# Chiral Effective-Field Theory in the $$\Delta$$(1232) Region: I. Pion Electroproduction on the Nucleon

## Abstract

We develop an extension of chiral perturbation theory to the {Delta}(1232)-resonance energy region and apply it to investigate the pion electroproduction off the nucleon (e{sup -} N {yields} e{sup -} N {pi}). We present a complete calculation of this process, in the {Delta}-resonance region, up to next-to-leading order in the {delta}-expansion. At this order, the only free parameters are the three low-energy constants corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) {gamma} N {yields} {Delta} transition strength. After fitting these parameters to a few well-known data, our calculation provides a prediction for observables and multipole amplitudes of pion electroproduction. These results compare favorably with the phenomenological multipole solutions and recent experimental results from MIT-Bates and MAMI. Our prediction for the pion-mass dependence of the {gamma}N{Delta} form factors offers an explanation for the discrepancy between the recent lattice-QCD results and the experimental value for the ''C2/M1 ratio'' at low Q{sup 2}.

- Authors:

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA

- Sponsoring Org.:
- USDOE - Office of Energy Research (ER)

- OSTI Identifier:
- 862406

- Report Number(s):
- JLAB-THY-06-458; DOE/ER/40150-3672

TRN: US0600696

- DOE Contract Number:
- AC05-84ER40150

- Resource Type:
- Journal Article

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; ELECTROPRODUCTION; FORECASTING; FORM FACTORS; MULTIPOLES; NUCLEONS; PERTURBATION THEORY; PIONS

### Citation Formats

```
Pascalutsa, Vladimir, and Vanderhaeghen, Marc.
```*Chiral Effective-Field Theory in the $\Delta$(1232) Region: I. Pion Electroproduction on the Nucleon*. United States: N. p., 2006.
Web.

```
Pascalutsa, Vladimir, & Vanderhaeghen, Marc.
```*Chiral Effective-Field Theory in the $\Delta$(1232) Region: I. Pion Electroproduction on the Nucleon*. United States.

```
Pascalutsa, Vladimir, and Vanderhaeghen, Marc. Fri .
"Chiral Effective-Field Theory in the $\Delta$(1232) Region: I. Pion Electroproduction on the Nucleon". United States. https://www.osti.gov/servlets/purl/862406.
```

```
@article{osti_862406,
```

title = {Chiral Effective-Field Theory in the $\Delta$(1232) Region: I. Pion Electroproduction on the Nucleon},

author = {Pascalutsa, Vladimir and Vanderhaeghen, Marc},

abstractNote = {We develop an extension of chiral perturbation theory to the {Delta}(1232)-resonance energy region and apply it to investigate the pion electroproduction off the nucleon (e{sup -} N {yields} e{sup -} N {pi}). We present a complete calculation of this process, in the {Delta}-resonance region, up to next-to-leading order in the {delta}-expansion. At this order, the only free parameters are the three low-energy constants corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) {gamma} N {yields} {Delta} transition strength. After fitting these parameters to a few well-known data, our calculation provides a prediction for observables and multipole amplitudes of pion electroproduction. These results compare favorably with the phenomenological multipole solutions and recent experimental results from MIT-Bates and MAMI. Our prediction for the pion-mass dependence of the {gamma}N{Delta} form factors offers an explanation for the discrepancy between the recent lattice-QCD results and the experimental value for the ''C2/M1 ratio'' at low Q{sup 2}.},

doi = {},

url = {https://www.osti.gov/biblio/862406},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2006},

month = {1}

}