The 8th International Workshop on the Physics of Excited Nucleons, Jlab, May 1720, 2011

Upload
quynnpetersen 
Category
Documents

view
27 
download
0
description
Transcript of The 8th International Workshop on the Physics of Excited Nucleons, Jlab, May 1720, 2011
1
P11 resonances withP11 resonances with DMTDMT dynamical dynamical model for πN scattering and pion e.m. model for πN scattering and pion e.m.
productionproduction
Shin Nan YangShin Nan YangNational Taiwan UniversityNational Taiwan University
The 8th International Workshop on the Physics of Excited Nucleons, Jlab, May 1720, 2011
Dubna: KamalovMainz: Drechsel, TiatorTaipei: Guan Yeu Chen, SNY
22
Motivation for DMT model
To construct a mesonexchange model forπN scattering and e.m. production of pion so that a consistent extraction of the resonance properties like, mass,
width, and form factors, from both reactions can be achieved. Comparison with LQCD results requires reliable extraction. consistent extractions → minimize model
dependence? The resonances we study are always of the type which results from dressing of the quark core by meson cloud. → understand the underlying structure and dynamics
33
TaipeiArgonne πN model: mesonexchange N model below 400 MeV
0
BetheSalpeter equation
N N N NT B B G T
Threedimensional reduction
0
0
0
Choose a such that
1. becomes
( , )
threedimensio
2. can reproduce N elas
na
tic
l
cut
N NN NT B B T
G k P
G
G
: CooperJennings reduction scheme which satisfies softpion theorem and unitarity
0G
44
Choose to be given byNB
42
24 2 2
10
,
n
nF p
n m p
n
55Hung, Yang, and Lee, Phys. Rev. C64, 034309 (2001)
renormalization of nucleon mass and pionnucleon coupling constant done forP11 channel
66
DMT πN model:extension of TaipeiArgonne model
to energies ≦ 2 GeV
Inclusion of ηN channel in S11
Introduce higher resonances as indicated by the data
G.Y. Chen et al., Phys. Rev. C 76 (2007) 035206.
77
Extraction of BreitWigner parameters
0
0
,
whe
,
,
,
re,
and
B B BN N N N
R R RN
B RN N N
N N N
t E E g
t E t E t E
E t E
t E E g E t E
0
(0)† (0)†0
0
0
,
( )
( )
( )
)( ) .(
,
RRN
R
R R RBN
B BN N
R
B BN N
R
h Et E
E M E
h E h E g E ht
E
t E t
h
g E Ev v
Note that both tNote that both tBB and tand tR R have the have the same phase of same phase of
N
With only one With only one resonance,resonance,
8
99
0 0
0 2
2 : phenomenological effect
, ; , ;,
s of the coupling with
N chann
;
2
el
,i i i j j
j
R R
i
R
jR
E
E
f q E g g f q Eq q E
iE M
2 4 22 2
2 02 02 2
2
2
2
0
0
2
02
,
( ), the momentum of the 2 system
: pion or
,
( )
bital mo
,
mentum
l
RR
RR
R
lq
q
X q
X q
q E
q E Mq
l
Eq
We only have elastic πN cut included !!
1010
Selfenergy ΣR(E)
00
0 0 0 00 0 0
R R
R R
R
BR RN
h g E h E
h g E h h g gt E
E
h
0
0 Re ,
2 I
e
m
R 0,
.
R R R R
R R R R
R R
M M M
M
E M E
M
BreitWigner mass MR andwidth ΓR
1111
To order e, the tmatrix for N → N is written as
Dynamical model for N → N
v, tN
0
where
transition potential,
matrix,
1
( )( ) ( ) ,
( )
k
k
k
N
kk
k
k
v v
v
k
t
N t
E
t E E
H
g E
g E
t
two two ingredientsingredients
Both on & offshell
1212
DubnaMainzTaipei (DMT)
Test of the backgrounds
13
and BBNv v
Near threshold,
0
0
0
( ) 0, ( ) ( ),
where
( ) ( )
( )
( )
,( )
R B
BN
BN
B BN
B
B B
B
BN
B
N N
t t t
t g t
v
v v
v v g
v
t
t g t
1414
Results of DMT model near threshold,
1515M. Weis et al., Eur. Phys. J. A 38 (2008) 27
1616
Photon Beam Asymmetry near ThresholdPhoton Beam Asymmetry near Threshold
Data: A. Schmidt et al., PRL 87 (2001) @ MAMIDMT: S. Kamalov et al., PLB 522 (2001)
17
D. Hornidge (CB@MAMI)private communication
18
19
The blue dashed lines correspond to the nonresonant background BNt
20
0RM RM R
1R
R 11P
Bare and physical resonance masses as well as total widths , all in units of MeV, single pion branching ratios , and background phases for resonances. Upper lines: our results, lower lines: results of the PDG.
(deg)
**** (PDG)
1612 1418
1445±25
436
325±125
44
65±10
32
*** (PDG)
1798 1803
1710±30
508
180±100
32
15±5
40
* (PDG)
2196 2247
2125±75
1020
260±100
42
12±2
32
N 0RM RM R %1 R R
11 1710P
11 1440P
11 1710P 2100
21
11PPole positions and residues for resonances.
(deg)
SP
RM(5)
**** (PDG)
1371
1366
1371
1365±15
95
90
95
95±15
50
48
50
46±10
79
87
78
100±35
SP
RM(6)
*** (PDG)
1746
1721
1756
1720±50
184
92
150
115±75
11
5
11
10±4
54
164
49
175±35
SP
RM
* (PDG)
1868
2120±240
238
240±80
7
14±7
216
35±35
N pWRe pWIm prp
144011P
171011P
210011P
22
Proton helicity element for fits obtained from LE and HE.
MAID 2001 MAID DMT PDG 2000
HE fit 71 81 77 65±4
LE fit 71 81 93 65±4
21 144011P
2
1310 GeVin
23
black line, full DMT modelBlue dashed line, background onlyred dashed line, no 2nd and 3rd P11 resonances in DMT model
24
black line, full DMT modelred dashed line, removing second P11 resonance from DMT model
25
red MAID 2007 black DMT 2001green SAID (FA06K)
with only P11(1710)
26
red MAID 2007 black DMT 2001green SAID (FA06K)
27
with addition of a narrow P11 resonance ofmass = 1700 MeV, width = 47 MeV with MAID2007
28
with addition of a narrow P11 resonance ofmass = 1700 MeV, width = 47 MeV with MAID2007
29
SUMMARYSUMMARY Within DMT model for pionnucleon scattering and
pion photoproduction, parameters for the three P11 resonances have been extracted. The extracted values agree well, in general, with the PDG values.
‧only one pole is found corresponding to the Roper.
‧2nd and 3rd P11 resonances are definitely needed in DMT model. ‧indication for a narrow P11 resonance at around 1700 MeV with a width ～ 50 MeV both πN and γπ reactions.
The choice of background potentials lead to excellent agreement with low energy neutral
pion production data production data from MAMI. → reliable separation of background and resonance contributions ?
and B BNv v
30
31
32