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Title: 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:
 [1];  [1];  [2];  [3]
  1. Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050, Vienna (Austria)
  2. (Russian Federation)
  3. 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}
}