K→2π Decays and Dispercion Relations

概要

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The purpose of this paper is twofold. The first is to show how the ΔI=1/2 rule for K→2π decays is derived according to the method used by Nishijima to explain the ΔI=1/2 rule for hyperon non-leptonic weak decays. The selection rule results from the charge independence of the strong interaction, under the assumptions that the weak decay amplitude must satisfy the unsubstracted dispersion relation and that the weak interaction Hamiltonian is CP-invariant, and under an approximation neglecting all electromagnetic interactions. The conclusion is strongly dependent on the s-wave pi-pi phase shifts and p-wave cutoffs. The second purpose is to investigate why the violation of the ΔI=1/2 rule arises. There the experimental ratio, |A(K^+→π^+π^0)/A(K_1^0→π^+π^-)|=4.6×10^<-2> is deduced from electromagnetic corrections to absorptive parts of the dispersion relation on the basis of the assumption in which the violation is reduced to the electromagnetic origin alone. We shall discuss it in detail using a fictitious photon mass λ as the infrared cutoff.
理論物理学刊行会の論文
1969-02-25