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### Overview of the [email protected] progress

B. Juliá-Díaz

Departament d’Estructura i Constituents de la Matèria

Universitat de Barcelona (Spain)

The players:

- H. Kamano (JLab)
- T.S.H. Lee (Argonne, JLab)
- A. Matsuyama (Shizuoka)
- T. Sato, N. Suzuki (Osaka)
- B. Saghai, J. Durand (Saclay)

Baryon Resonances

Exciting the substructure we can learn about the forces which keep the quarks together, e.g. using the quark model picture some of the predicted states are:

J=1/2

J=3/2

J=3/2

J=1/2

0p

D33 (1700)

S31 (1620)

L=1, S=1/2, J=3/2-

S11 (1535)

D13 (1520)

L=1, S=1/2, J=1/2-

L=1, S=1/2, J=1/2-

L=1, S=1/2, J=3/2-

0s

P11 (939)

P33 Δ(1232)

L=0, S=1/2, J=1/2+

L=0, S=3/2, J=3/2+

qqq

N*: 1440, 1520, 1535, 1650, 1675, 1680, ...

Δ : 1600, 1620, 1700, 1750, 1900, …

The Δ (1232) and others100

Δ (1232)

πN X, πN

- The Delta (1232) resonance stands as a clear peak
- The region 1.4 GeV – 2 GeV hosts ~ 20 resonances

PDG *s and N*’s origin

π

N

- Most of their properties are extracted from
- N N
- N N
- Are they all genuine quark/gluon excitations?
- |N*> =| qqq >
- Is their origin dynamical?
- E.g. some could be understood as arising from meson-baryon dynamics
- |N*>= | MB >

N*s

Dynamical Coupled-Channels Analysis @ EBAC

[email protected]Reaction Data

N* properties

N-N* form factors

Hadron Models

Lattice QCD

QCD

E.m. probes

e.g: p η

- Key points:
- Couplings of mesons to baryons
- Electromagnetic vertices

- Coupling of resonances to MB
- Electromagnetic structure of resonances

e.m.

Multi step (unitarity)

How do we produce meson-baryon states?

- Directly
- Through MB states
- Through MMB states

- We need to incorporate all the possibilities
- Unitarity:

Coupled-channels

p

σTOT (b)

MS

C.C. ingredients

- Non-resonant + resonant
- Dressed resonant vertex
- Resonance self energies
- Non-resonant amplitude (resummation)

CC

MBMB

We introduce explicitly (impose) a minimal number of resonances, 16 of 23:

(4* and 3 * from PDG):

N: S11(2), P11(2), P13(1), D13(1), D15(1), F15(1)

Δ: S31(1), P31(1), P33(2), D33(1), F35(1), F37(1)

Full approach described in great detail:

A. Matsuyama, T. Sato, T.-S.H. Lee, Phys. Rep. 2007

CC

i.e. VNN,N

Full approach described in great detail:

A. Matsuyama, T. Sato, T.-S.H. Lee, Phys. Rep. 2007

CC

Resonance t

Full approach described in great detail:

A. Matsuyama, T. Sato, T.-S.H. Lee, Phys. Rep. 2007

CC

Dynamical CC|SL/EBAC

Physics:

- Unitarity fulfilled within the model
- Most relevant channels included
- Consistent study of all production reactions
- Exact treatment of 3 body cut

Technical

- Parallel computing version exists
- Slow evaluation

∫vgt

Meson-baryon building

(1) SAID Energy dependent PWA with fake error bars

FIT

Bg

N* param

(2) SAID Energy independent PWA

REFIT (almost final)

MINUIT used extensively

(3) EXP DATA

Fine tune

N

Involved system of coupled integral equations with singularities. No further approximations taken.

