Prog. Theor. Phys. Vol. 37 No. 2 (1967) pp. 470-471

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|ΔI| = 1/2 Rule and K →2π Decays

Department of Physics, Tokyo University of Education, Tokyo

(Received November 28, 1966)

URL : http://ptp.ipap.jp/link?PTP/37/470/
DOI : 10.1143/PTP.37.470

R. O. Bangerter et al., Phys. Rev. Lett. 17 (1966), 495[APS].
If we assume the weak interaction (1), we cannot assume that the mass differences, such as m(K²)-m(π²), are caused by the Lagrangian, δm \intq(x) λ_s q(x) d³x.
See, for example, S. Coleman and S. Glashow, Phys. Rev. 134 (1964), B671[APS].
For example, [m(π⁺)-m(π⁰)/m(π)]².
Y. Hara and Y. Nambu, Phys. Rev. Lett. 16 (1966), 875[APS].
The assumption that the K →2π decay amplitudes are quadratic functions of meson four-momenta has been justified by Fujii. Y. Fujii, Phys. Rev. Lett. 17 (1966), 613[APS].
In evaluating ratios (7) and (8), we have included corrections due to the differences of final momenta and the K⁺ - K⁰ mass difference.
The phase volume of the π⁺ π^- final state is about twice as big as that of 2π⁰ final state.
A. H. Rosenfeld et al., UCRL-8030, August 1966 Revision.
The relation (5) results if the strong interactions are U(3)×U(3) symmetric.
We cannot compare <P_j|H_w|P_l> with mass differences of pseudoscalar mesons.
If we assume the current × current interaction with charged and neutral currents, a=-2b.

Progress of Theoretical Physics Vol. 50 No. 6 (1973) pp. 1973-1980 :
Violation of the |ΔI|=1/2 Rule in K→3π Decays

Kiyoshi Kudo, Katsuhiko Ohya and Takamitsu Oka