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Crossed-Channel Partial-Wave Expansions and the Bethe-Salpeter Equation

Journal Article · · Physical Review. D, Particles Fields
 [1];  [1];  [2]
  1. Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics; SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Stanford Univ., CA (United States)
  2. Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics; Brown Univ., Providence, RI (United States)
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The Bethe-Salpeter equation for the direct-channel absorptive part of the scattering amplitude is analyzed in the ladder approximation to investigate the relationship between SO⁡(1,3) and SO⁡(1,2) crossed-channel partial-wave analyses. The SO⁡(1,2) expansion, used when the momentum transfer Q is spacelike, is studied in detail in the limit Qμ→0. Further, the connection between the SO⁡(1,3) and SO⁡(1,2) partial-wave amplitudes at Qμ = 0 is obtained explicitly, as is the familiar result that a Toller pole is equivalent to an infinite sequence of integrally spaced Regge poles at Qμ = 0.
Research Organization:
Brown Univ., Providence, RI (United States); Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics
Sponsoring Organization:
US Air Force Office of Scientific Research (AFOSR); US Atomic Energy Commission (AEC); USDOE
NSA Number:
NSA-25-005426
OSTI ID:
4096651
Alternate ID(s):
OSTI ID: 4036932
Report Number(s):
NYO--2262-TA-226
Journal Information:
Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 3; ISSN 0556-2821
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (9)

Integral equation for high-energy pion-pion scattering journal August 1962
Theory of high-energy scattering and multiple production journal December 1962
Decomposition of the Unitary Irreducible Representations of the Group SL (2 C ) Restricted to the Subgroup SU (1, 1) journal June 1967
Amplitude Bounds in the Ladder Graph Approximation journal August 1964
Regge Poles and Unequal-Mass Scattering Processes journal January 1967
Four-Dimensional Symmetry journal July 1967
O(4), Off-ShellNN¯Scattering, and Massless Pions journal August 1968
Properties of Bethe-Salpeter Wave Functions journal November 1954
Laplace Transforms and the Diagonalization of Bethe-Salpeter Equations for Absorptive Parts journal August 1970

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BETHE-SALPETER EQUATION
PARTIAL WAVES
SCATTERING AMPLITUDE
SO GROUP