K → μ + μ − as a clean probe of short-distance physics
Avital Dery (Department of Physics, LEPP, Cornell University, Ithaca, NY, 14853, USA); Mitrajyoti Ghosh (Department of Physics, LEPP, Cornell University, Ithaca, NY, 14853, USA); Yuval Grossman (Department of Physics, LEPP, Cornell University, Ithaca, NY, 14853, USA); Stefan Schacht (Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, U.K.)
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 $$ \mid {V}_{ts}{V}_{td}\sin \left(\beta +{\beta}_s\right)\mid \approx \mid {A}^2{\lambda}^5\overline{\eta}\mid $$ with hadronic uncertainties below 1%.
