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![Page 1: 1 Keitaro Nagata, Chung-Yuan Christian University Atsushi Hosaka, RCNP, Osaka Univ. Structure of the nucleon and Roper Resonance with Diquark Correlations.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfd31a28abf838cac44d/html5/thumbnails/1.jpg)
1
Keitaro Nagata, Chung-Yuan Christian University
Atsushi Hosaka, RCNP, Osaka Univ.
Structure of the nucleon and Roper Resonance with Diquark Correlations
Chiral 07 @ Osaka University, 13-16 November, 2007
N and R in QD Model : K.N, A.H, J.Phys. G32,777 (‘06).
EM structures : K.N, A.H, arXiv: 0708.3471.
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1. QD- Description of the Roper with (i) Relativistic description of the nucleon (ii) Diquark correlations (iii) Chiral symmetry
2. Electric properties of the Roper
Roper Resonance: N(1440) I(J)P=1/2(1/2)+
The mechanism of the E.E. of Roper and its structures are longstanding problem.Various descriptions have been investigated; unharmonicity in QM, collective excitation, deformation, Goldstone boson exchange, two-pole, gluonic-hybrid…
Today, I want to talk about
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Wave-function of N ([S1+S2,S3]STotal)
Quarks with (0s)3 config.
2/12/1 2/1,1,2/1,0
2/12/1 ]2/1,1[]2/1,0[ N2/12/1 ]2/1,1[]2/1,0[ N
N and Roper in NRQM
In the non-relativistic description or the spin-flavor symmetry of N, the E.E of Roper is about 1GeV (>> 0.5 GeV).
Pauli principle
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Relativistic description (local interpolator)
4
ckbjTaiijabc
Sk qqCqB )( 5
ckbjijTaiabc
Ak qqiCqB
52 ))((
a,b,c: color
i,j,k: isospin
(Ioffe, Z.Phys C18, 67 (83))
AS
AS
BBR
BBN
cossin
sincos
forbidden in NRQM
2/12/1,1
2/12/1,0
There are 5 possible operators for N, 2 among 5 are independent (Fierz transformation).
NRLimit
We choose the following operators (good NRLimit)
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5
qDA
qDqqqB SS )~(
qDqqqB AA
555 )~(
Diquark correlation with
NMM SA MM spin-spin
interaction
attraction
repulsion
)0(0)( JI
)1(1)( JI
If there is an interaction, (e.g., spin-spin), the two nucleon states have the mass diff. ~ M-MN
Recent lattice calculations: MA-MS ~100-400 MeV
Babich et.al. PRD76,074021(‘07), Alexandrou,PRL97,222002(‘06),
Orginos,hep-lat/0510082.
good diquark
bad
Jaffe, Phys. Rept. 409, 1(05)
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Chiral quark-Diquark modelMesons ~ q q-bar in NJL model
Two diquarks: DS [I(J)=0(0)], DA [I(J)=1(1)]
qD interaction ~ chiral invariant four point int.
Two nucleons: BS=qDS , BA= qDA
Non-linear realization of chiral sym.
