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

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

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

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


Reaction Data

Dynamical Coupled-Channels Analysis @ EBAC

N* properties

Hadron Models

Lattice QCD

QCD

Approaches to extracting N* properties


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 @ 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


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

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)


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 scattering

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

Angular distribution

Target polarization

EBAC

SAID06


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 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?

  • 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

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

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


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

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


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 !!


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

=

+

part of V23

part of


Dynamical coupled-channels modelfor double pion production reactions

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

where


Results

full

c.c. effect off

res. only

nonres. only


Contribution of V23

PRC result

PRC result + V23


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