ANALYSIS OF DIVERGENCES IN A NEUTRAL-SPIN-1-MESON THEORY WITH PARITY-NONCONSERVING INTERACTIONS

The unrenormalizable theory of the neutral spin-1 meson with a parity-nonconserving interaction is analyzed. The formal series expansion of any transition amplitude in powers of the coupling constant g can be written as, lowest-order expression × {1+ΣA n(g 2 Λ 2) n + +ΣB gg2(ln Λ 2)(g 2 Λ 2) n-1+ΣC ng2(g 2 Λ 2) n-1+...}, where Λ is the fourmomentum cut-off parameter. It is shown that these singular sums can be carried out for arbitrary processes. The most singular sum ΣA n(g 2 Λ 2) n of all processes can be completely removed by a single mass renormalization. The next and the third most singular sums, ΣB ng2(ln Λ 2)(g 2 Λ 2) n-1 and ΣC ng2(g 2 Λ 2) n-1, of different processes are also related; these can be removed by introducing further renormalization constants. © 1969 Società Italiana di Fisica.