 Charge-two cubic complex-scalar interaction

This interaction preserves the global U(1) symmetry with relative charges $q_{\varphi }=1$, $q_{\Phi }=2$. The two conjugate interaction vertices have Feynman rule $-ig$, with either one charge-two arrow entering and two charge-one arrows leaving, or all arrows reversed. For $\varphi \varphi \to \varphi \varphi$ only the heavy $s$-channel exchange occurs at tree level. For $\varphi \bar{\varphi }\to \varphi \bar{\varphi }$, with outgoing particle labelled 3 and outgoing antiparticle labelled 4, only the heavy $u$-channel exchange occurs. For small momenta and heavy mediator mass, the amplitudes coincide but the identical-particle total scattering cross-section is smaller by the identical final-state symmetry factor $1/2$.