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Overview of the [email protected] progress

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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)

The problem

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, …

100

Δ (1232)

πN X, πN

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

(LIJ)

π

N

- Most of their properties are extracted from
- N N
- N N

- |N*> =| qqq >

- E.g. some could be understood as arising from meson-baryon dynamics
- |N*>= | MB >

N*s

Dynamical Coupled-Channels Analysis @ EBAC

Reaction Data

N* properties

N-N* form factors

Hadron Models

Lattice QCD

QCD

e.g: p η

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

- Coupling of resonances to MB
- Electromagnetic structure of resonances

e.m.

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

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

CC

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

Full approach described in great detail:

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

CC

Full approach described in great detail:

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

CC

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

(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

- 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

EBAC

SAID06

N

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

- 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

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

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

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

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

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

- Electromagnetic structure of resonances

Q2 independent analyses?

Error?

Which N*s ? All?

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)

- 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)

- 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

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

EBAC progress

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)