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 17-20, 2011

Dubna: KamalovMainz: Drechsel, TiatorTaipei: Guan Yeu Chen, SNY

22

Motivation for DMT model

To construct a meson-exchange 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

Taipei-Argonne πN model: meson-exchange N model below 400 MeV

0

Bethe-Salpeter equation

N N N NT B B G T

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 which satisfies soft-pion 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 pion-nucleon coupling constant done forP11 channel

66

DMT πN model:extension of Taipei-Argonne 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 Breit-Wigner 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

Self-energy 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

Breit-Wigner mass MR andwidth ΓR

1111

To order e, the t-matrix 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- & off-shell

1212

Dubna-Mainz-Taipei (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 pion-nucleon 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