Unitarnyye pravila summ i amplitudy myagkikh pionov

Carl Rosenzweig, G. Veneziano

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We examine unitarity bounds on scattering amplitudes by using « unitarity sum rules » at high energy. Threshold conditions emerge when certain mass parameters approach zero. For ππ scattering a bound similar to (but somewhat weaker than) the Adler condition is shown to be needed in order to avoid a dangerous mass (infra-red) singularity. A different argument, which uses crucially the pseudoscalar nature of the pion and a few very plausible dynamical assumptions, yields a stronger bound as well as the possibility of extension to general pion amplitudes. We finally discuss our results as well as the possibility of understanding spontaneously broken symmetries from general S-matrix principles.

Original languageEnglish (US)
Pages (from-to)409-424
Number of pages16
JournalIl Nuovo Cimento A Series 11
Volume12
Issue number2
DOIs
StatePublished - Nov 1972
Externally publishedYes

Fingerprint

pions
scattering amplitude
sum rules
broken symmetry
thresholds
matrices
scattering
energy

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics

Cite this

Unitarnyye pravila summ i amplitudy myagkikh pionov. / Rosenzweig, Carl; Veneziano, G.

In: Il Nuovo Cimento A Series 11, Vol. 12, No. 2, 11.1972, p. 409-424.

Research output: Contribution to journalArticle

Rosenzweig, Carl ; Veneziano, G. / Unitarnyye pravila summ i amplitudy myagkikh pionov. In: Il Nuovo Cimento A Series 11. 1972 ; Vol. 12, No. 2. pp. 409-424.
@article{ef9c38bc9e0a46f78a71b4f9343df181,
title = "Unitarnyye pravila summ i amplitudy myagkikh pionov",
abstract = "We examine unitarity bounds on scattering amplitudes by using « unitarity sum rules » at high energy. Threshold conditions emerge when certain mass parameters approach zero. For ππ scattering a bound similar to (but somewhat weaker than) the Adler condition is shown to be needed in order to avoid a dangerous mass (infra-red) singularity. A different argument, which uses crucially the pseudoscalar nature of the pion and a few very plausible dynamical assumptions, yields a stronger bound as well as the possibility of extension to general pion amplitudes. We finally discuss our results as well as the possibility of understanding spontaneously broken symmetries from general S-matrix principles.",
author = "Carl Rosenzweig and G. Veneziano",
year = "1972",
month = "11",
doi = "10.1007/BF02729554",
language = "English (US)",
volume = "12",
pages = "409--424",
journal = "Il Nuovo Cimento A",
issn = "0369-3546",
publisher = "Zanichelli Editore SpA",
number = "2",

}

TY - JOUR

T1 - Unitarnyye pravila summ i amplitudy myagkikh pionov

AU - Rosenzweig, Carl

AU - Veneziano, G.

PY - 1972/11

Y1 - 1972/11

N2 - We examine unitarity bounds on scattering amplitudes by using « unitarity sum rules » at high energy. Threshold conditions emerge when certain mass parameters approach zero. For ππ scattering a bound similar to (but somewhat weaker than) the Adler condition is shown to be needed in order to avoid a dangerous mass (infra-red) singularity. A different argument, which uses crucially the pseudoscalar nature of the pion and a few very plausible dynamical assumptions, yields a stronger bound as well as the possibility of extension to general pion amplitudes. We finally discuss our results as well as the possibility of understanding spontaneously broken symmetries from general S-matrix principles.

AB - We examine unitarity bounds on scattering amplitudes by using « unitarity sum rules » at high energy. Threshold conditions emerge when certain mass parameters approach zero. For ππ scattering a bound similar to (but somewhat weaker than) the Adler condition is shown to be needed in order to avoid a dangerous mass (infra-red) singularity. A different argument, which uses crucially the pseudoscalar nature of the pion and a few very plausible dynamical assumptions, yields a stronger bound as well as the possibility of extension to general pion amplitudes. We finally discuss our results as well as the possibility of understanding spontaneously broken symmetries from general S-matrix principles.

UR - http://www.scopus.com/inward/record.url?scp=51649186247&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649186247&partnerID=8YFLogxK

U2 - 10.1007/BF02729554

DO - 10.1007/BF02729554

M3 - Article

AN - SCOPUS:51649186247

VL - 12

SP - 409

EP - 424

JO - Il Nuovo Cimento A

JF - Il Nuovo Cimento A

SN - 0369-3546

IS - 2

ER -