Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-305/1/i/solution

The range of a force is controlled by the lightest state that can carry it. Exchange of a particle of mass produces a Yukawa potential proportional to , with range . The electromagnetic interaction is long range because its carrier, the photon, is massless. The weak interaction is short range because the W bosons and Z boson are massive. Although the gluons of the strong interaction are massless in the Lagrangian, Quantum chromodynamics confines color and has a mass gap; only color-singlet hadrons propagate over macroscopic distances. The residual nuclear force is consequently controlled at long distance by massive pion exchange.

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