*(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

qq

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