# Dynamical test of constituent quark models with {pi}N reactions

## Abstract

A dynamical approach is developed to predict the {pi}N scattering amplitudes starting with the constituent quark models. The first step is to apply a variational method to solve the three-quark bound state problem. The resulting wave functions are used to calculate the N{sup *}{yields}{pi}N,{eta}N,{pi}{delta} vertex functions by assuming that the {pi} and {eta} mesons couple directly to quarks. These vertex functions and the predicted baryon bare masses then define a Hamiltonian for {pi}N reactions. We apply a unitary transformation method to derive from the constructed Hamiltonian a multichannel and multiresonance reaction model for predicting the {pi}N scattering amplitudes up to W=2 GeV. With the parameters constrained by the {delta}(1232) excitation, we have examined the extent to which the {pi}N scattering in the S{sub 11} channel can be described by constituent quark models based on one-gluon-exchange or one-meson exchange mechanisms. It is found that the data seem to favor the spin-spin interaction due to one-meson exchange and the tensor interaction due to one-gluon exchange. A phenomenological quark-quark potential has been constructed to reproduce the S{sub 11} amplitude. (c) 2000 The American Physical Society.

- Authors:

- Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, (Japan)
- Department of Physics, Osaka City University, Osaka 558-8585, (Japan)
- Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)

- Publication Date:

- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL

- OSTI Identifier:
- 20216934

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. C, Nuclear Physics

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 6; Other Information: PBD: Jun 2000; Journal ID: ISSN 0556-2813

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; PION-NUCLEON INTERACTIONS; QUARK MODEL; VARIATIONAL METHODS; ETA MESONS; DELTA-1232 BARYONS; SPIN; QUARK-QUARK INTERACTIONS; BOUND STATE; THEORETICAL DATA

### Citation Formats

```
Yoshimoto, T., Sato, T., Arima, M., and Lee, T.-S. H.
```*Dynamical test of constituent quark models with {pi}N reactions*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevC.61.065203.

```
Yoshimoto, T., Sato, T., Arima, M., & Lee, T.-S. H.
```*Dynamical test of constituent quark models with {pi}N reactions*. United States. doi:10.1103/PhysRevC.61.065203.

```
Yoshimoto, T., Sato, T., Arima, M., and Lee, T.-S. H. Thu .
"Dynamical test of constituent quark models with {pi}N reactions". United States. doi:10.1103/PhysRevC.61.065203.
```

```
@article{osti_20216934,
```

title = {Dynamical test of constituent quark models with {pi}N reactions},

author = {Yoshimoto, T. and Sato, T. and Arima, M. and Lee, T.-S. H.},

abstractNote = {A dynamical approach is developed to predict the {pi}N scattering amplitudes starting with the constituent quark models. The first step is to apply a variational method to solve the three-quark bound state problem. The resulting wave functions are used to calculate the N{sup *}{yields}{pi}N,{eta}N,{pi}{delta} vertex functions by assuming that the {pi} and {eta} mesons couple directly to quarks. These vertex functions and the predicted baryon bare masses then define a Hamiltonian for {pi}N reactions. We apply a unitary transformation method to derive from the constructed Hamiltonian a multichannel and multiresonance reaction model for predicting the {pi}N scattering amplitudes up to W=2 GeV. With the parameters constrained by the {delta}(1232) excitation, we have examined the extent to which the {pi}N scattering in the S{sub 11} channel can be described by constituent quark models based on one-gluon-exchange or one-meson exchange mechanisms. It is found that the data seem to favor the spin-spin interaction due to one-meson exchange and the tensor interaction due to one-gluon exchange. A phenomenological quark-quark potential has been constructed to reproduce the S{sub 11} amplitude. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevC.61.065203},

journal = {Physical Review. C, Nuclear Physics},

issn = {0556-2813},

number = 6,

volume = 61,

place = {United States},

year = {2000},

month = {6}

}