN
12
3
5
6
7
8
9
4
![Page 16: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/16.jpg)
)ˆ(,
*)1440*( pYTT
l
llml
lmlmNN
211,, 22
'''' QB
QA
PgTlZZZZl mTTSSlm
Expand the total transition amplitude in partial wave
Rcbaml ,,,,depend on
'2colorflavorspin
colorflavorspin1 gN NOQ
'4colorflavorspin
colorflavorspin2 gN NOQ
![Page 17: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/17.jpg)
ml Sz Q1 Q2
-1 -1/2
1/2
-0.148
-0.444
0.131
0.079
0 -1/2
1/2
-0.296
0.296
-0.052
0.052
1 -1/2
1/2
0.444
0.148
-0.079
-0.131
Values of Q1 and Q2 for different initial and final states
*(1440)N N
![Page 18: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/18.jpg)
Preliminary Results *(1440)N N
Z l
l
S m
m
N
NNN
QB
QA
ppgM
EE
2
21
232
*)1440*(
221
2exp
NN )1440(*Decay width of
spin-flavor-colorN
2 4g g*(1440) A N N+B
NN )1440*(
1/:1/:1,0:0,1 BABABABA
173.1:624.0:261.0:536.1
Independent of Rcbag and,,,
Rcba ,,,depend on
![Page 19: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/19.jpg)
Hybrid Baryon Model
A=0 A=1 A/B=1 A/B= -1
B=1 B=0 A= A=
Experimental Data
NN
NN
)1440*(
)1440*(
NN
NN
)1440*(
)1440*(
024.075.0
01.000.0
024.075.0
01.000.0
2
1
2
1
0
072.0
0
018.0
0
054.0
0
011.0
Z. Li et.al. Phys. Rev. D. 46 (1992) p70-74
Preliminary Results 1;1 IJ0;0 IJ
![Page 20: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/20.jpg)
Conclusions
is treated as a hybrid baryon, , in nonrelativistic regime
The method developed is very general, it could be applied to evaluate other decay process like
)1440(*N Gq3
)1440(*N
Next Step
Determine the parameters
Work out the decay width of in other channel
)1440(*N
![Page 21: Decays in a Hybrid Baryon Model](https://reader034.fdocuments.in/reader034/viewer/2022052414/56813b5c550346895da452d6/html5/thumbnails/21.jpg)
Thank you for your attention