Shin Nan Yang National Taiwan University Collaborators: S. S. Kamalov (Dubna) Guan Yeu Chen (Taipei)...
-
date post
20-Dec-2015 -
Category
Documents
-
view
218 -
download
0
Transcript of Shin Nan Yang National Taiwan University Collaborators: S. S. Kamalov (Dubna) Guan Yeu Chen (Taipei)...
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
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
2
Motivation
low energies ─ ChPT high energies, high momentum transfer─ pQCD medium energies ․LQCD ․Phenomenology : hadron models, reaction theory
QCD Hadronic phenomena
3
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
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
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
6
Choose to be given byNB
7
C.T. Hung, S.N. Yang, and T.-S.H. Lee, Phys. Rev. C64, 034309 (2001) 8
Both on- & off-shell
Dynamical model for electromagnetic pion production
9
( )
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
Bv
DMT Model
PV only
11
12
13
14
Frolov et al., PRL, 1999
15
0
2 24.0
Q e
e e p
G V
p
16
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
17
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 ������������� �
18
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
2R
3R
4R
- - - - TB = VB + VBg0TB
20
S11
---------- 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
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
23
full
BtRt
Need 4 S11
Resonances
2=64
2=3.5
24
(3,3)
25
S13
(3,3), red PDG, blue DMT
(3,3)
26
P11
(2,3)
27
P31
(2,2)
28
D15
(2,2)
29
F15
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
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
31
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
32
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
33
The End
(3,4), red PDG, blue DMT
25
S11
(2,2)
35
(3,3)
37
(3,3)
38
(2,2)
40
(2,1)
41
(2,2)
43
(2,1)
44