Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

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)

Zur Darstellungstheorie der inhomogenen Lorentzgruppe als Grundlage quantenmechanischer Kinematik journal January 1962
Two-dimensional expansions of relativistic amplitudes in the Mandelstam triangle and crossing symmetric reactions journal December 1969
An expansion of the scattering amplitude at vanishing four-momentum transfer using the representations of the Lorentz group journal February 1968
On the group-theoretical approach to complex angular momentum and signature journal March 1968
Clebsch-Gordan Coefficients for the Coupling of SL(2, C) Principal-Series Representations journal March 1970
Recursion and Symmetry Relations for the Clebsch-Gordan Coefficients of the Homogeneous Lorentz Group journal March 1970
Crossing Symmetric Expansions of Physical Scattering Amplitudes; The O(2, 1) Group and Lamé Functions journal February 1971
Wigner Coefficients for the R 4 Group and Some Applications journal May 1961
Kinematics of General Scattering Processes and the Mandelstam Representation journal February 1960
Four-Dimensional Symmetry journal July 1967
Simultaneous "Partial-Wave" Expansion in the Mandelstam Variables: Crossing Symmetry for Partial Waves journal August 1968
Relativistic Partial-Wave Analysis in Two Variables and the Crossing Transformation journal February 1970
Two-Variable Expansion of the Scattering Amplitude for any Mass and Spin and Crossing Symmetry for Partial Waves journal March 1970
Crossing-Symmetric Expansions of Scattering Amplitudes, Threshold Behavior, and Asymptotics journal April 1971
Search for Violation ofCPInvariance inτ±Decay journal November 1970

Similar Records

Two-Variable Expansions and theK→3π Decays
Journal Article · Thu Jun 01 00:00:00 EDT 1972 · Physical Review. D, Particles Fields · OSTI ID:4660885
Radiative corrections to the Dalitz plot of charged and neutral baryon semileptonic decays with angular correlation between polarized emitted baryons and charged lepton
Journal Article · Wed Jul 02 00:00:00 EDT 2008 · AIP Conference Proceedings · OSTI ID:21149118

Related Subjects

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