# Soft-photon expansion and soft-photon theorem

## Abstract

The question of the existence of the soft-photon expansion and its connection with the derivation of the soft-photon theorem is studied. We find that the soft-phonon expansion does not necessarily exist for all possible bremsstrahlung cross sections, and if such an expansion does not exist for some types of cross section, then the soft-photon theorem cannot be derived for them. We define two different classes of bremsstrahlung cross section for our study, which we call the H-type cross section and the R-type cross section. We find that the R-type cross section can be expanded in powers of k (photon momentum) with all coefficients of the expansion which are independent of k, while the H-type cross section can only have an expansion whose coefficients are all functions of k. Moreover, we have shown that those coefficients which are functions of k must necessarily contain off-shell parameters. Therefore, we conclude that the soft-photon expansion exists and hence the soft-photon theorem can be derived only for the R-type cross section. This strongly implies that the R-type cross section is to be preferred for the study of bremsstrahlung processes.

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics and Institute for Nuclear Theory, Brooklyn College of the City University of New York, Brooklyn, New York 11210

- OSTI Identifier:
- 6773083

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., D; (United States)

- Additional Journal Information:
- Journal Volume: 18:9

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BREMSSTRAHLUNG; CROSS SECTIONS; ELASTIC SCATTERING; PION-PROTON INTERACTIONS; SERIES EXPANSION; ELECTROMAGNETIC RADIATION; HADRON-HADRON INTERACTIONS; INTERACTIONS; MESON-BARYON INTERACTIONS; MESON-NUCLEON INTERACTIONS; PARTICLE INTERACTIONS; PION-NUCLEON INTERACTIONS; RADIATIONS; SCATTERING; 645202* - High Energy Physics- Particle Interactions & Properties-Theoretical- Electromagnetic Interactions & Properties

### Citation Formats

```
Liou, M K.
```*Soft-photon expansion and soft-photon theorem*. United States: N. p., 1978.
Web. doi:10.1103/PhysRevD.18.3390.

```
Liou, M K.
```*Soft-photon expansion and soft-photon theorem*. United States. doi:10.1103/PhysRevD.18.3390.

```
Liou, M K. Wed .
"Soft-photon expansion and soft-photon theorem". United States. doi:10.1103/PhysRevD.18.3390.
```

```
@article{osti_6773083,
```

title = {Soft-photon expansion and soft-photon theorem},

author = {Liou, M K},

abstractNote = {The question of the existence of the soft-photon expansion and its connection with the derivation of the soft-photon theorem is studied. We find that the soft-phonon expansion does not necessarily exist for all possible bremsstrahlung cross sections, and if such an expansion does not exist for some types of cross section, then the soft-photon theorem cannot be derived for them. We define two different classes of bremsstrahlung cross section for our study, which we call the H-type cross section and the R-type cross section. We find that the R-type cross section can be expanded in powers of k (photon momentum) with all coefficients of the expansion which are independent of k, while the H-type cross section can only have an expansion whose coefficients are all functions of k. Moreover, we have shown that those coefficients which are functions of k must necessarily contain off-shell parameters. Therefore, we conclude that the soft-photon expansion exists and hence the soft-photon theorem can be derived only for the R-type cross section. This strongly implies that the R-type cross section is to be preferred for the study of bremsstrahlung processes.},

doi = {10.1103/PhysRevD.18.3390},

journal = {Phys. Rev., D; (United States)},

number = ,

volume = 18:9,

place = {United States},

year = {1978},

month = {11}

}