# Dispersion representations and anomalous singularities of the triangle diagram

## Abstract

We discuss dispersion representations for the triangle diagram F(p{sub 1}{sup 2},p{sub 2}{sup 2},q{sup 2}), the single dispersion representation in q{sup 2} and the double dispersion representation in p{sub 1}{sup 2} and p{sub 2}{sup 2}, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations. For the double dispersion representation in p{sub 1}{sup 2} and p{sub 2}{sup 2}, the appearance of the anomalous cut in the region q{sup 2}>0 is demonstrated, and a new derivation of the anomalous double spectral density is given. We point out that the double spectral representation is particularly suitable for applications in the region of p{sub 1}{sup 2} and/or p{sub 2}{sup 2} above the two-particle thresholds. The dispersion representations for the triangle diagram in the nonrelativistic limit are studied and compared with the triangle diagram of the nonrelativistic field theory.

- Authors:

- Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050, Vienna (Austria)
- (Russian Federation)
- INFN, Sezione di Roma III, Via della Vasca Navale 84, I-00146, Rome(Italy)

- Publication Date:

- OSTI Identifier:
- 20933256

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevD.75.016001; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FEYNMAN DIAGRAM; FIELD THEORIES; FORM FACTORS; SINGULARITY; SPECTRAL DENSITY

### Citation Formats

```
Lucha, Wolfgang, Melikhov, Dmitri, Nuclear Physics Institute, Moscow State University, 119992, Moscow, and Simula, Silvano.
```*Dispersion representations and anomalous singularities of the triangle diagram*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.016001.

```
Lucha, Wolfgang, Melikhov, Dmitri, Nuclear Physics Institute, Moscow State University, 119992, Moscow, & Simula, Silvano.
```*Dispersion representations and anomalous singularities of the triangle diagram*. United States. doi:10.1103/PHYSREVD.75.016001.

```
Lucha, Wolfgang, Melikhov, Dmitri, Nuclear Physics Institute, Moscow State University, 119992, Moscow, and Simula, Silvano. Mon .
"Dispersion representations and anomalous singularities of the triangle diagram". United States.
doi:10.1103/PHYSREVD.75.016001.
```

```
@article{osti_20933256,
```

title = {Dispersion representations and anomalous singularities of the triangle diagram},

author = {Lucha, Wolfgang and Melikhov, Dmitri and Nuclear Physics Institute, Moscow State University, 119992, Moscow and Simula, Silvano},

abstractNote = {We discuss dispersion representations for the triangle diagram F(p{sub 1}{sup 2},p{sub 2}{sup 2},q{sup 2}), the single dispersion representation in q{sup 2} and the double dispersion representation in p{sub 1}{sup 2} and p{sub 2}{sup 2}, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations. For the double dispersion representation in p{sub 1}{sup 2} and p{sub 2}{sup 2}, the appearance of the anomalous cut in the region q{sup 2}>0 is demonstrated, and a new derivation of the anomalous double spectral density is given. We point out that the double spectral representation is particularly suitable for applications in the region of p{sub 1}{sup 2} and/or p{sub 2}{sup 2} above the two-particle thresholds. The dispersion representations for the triangle diagram in the nonrelativistic limit are studied and compared with the triangle diagram of the nonrelativistic field theory.},

doi = {10.1103/PHYSREVD.75.016001},

journal = {Physical Review. D, Particles Fields},

number = 1,

volume = 75,

place = {United States},

year = {Mon Jan 01 00:00:00 EST 2007},

month = {Mon Jan 01 00:00:00 EST 2007}

}