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?

I helped measure the Z-exchange contribution at low energy. For elastic charged-current scattering, the lowest-order contribution is a doubly-weak “box diagram.” — rob, Jun 06 '22 at 15:17

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

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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.

answered Jun 06 '22 at 15:13

CStarAlgebra

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Thanks. What is the centre-of-mass energy for the ep-->ep scattering to remain elastic? Is it much below the mass of $W/Z$? – Solidification Jun 06 '22 at 15:27
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@Solidification Elastic scattering is always part of the phase space. The elastically scattered particles can be isolated based on their kinematics. The first inelastic process is production of pions and/or delta baryons, with excitation energy of order 100 MeV. – rob Jun 06 '22 at 15:33

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?

1 Answers1