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Relativistic Two-Variable Expansions for Three-Body Decay Amplitudes

Journal Article · · Physical Review. D, Particles Fields
 [1];  [2]
  1. Carnegie Mellon Univ., Pittsburgh, PA (United States)
  2. Univ. of Pittsburgh, PA (United States)
+ Show Author Affiliations
Three-body decays 1→2+3+4 are considered using a frame of reference analogous to the c.m. system for scattering. The physical decay region is mapped onto an O(4) sphere, so that the decay amplitude f⁡(α,θ) is a function on this sphere (depending only on two of the three angles α, θ, and φ). The amplitude is then expanded in terms of the basis functions of O(4) and we obtain two-variable expansions, in which all the dependence on the kinematic parameters is explicitly displayed in special functions. These expansions make it possible to treat decays and scattering on the same footing, in that they are intimately related to O(3,1) expansions of scattering amplitudes, considered previously. Some analyticity properties are built in, so that each partial wave has the correct behavior at the threshold (m3+m4)2 and pseudothreshold (m1–m2)2. Finally, the expansions make it possible to perform a kinematically (or group-theoretically) motivated harmonic analysis of Dalitz-plot distributions for K → 3⁢π and η →3⁢π decays (the results will be presented separately).
Research Organization:
Carnegie Mellon Univ., Pittsburgh, PA (United States); Univ. of Pittsburgh, PA (United States)
Sponsoring Organization:
US Atomic Energy Commission (AEC)
NSA Number:
NSA-26-003267
OSTI ID:
4727778
Alternate ID(s):
OSTI ID: 4705932
Report Number(s):
NYO--3829-73
Journal Information:
Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 4; ISSN 0556-2821
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (15)

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Related Subjects

DECAY
ETA RESONANCES
Electromagnetic
High Energy Physics
KAONS
Mesons
PIONS
PRODUCTION
RELATIVITY THEORY
SCATTERING AMPLITUDE
Theoretical Particle Interactions & Properties