Shin Nan Yang National Taiwan University Collaborators: S. S. Kamalov (Dubna) Guan Yeu Chen (Taipei)...
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A meson-exchange model for N scattering
up to energies s 2
GeV
Shin Nan YangNational Taiwan University
Collaborators: S. S. Kamalov (Dubna) Guan Yeu Chen (Taipei)
18th International Conference on “Few-body Problems in Physics”
August 20 – 26, 2006, Santos, Brazil 1
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OutlineMotivation
Previous works
Meson-exchange N model below 400 MeV
Dubna-Mainz-Taipei (DMT) dynamical model for pion e.m. production
Extension to higher energies
Conclusion
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Motivation
low energies ─ ChPT high energies, high momentum transfer─ pQCD medium energies ․LQCD ․Phenomenology : hadron models, reaction theory
QCD Hadronic phenomena
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Aim: To construct a coupled-channel dynamical model to study N scattering and pion electromagnetic production
Aim: To construct a coupled-channel dynamical model to study N scattering and pion electromagnetic production
low energies:
e.m. threshold pion production, low energy theorems and compare with ChPT
medium energies:
N-transition form factors, resonance parameters
high energy and high momentum transfer:
transition to pQCD region?4
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N
0
0
Bethe-Salpeter equation
,
where
sum of all irreducible two-particle Feynman amplitues
relativistic free pion-nuc
can be r
leon propagator
ewritten as
N N
N
N N
N
T B B G T
T
B
G
B B
N
N
0
00
,
with
( .)
N
NN N
T
B B B
G
B G G
Meson-exchange N model below 400 MeV
5
N 0
Find good
and B G
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Three-dimensional reduction
0
0
0
Choose a such that
1. becomes
( , )
three-dimensio
2. can reproduce N elas
na
tic
l
cut
N NN NT B B T
G k P
G
G
Cooper-Jennings reduction scheme Cooper-Jennings reduction scheme
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Choose to be given byNB
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C.T. Hung, S.N. Yang, and T.-S.H. Lee, Phys. Rev. C64, 034309 (2001) 8
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Both on- & off-shell
Dynamical model for electromagnetic pion production
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( )
background transition potential
cont
(
ribution of a bare resonance
)
(
( )
(
)
the transition potential consists ot two terms,
,
where
then one obtai
f
ns
IB
B
R
B
Rv E
v
v E
R
t E
v E
v
t
v
0
0
( )
)
( ) ( )
( ) (
(
( )
)
)
,
with
B
N
B
R
N
E
t E v v g E t E
v v E t E
t E
t E g
both tB and tR satisfyFermi-Watson theorem,respectively.
10
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Bv
DMT Model
PV only
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Frolov et al., PRL, 1999
15
0
2 24.0
Q e
e e p
G V
p
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Extension to higher energies
coupled , , 2 channels
Include resonances R’s with couplings to
, , 2 channels
coupled , , 2 channels
Include resonances R’s with couplings to
, , 2 channels
( ) ( ) ( ),
( , , , )
ij ij ik k kjk
t E v v g E t E
i j k
( ) ( ) ( )B Rij ij ijv E v E v E
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Non-resonant background :
as given before,
0 .
Bij
B
B B Bv
v
v
v
v
(0) (0) h.c.I NR NRL ig R N ig R N ������������� �
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1
( ) ( )(0) (0)
(0)
0, 2
2
( )
2
,
( )
2
0
(0)n
( , ; ),
( , ; ) ( , : )
( )1
2
,
Resonan :ce contribution
for N overlapping resonances.
bare mass of resonance R ,
n
n
n
NRR
ij ij
n
n n
i ji jR
ij
R
n
n
n
n
n
Rij
R
v v q q E
f q E g g f qv
E E
E
M i
q
q
v
M
2 4 22 2
0,
2 2
2
effects of N d e cay channel
l l
nX q
X q
19
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2R
3R
4R
- - - - TB = VB + VBg0TB
20
S11
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---------- 1R
2R
3R
No evidence for the 4th S11 resonance in
N -> N
No evidence for the 4th S11 resonance in
N -> N
21
Consistent with data from ELSAN N
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Extraction of resonance parameters
1
1
( ) ,
wh
( )
( )
( )
ere
( ) ( ) ( ) ( ),
( ) ( ) ( ) ( ).
( )
(
/ )
)
2 (
n n
n
n
n
n n
R
R
N
n
B Bk k k
k
R Rk k k
R
R
B
R
B
k
t E
t E
t E
t E
v E v E g E t E
v E v E g E t E
E i
t
M
t E
E
22
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full
BtRt
Need 4 S11
Resonances
2=64
2=3.5
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(3,3)
25
S13
(3,3), red PDG, blue DMT
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(3,3)
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P11
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(2,3)
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P31
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(2,2)
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D15
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(2,2)
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F15
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1st Resonance 2nd Resonance 3rd Resonance
N* Wp Γp Wp Γp Wp Γp
S111499
(1505, 1501)
67(170, 124)
1642(1660, 1673)
97(160, 82)
2065(2150±70)
223(350±100)
S311598
(1600, 1585)
136(115, 104)
1775(1870±40)
36(1850±50)
2012(2140±80)
148(200±80)
P111366
(1365, 1346)
179(210, 176)
1721(1720, 1770)
185(230, 378)
1869(2120±40,
1810)
238(240±80, 622)
P131683
(1700, 1717)
239(250, 388)
1846(not listed)
180(not listed)
P311729(1714)
70(68)
1896(1855, 1810)
130(350, 494)
2065 161
P331218
(1210, 1211)
90(100, 100)
1509(1600, 1675)
236(300, 386)
2149(1900,
1900±80)
400(300, 300±100)
Pole Positions and Residues in [ MeV ] (preliminary)
Red : PDG04 Blue : Arndt95
Green : Cutkovsky80 Orange : Vrana00 30
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1st Resonance 2nd Resonance 3rd Resonance
N* Wp Γp Wp Γp Wp Γp
D13 (3,3) 1516 (1510, 1515)
123(115, 110)
not seen(1680, not seen)
not seen(100, not seen)
1834(1880±100)
210(160±80)
D33 (2,2) 1609(1660, 1655)
133(200, 242)
2070(1900±100)
267(200±60)
D15 (2,2) 1657(1660, 1663)
132(140, 152)
2188(2100±60)
238(360±80)
D35 (2,1) 1992(1890, 1913)
270(250, 246)
not seen
(2400±60)
not seen
(400±150)
F15 (2,2) 1663(1670, 1670)
115(120, 120)
1931(not listed)
62 (not listed)
F35 (2,2) 1771(1830, 1832)
190(280, 254)
2218(2150±100,
1697)
219(350±100, 112)
F37 (2,1) 1860(1885, 1880)
201(240, 236)
2207(2350±100)
439(260±100)
Pole Positions and Residues in [ MeV ] (preliminary)
Red : PDG04 Blue : Arndt95
Green : Cutkovsky80 Orange : Vrana00
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Summary
The DMT coupled-channel dynamical model gives excellent description of the pion scattering and pion e.m. production data from threshold to first resonance region
The model has been extended up to c.m. energy 2 GeV in the
sector and resonance parameters extracted
and N N
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Our analysis at W > 1750 GeV yields considerable strength, which can be explained by a third and a fourth S11 resonance with masses 1846(47) and 2113(70) MeV
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The End
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(3,4), red PDG, blue DMT
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S11
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(2,2)
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(3,3)
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(3,3)
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(2,2)
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(2,1)
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(2,2)
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(2,1)
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