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*(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
Outline
• Introduction• The Hybrid Baryon Model• Interaction Operator• The transition amplitude for N*(1440)
decay• Preliminary Results• Conclusions
Introduction
Strong Interaction
Atom
Nucleus
electron
Nucleon
fundamental theoryof strong interaction
QCD
Low energy
???
Model
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
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
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
*(1440)N N
Wave functions
Interaction Operator
*(1440)NN
*(1440)N N
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
''
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
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
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
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
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
Interaction Operator *(1440)N N
*(1440)NN
Nonreletivistic approximation
kppAgV jiFijijij
2
11 1
2int AgL
k
jp
ip
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
)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
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
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
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
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
Thank you for your attention