Two-Variable Expansions and the K→3π Decays

Journal Article · Thu Jun 01 00:00:00 EDT 1972 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/physrevd.5.2877· OSTI ID:4660885

Hicks, H. R. ^[1]; Winternitz, P. ^[2]

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1. Carnegie Mellon Univ., Pittsburgh, PA (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
2. Univ. of Pittsburgh, PA (United States)

Previously suggested two-variable expansions of three-body decay amplitudes in terms of harmonic functions of an O(4) group are discussed and applied to analyze the Dalitz-plot distribution of over 3.2 million K^± →π^±⁢π^±⁢π^∓ decay events. Among the general features of the O(4) expansions we wish to stress that they are written in the c.m. system of two of the final particles, the angular momentum of which is displayed explicitly, and that each term in the expansion has a good behavior at the threshold, pseudothreshold, and at the boundary of the physical region. We analyze the recent data of Ford et al. on charged K → 3π decays, using both O(4) expansion and the standard power-series expansion in terms of the Dalitz-Fabri variables. In both cases it is perfectly adequate to keep four terms in the corresponding expansion. The χ² fit is marginally better for the O(4) expansion. We conclude that the K →3⁢π Dalitz plot has too little structure in it to provide a real test of the advantages or disadvantages of different treatments. It is thus most desirable to apply the O(4) expansions to Dalitz plots of other processes, like η →3π or $$\overline{p}n$$ →π⁢ππ. No conclusive evidence is found for CP violation. However, the "linear" term in the O(4) expansion of the difference between the squared matrix elements for K⁺ and K^– decays does differ from zero by more than two standard deviations. The effect is stable with regard to the number of terms kept in the expansions. Finally, an important distinctive feature of the O(4) expansions is their intimate relation to two-variable O(3, 1) expansions of physical scattering amplitudes.

• 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-26-026705
• OSTI ID: 4660885
• Alternate ID(s): OSTI ID: 4623401
• Report Number(s): NYO--3829-84
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 11 Vol. 5; ISSN 0556-2821
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

DECAY AMPLITUDES
DISTRIBUTION
EMISSION
FUNCTIONS
High Energy Physics
KAONS MINUS
Mesons
O GROUPS
PIONS MINUS
PIONS PLUS KAONS PLUS
Symmetry Groups