Srednicki — Quantum Field Theory · Problem 51.3

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · scalar-yukawa-renormalization

Problem

Consider making φ\varphi a scalar rather than a pseudoscalar, so that the Yukawa interaction is LYuk=gφΨ‾Ψ\mathcal{L}_{\text{Yuk}} = g\varphi\overline{\Psi}\Psi. In this case, renormalizability requires us to add a term Lφ3=16Zκκφ3\mathcal{L}_{\varphi^3} = \frac{1}{6}Z_\kappa \kappa \varphi^3, as well as term linear in φ\varphi to cancel tadpoles. Find the one-loop contributions to the renormalizing ZZ factors for this theory in the MS‾\overline{\mathrm{MS}} scheme.

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