K → μ ⁺ μ ⁻ as a clean probe of short-distance physics

The K → μ⁺μ⁻ decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, ℬ(K_S → μ⁺μ⁻)_ℓ=0 can be experimentally determined without the need to separate the ℓ = 0 and ℓ = 1 final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination ∣ V_tsV_tdsin (β+ β_s) ∣ ≈ ∣ A²λ⁵η¯ ∣ with hadronic uncertainties below 1%.