Study of excited nucleon states at ebac status and plans
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Study of Excited Nucleon States at EBAC: Status and Plans. Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) in collaboration with B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki. NSTAR 2009, April 19-22, 2009. PDG *s and N*’s origin.

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Study of Excited Nucleon States at EBAC: Status and Plans

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Study of excited nucleon states at ebac status and plans

Study of Excited Nucleon States at EBAC: Status and Plans

Hiroyuki Kamano

(Excited Baryon Analysis Center, Jefferson Lab)

in collaboration with

B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama,

T. Sato, N. Suzuki

NSTAR 2009, April 19-22, 2009


Pdg s and n s origin

PDG *s and N*’s origin

Most of their properties are extracted from

Are they all genuine quark/gluon excitations (with meson cloud) ?

Is their origin dynamical ?

some could be understood as arising from meson-baryon dynamics

?

?

meson cloud

?

core

?

baryon

?

Arndt, Briscoe, Strakovsky, Workman PRC 74 045205 (2006)

meson

Need consistent analysis of

pN and ppN channels


Data will change n structure study

Data will change N* structure study

Recent high precision data of meson photo- and

electro-production reactionsopen a great opportunity of

making quantitative study of the N* structure.

ELSA, JLab, MAMI, …

e.g.) single pion electroproduction

g*

N

N

Corresponds to beam resolution

N*

N-N* e.m. transition form factors


Approaches to extracting n properties

Reaction Data

Dynamical Coupled-Channels Analysis @ EBAC

N* properties

Hadron Models

Lattice QCD

QCD

Approaches to extracting N* properties


Dynamical coupled channels model @ ebac

Dynamical coupled-channels model @ EBAC

N* spectrum, structure, …

Meson production data

Reaction mechanism

Dynamical coupled-channels model of meson production reactions

A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193

Maintain coupled-channels unitarity of

  • a

  • a

Singular!

Can treat 3-body unitary cut


Dynamical coupled channels model @ ebac1

Dynamical coupled-channels model @ EBAC

For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)

  • Partial wave (LSJ) amplitude of a  b reaction:

  • Reaction channels:

  • Potential:

coupled-channels effect

Impose minimal number of

bare N* state: at present

16 of 18(= # of 3* and 4* N*s

below 2 GeV)

meson exchange

bare N* state


Strategy for n study @ ebac

Extraction of N* poles and N*  MB decay form factors

Extract N*  hN, KY, wN

Application

Fit hadronic part

of parameters

Refit hadronic part

of parameters

Pass hadronic parameters

Pass hadronic parameters

Extraction of N-N* ele.-mag. transition form factors

Application

Extract N*  hN, KY, wN

Strategy for N* study @ EBAC

Feedback

Application

Develop a method to connect our f.f.s with hadron structure calculations

Feedback

Refit electro-magnetic

part of parameters

Fit electro-magnetic

part of parameters

Application


Current status of the analysis @ ebac

Current status of the analysis @ EBAC

Hadronic part

  • p N  pN : fitted to the SAID PWA up to W = 2 GeV.

    Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

  • p N  pp N : cross sections calculated with the pN model; fit is not finished.

    Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)

  • p N  h N : fitted to the data up to W = 2 GeV

    Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)

  • g(*) N  p N : fitted to the data up to W = 1.6 GeV (and up to Q2 = 1.5 GeV2)

    (photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)

    (electroproduction)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, arXiv:0904.1918

  • g(*) N  pp N : in progress

  • g(*) N  h N : in progress

  • g N  K L : in progress

Electromagnetic part

Explained in detail by

Bruno Julia-Diaz

(PS7, Apr. 22 11:15-11:40)


Pion nucleon elastic scattering

Re(T) with I = 1/2

Pion-nucleon elastic scattering

Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

  • coupled-channels is considered.

  • Fitted tothe SAID pN partial wave amplitudes up to 2GeV.

  • MINUIT library is employed for the numerical minimization.

Unitarity is satisfied in ~ 1 % !!


Pion nucleon elastic scattering1

Pion-nucleon elastic scattering

Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

Angular distribution

Target polarization

EBAC

SAID06


Pi n pi pi n reaction

pi N  pi pi N reaction

Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)

Parameters used in the calculation are from pN  pN analysis.

Need combined analysis of p N and pp N !


Pi n pi pi n reaction1

pi N  pi pi N reaction

Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)

Invariant mass

distributions

Full result

Phase space

Data handled with the help of R. Arndt


How can we extract n information

How can we extract N* information?

  • PROPER definition of

  • N* mass and width  Pole position of the amplitudes

  • N*  MB, gN decay vertices  Residueat the pole

Need analytic continuation of the amplitudes !!

N*  b

decay vertex

Explained in detail

by

Toru Sato

(Apr. 20 14:00-14:30)

N* pole position

( Im(E0) < 0 )


Comparison with pdg values

Comparison with PDG values

1540 –191i

1642 –41i

PRELIMINARY

Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, in preparation

All extracted N*s originate from bare N* states.

(At present it is found no pole associated with meson exchanges.)

PDG values are close to ours!


Future works

Future works

N* Study

  • Extracting N*  MB, gN decay form factors from the EBAC model

  • Searching for new N* states via the analysis of g N  K Y, w N

  • Developing a method linking our form factors to Hadron models

    and Lattice QCD calculations

  • Refinement of the model parameters with

    the combined analysis of p N, g(*) N  p N, p p N

  • Full treatment of the direct ppN 3-body unitarity cut.

Model Upgrade


Back up

back up


Meson baryon potentials driving terms of ls eq

Meson-baryon potentials (Driving terms of LS eq.)

All potentials are described in Matsuyama, Sato, Lee, Phys. Rep. 439 193 (2007)


Dynamical coupled channels model for double pion production reactions

Attach appropriate Green functions ( ) and vertex functions ( )

to p N(on-shell) → MB (off-shell) amplitude ( )

Dynamical coupled-channels model for double pion production reactions

All ingredientsalready prepared in 2-body calculation !!


Dynamical coupled channels model for double pion production reactions1

Not included in

No new parameter introduced

Dynamical coupled-channels model for double pion production reactions

+

2 → 3 effective potential

+

+

=


Approximate treatment of direct term

Approximate treatment of direct term

=

+

part of V23

part of


Dynamical coupled channels model for double pion production reactions2

Dynamical coupled-channels modelfor double pion production reactions

To obtain g N → p p N amplitude, just make replacement below:

where


Results

Results

full

c.c. effect off

res. only

nonres. only


Contribution of v23

Contribution of V23

PRC result

PRC result + V23


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