Auxiliary field method : qD model -> chiral MB Lagrangian
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DS
DS
DA
DA DA
DS
q
Chiral Q-D interaction (three types)
Scalar channel
Axial-vector
channel
SG AG v
Mixing betweentwo channels
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8
B1
q
DS B1 B2
q
DA B2
B1
BGv
vGB
GBBL
S
A
A
S
|ˆ|
1
0
0
B1,2 B1,2
G
Masses of two states
]GeV[6.0
]GeV[05.1
]GeV[65.0
]GeV[39.0
A
S
q
m
m
m
]GeV[23
]GeV[11
]GeV[103
1
1
1
v
G
G
A
S
18
]GeV[44.1
]GeV[94.0
R
N
M
M
[K.N, A.H, J. Phys. G32, 777 (2006)]
scalardominance of N
input
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9
)()()()2(
)(4
4
kpSkpSkkd
ZNiQq SScqSq
554
4
30
)(),()()2(
)2(3)(
kSppkpkd
ZiNq
AAA
AcAD
)()(),()()2(
)(4
4
kSkpppkpkd
ZNiQq SSSScSSD
554
4
30
)()()()2(
)(2
3)(
kpSkpSkkd
ZiNq
A
AcAq
BS BS
Scalar
BABA
Axial-vector
iso-doublet space
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Intrinsic diquark form factor (IDFF)
)()()()( intrinsic, qFqqq DTotalADSD
point
Scalar )96.0/1/(1)( 2qqF S
22 )7.0/1/(1)( qqF A
(Monopole and dipole shape from Kroll et al. PLB316,546('93))
0.5 fm
0.6-0.9 -> 0.8 fm
Weiss, et al,PLB312,6,(93)
Axial
)51.0/1/(1)( 2qqF S in SD calculationMaris, nucl-th/0412059
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EM form factors of p, n, p*, n*
BS BSBS BS BA
BA BA BA
Nucleon Breit frame
),,,(
00
ADAqSDSq
qiF
Fi
kjijkM
E
22
22
sin3
1
3
1cos
3
1
3
1
sin0cos3
1
3
2
EAD
EAq
ESD
ESq
En
EAD
EAq
ESD
ESq
Ep
FFFFG
FFFFG
22
22
sin3
1
3
1cos
3
1
3
12/
sin0cos3
1
3
22/
MAD
MAq
MSD
MSqN
Mn
MAD
MAq
MSD
MSqN
Mp
FFFFMG
FFFFMG
![Page 12: 1 Keitaro Nagata, Chung-Yuan Christian University Atsushi Hosaka, RCNP, Osaka Univ. Structure of the nucleon and Roper Resonance with Diquark Correlations.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfd31a28abf838cac44d/html5/thumbnails/12.jpg)
12
Electric form factors(with IDFF)
IDFF of scalar improve both GE of proton and neutron
axial improve GE of proton but not of neutron.
q2[GeV]
Proton Neutron
q2[GeV]
IDFF
Scalar
Axial
Both
Neither
fm8.0A
r
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Electric form factor of Roper with IDFF
Charge radii of Roper resonance
for proton : p* is slightly larger than p
for neutron : n* is slightly smaller than n (~0)
Q2[GeV] q2[GeV] q2[GeV]
n*
n
p
p*
Proton(p*) Neutron(n*)
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Summary and Conclusion
QD picture for the nucleon and Roper resonance.In a relativistic framework, two kinds of the wave-functions are available for the the nucleon.
With diquark correlations, the mass difference between the two states are about 500 MeV.
The charge radii of the Roper are almost comparable to that of the nucleon.
Future work : helicity amplitude (off-diagonal terms)
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15
Discussion proton component
(R.M.S) size of Bs and BA are almost the same.
ud
u BE =50MeV
E
SDE
SqEp FFG
3
1
3
2~ E
ADE
AqEp FFG 0~*
0.6fm 0.8fm
Charge radii of N and R
uu, ud
d, u
0.8fm
p p*
0.8 0.6+0.1 0.8 0.8+0.1
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Discussion neutron component
(R.M.S) size of Bs and BA are almost the same.
Charge radii of N and R
E
ADE
AqER FFG
3
1
3
1~
E
SDE
SqEn FFG
3
1
3
1~
ud
d
0.6fm 0.8fm
ud, dd
d, u
0.8fm
n n*
0.8 0.6+0.1 0.8 0.8+0.1
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•Roper-like excitation mode for octet,
•Not confirmed for decuplet.
Roper in SU(3)
N
G.S.
Excitation Energy[GeV]
J=1/2 J=3/2
1
N(940)
N(1440)
N(1535)
N(1650)N(1710)
(1115)
(1405)
(1600)
(1670)
(1800)(1810)
(1190)
(1660)
(1750)
(1315) (1232)
(1600)
(1700)
(1920)
(1385)
(1670)
(1940)
(1530)
(1820)
(1670)
(1690)
(1950)
(2030)
(2250)
(2250)
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Assuming the non-relativistic description or the spin-flavor symmetry of thenucleon, the E.E of Roper is about 1GeV. Relativistic description of N Two types of wave-functions (and)is available. Each w.f. independently satisfies Pauli priciple. (spin flavor symmetry is not a good symmetry there)
The second nucleon states (orthogonal to N(940)) ? (i) Relativistic descriptions of the nucleon (ii) Chiral symmetry (iii) Diquark correlations
What is the structure of the Roper ?
-> Nucleon and Roper resonance