On the introduction of Lorentz poles into the unequal-mass scattering amplitude

K. Szegö, K. Tóth

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We suggest a new type of kinematical decomposition of the unequal-mass scattering amplitude. We introduce two noncommuting, nondisjunct Poincaré groups, P+ and P(), both of them are subgroups of the P1 ⊗P2 direct-product group, where P1 and P2 are the Poincaré groups of the one-particle transformations for the first and the second particle of the two-particle states, respectively. The group P+ is identical to the group of the two-particle Poincaré transformations. Our first decomposition for the scattering amplitude is a double expansion with respect to the representations of both the P+ and P groups, simultaneously. The second proposal of ours is the partial-wave analysis not of the centre-of-mass states but of the «equal velocity» states, in which the individual particles move with the same velocity. Our expansions are valid for any s and t. In the equal-mass case they give the usual Lorentz-pole decomposition at t=0. The formalism seems to be adequate for understanding the meaning of the «spectrum generating group» in the unequal-mass case. The variables of the expansion functions are unambiguously defined by the kinematical variables, and have branch points only at the thresholds and pseudothresholds, in opposition to other approaches.

Original languageEnglish
Pages (from-to)371-400
Number of pages30
JournalIl Nuovo Cimento A Series 11
Volume66
Issue number2
DOIs
Publication statusPublished - 1970

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scattering amplitude
poles
decomposition
expansion
subgroups
center of mass
proposals
formalism
thresholds
products

ASJC Scopus subject areas

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

Cite this

On the introduction of Lorentz poles into the unequal-mass scattering amplitude. / Szegö, K.; Tóth, K.

In: Il Nuovo Cimento A Series 11, Vol. 66, No. 2, 1970, p. 371-400.

Research output: Contribution to journalArticle

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