Unsubtracted Dispersion Relations in Weak Interactions and Composite Particles

概要

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The π→μ+ν and baryon+antibaryon→μ+ν processes are investigated under the condition that a pion is a Regge particle. A somewhat simplified model is used, i.e. baryons have degenerate mass and only the baryon-antibaryon states are taken into account for the unitarity. It is found that (1) the unsubtracted dispersion relation does not hold for the invariant amplitude of the π→μ+ν decay, and (2) the eigenvalue restriction on the strong-interaction parameters, suggested by Nishijima, does not occur. These results are the immediate consequence of the Regge pion. The following properties of the Regge pion play a crucial role : The composite pion can couple only to one eigenchannel but not to many eigenchannels, and the improper vertex function with the pion off the mass shell (form factor) has a certain high-energy behavior. The amplitude of the baryon-antibaryon process can satisfy the unsubtracted dispersion relation even for the Regge pion. The partially-conserved axial-vector current hypothesis is established if and only if the weak decay can occur through only the eigenchannel to which the pion be coupled.
理論物理学刊行会の論文
1967-12-25