A. Zee, Quantum Field Theory in a Nutshell · Problem III.8.2

Field Theory Redux

Physics — QFT

Problem

Suppose we add a term gφ3g\varphi^3 to our scalar φ4\varphi^4 theory. Show that to order g4g^4 there is a "box diagram" contributing to meson scattering p1+p2→p3+p4p_1 + p_2 \to p_3 + p_4 with the amplitude I=g4∫d4k(2π)41(k2−m2−iε)((k+p2)2−m2−iε)((k−p1)2−m2−iε)((k+p2−p3)2−m2−iε)I = g^4 \int \frac{d^4k}{(2\pi)^4} \frac{1}{(k^2 - m^2 - i\varepsilon)((k + p_2)^2 - m^2 - i\varepsilon)((k - p_1)^2 - m^2 - i\varepsilon)((k + p_2 - p_3)^2 - m^2 - i\varepsilon)}

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