Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/iii/paper-305/3/a/i/solution

Allowed through an s-channel W boson. The initial up quark and down antiquark annihilate into a virtual , which produces the final charm quark and strange antiquark. The two weak charged current vertices contain the nonzero CKM matrix elements and , with complex conjugations determined by fermion-flow conventions.
The left panel shows the unique physical-particle tree-level Feynman diagram. A neutral exchanged gauge boson cannot connect these charged annihilation currents, and flavour-diagonal neutral vertices cannot turn an up quark into a charm quark. There is no additional elementary charged scalar in the minimal Standard Model.

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