Physics Asked on October 17, 2020
Sidney coleman in his lecture 253a of QFT stated that " one-meson-to-one-meson S-matrix element, we should find it equal to 1" i.e $$langle p’|S|prangle = (2pi)^32E_pdelta^{(3)}(vec{p}’-vec{p})tag{1}$$ for the scalar theory $$ mathcal{L}=frac{1}{2} partial_{mu} phi partial^{mu} phi-frac{mu^{2}}{2} phi^{2}-gphipsi^*psi+partial_{mu} psi partial^{mu} psi^*-m^2psi^*psi$$
But a single meson state of this theory can decay into nucleon and anti nucleon state. Then how come we can use the condition (1) to fix the counterterm as given in coleman’s note?(https://arxiv.org/abs/1110.5013). I know similar question was raised in Renormalization and Particle Decay but the answer was never accepted and inconclusive.
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