Low-energy charged-scalar scattering through a neutral scalar ($\mathcal{M}\simeq 2g^2/m^2$)

For interaction $-g{\phi }^{†}\phi \varphi$ with a real mediator of mass $m$, fixed-charge particle–antiparticle scattering has $s$- and $t$-channel exchange. At $|s|,|t|\ll m^2$, their amplitudes add to $2g^2/m^2$. Distinguishable massless final particles then give $\sigma \simeq g^4/(4\pi m^{4}s)$. There is no extra $u$ channel for the same fixed assignment of final charges.