Is the amplitude of electron-proton elastic scattering via a $W^\pm$ or Z-boson exchange negligible compared to the one via a virtual photon exchange?

Question

Particle physics book by Halzen and Martin talks about electron-proton elastic scattering via the exchange of a virtual photon. But the same process is also allowed via the exchange of a virtual $W^\pm$ or Z-boson which is not considered in the book. Does one expect that the amplitude of the $ep\to ep$ elastic scattering via $W^\pm$ or Z-boson exchange will be much smaller than that via a virtual photon exchange? If so, can we understand it simply?

score 2 · Answer 1 · answered Jun 06 '22 at 15:13

The amplitude for electron proton scattering via the exchange of a W or Z is suppressed by the mass of the W/Z bosons $\mathcal{A} \approx 1/M_{\rm{w}}^{4}$, I'm obviously omitting dimensional factors and such, but it is not until the center of mass energies that you are scattering at reach near the mass of the W/Z that these contributions become important.

Is the amplitude of electron-proton elastic scattering via a $W^\pm$ or Z-boson exchange negligible compared to the one via a virtual photon exchange?

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