## An attempt to construct pion distribution amplitude from the PCAC relation in the nonlocal chiral quark model

## Abstract

Using the PCAC relation, we derive a compact formula for the pion decay constant F π in the nonlocal chiral quark model. For practical calculations this formula may be used both in the Minkowski and in the Euclidean space. For the pion momentum P μ ← 0 it reduces to the well known expression derived earlier by other authors. Using a generalized dipole Ansatz for the momentum dependence of the constituent quark mass in the Minkowski space, we express F π 2 in terms of a single integral over the quark momentum fraction μ. We interpret the integrand as a pion distribution amplitude φ(u). We discuss its properties and compare with the πDA's obtained in other models.

- Authors:

- Jagellonian Univ., Krakow, PL (United States). M. Smoluchowski Inst. of Physics

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1407036

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Acta Physica Polonica. Series B

- Additional Journal Information:
- Journal Volume: 34; Journal Issue: 6; Journal ID: ISSN 0587-4254

- Publisher:
- Jagiellonian University

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Bzdak, Adam, and Praszalowicz, Michael. An attempt to construct pion distribution amplitude from the PCAC relation in the nonlocal chiral quark model. United States: N. p., 2003.
Web.
```

```
Bzdak, Adam, & Praszalowicz, Michael. An attempt to construct pion distribution amplitude from the PCAC relation in the nonlocal chiral quark model. United States.
```

```
Bzdak, Adam, and Praszalowicz, Michael. Sun .
"An attempt to construct pion distribution amplitude from the PCAC relation in the nonlocal chiral quark model". United States. https://www.osti.gov/servlets/purl/1407036.
```

```
@article{osti_1407036,
```

title = {An attempt to construct pion distribution amplitude from the PCAC relation in the nonlocal chiral quark model},

author = {Bzdak, Adam and Praszalowicz, Michael},

abstractNote = {Using the PCAC relation, we derive a compact formula for the pion decay constant F π in the nonlocal chiral quark model. For practical calculations this formula may be used both in the Minkowski and in the Euclidean space. For the pion momentum P μ ← 0 it reduces to the well known expression derived earlier by other authors. Using a generalized dipole Ansatz for the momentum dependence of the constituent quark mass in the Minkowski space, we express F π 2 in terms of a single integral over the quark momentum fraction μ. We interpret the integrand as a pion distribution amplitude φ(u). We discuss its properties and compare with the πDA's obtained in other models.},

doi = {},

journal = {Acta Physica Polonica. Series B},

number = 6,

volume = 34,

place = {United States},

year = {2003},

month = {6}

}

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