Need for extensive parameter search. Several unknowns: e.g. couplings of resonances to MB states

We developed a parallel code, CCEBA, and got several supercomputing resources

Technical aspects- Time gain resulting from using parallel computers scales ~ linearly with the number of processors
- First: parallelization in Energy
- Second: parallelization in partial wave
- BSC, Spain (340 kh), PI: B. Julia-Diaz
- NERSC LBNL (500 kh), PI: TSH Lee

Tech

Meson-baryon (ii)

d/d

Polarization

B. Julia-Diaz, A. Matsuyama, T.-S.H. Lee, T. Sato, Phys. Rev. C 76, 065201 (2007)

data obtained through D. Arndt et al, SAID , gwdac.phys.gwu.edu

N

Meson-baryon (iii)

- Amplitudes compared to GWU/SAID amplitudes for the I=1/2 sector
- Total Cross sections compared to experimental data
- Prediction for the total cross sections for each individual channel

Real part of the amplitude

B. Julia-Diaz, A. Matsuyama, T.-S.H. Lee, T. Sato, Phys. Rev. C 76, 065201 (2007)

N

(II)

Invariant mass

distributions

Full model

Phase space

H. Kamano, B. Julia-Diaz, TSH Lee, A. Matsuyama, T. Sato, Phys. Rev. C 79 (2009) 025206

(Using the MB model of BJD, AM, TSHL and TS, Phys. Rev. C 76, 065201 (2007))

Data handled with the help of D. Arndt

Resonance states

Analytic continuation of T(W) to the unphysical sheet by using contour deformation

Pole can be both in the non-resonant and resonant amplitudes

Pole of T as a function of W, p’s are arbitrary

Resonance Mass

Extraction of Resonances from Meson-Nucleon Reactions.

N. Suzuki, T. Sato, T.-S.H. Lee, Phys. Rev. C 79 (2009) 025205

Current N*

Suzuki, BJD, HK, AM,TSHL, TS, in preparation (2009)

Single pion production

- Strong pieces fixed
- E.g.e.m. vertex of nucleon: fixed

- Electromagnetic structure of resonances

Q2 independent analyses?

Error?

Which N*s ? All?

Single pion photoproduction

p+n

- Comparison to data
- Total cross section
- Differential cross sections
- Target polarization

p0p

σTOT (b)

B. Julia-Diaz, A. Matsuyama, T.-S.H. Lee, T. Sato, L.C. Smith, Phys. Rev. C77, 045205 (2008)

Single pion electroproduction

- Delta region:
- We revisited the original SL model and extracted the form factors of NDelta transition from single Q2 fits.

Julia-Diaz, Lee, Sato, Smith, Phys. Rev. C 75, 015205, (2007)

Single pion electroproduction

- On going work:
- Fix the strong pieces
- Resonance content fixed in strong part
- First fit the structure functions available where they have been extracted
- First goal is to go up to W=1.65 and Q2=4 GeV2
- Current status
- Preliminar Q2 evolution of helicities available
- Need to control de error

B. Julia-Diaz, A. Matsuyama, T.-S.H. Lee, T. Sato, L.C. Smith, Phys. Rev. C77, 045205 (2008)

Single and double meson production

*N N up to W=1.6 GeV (preparation)

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

Currently using CLAS structure functions to fix the Q2 evolution of the helicity amplitudes

PRELIMINARY RESULTS AVAILABLE

*N N (preparation)

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

In progress (~ 2009)N* properties

- N* properties from the EBAC N model

N. Suzuki, B. Julia-Diaz, H. Kamano, A. Matsuyama, T.-S.H. Lee, T. Sato.

- Extraction of N* MB and N* N decay vertices

B. Julia-Diaz, H. Kamano, A. Matsuyama, T.-S.H. Lee, T. Sato, N. Suzuki

END

Extraction of Resonances from Meson-Nucleon Reactions.

N. Suzuki, T. Sato, T.-S.H. Lee, Phys. Rev. C 79 (2009) 025205

Dynamical coupled-channels study of pi n --> pi pi n reactions

H. Kamano, B. Julia-Diaz, T.-S.H. Lee, A. Matsuyama, T. Sato, Phys. Rev. C 79 (2009) 025206

Coupled-channels study of the pion- p --> eta n process

J. Durand, B. Julia-Diaz, T.-S.H. Lee, B. Saghai, T. Sato, Phys. Rev. C 78, 025204 (2008)

Dynamical coupled-channels effects in pion photoproduction

B. Julia-Diaz, T.-S.H. Lee, A. Matsuyama, T. Sato, and L.C. Smith, Phys. Rev. C 77, 045205 (2008)

Dynamical coupled-channels model of pi N scattering in the W <= 2-GeV nucleon resonance region.

B. Julia-Diaz, T.-S.H. Lee, A. Matsuyama, T. Sato, Phys. Rev. C 76, 065201 (2007)

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