 Solution

ID: past-exam-of-the-particle-physics-course-of-the-university-of-oxford/2018/3/c/solution

Starting with an antikaon instead gives

\overset{ˉ}{A}_{f} (t) = \overset{ˉ}{A}_{f} g_{+} + \frac{p}{q} A_{f} g_{-} = \overset{ˉ}{A}_{f} [g_{+} + λ^{- 1} g_{-}] .

Thus

Γ (\overset{ˉ}{K} (t) \to f) = ∣ \overset{ˉ}{A}_{f} ∣^{2} [∣ g_{+} ∣^{2} + ∣ λ^{- 1} ∣^{2} ∣ g_{-} ∣^{2} + 2 Re (λ^{- 1} g_{-} g_{+}^{*})] .

This factored form assumes

A_{f}, \overset{ˉ}{A}_{f} \neq = 0

; otherwise use the preceding probability amplitude. The three mechanisms are separated below. Comparisons for distinct final states must pair

f

with its CP conjugate

\overset{ˉ}{f}

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