K → μ+μ− as a clean probe of short-distance physics
Avital Dery, Mitrajyoti Ghosh, Yuval Grossman, Stefan Schacht
Abstract
A bstract 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 $$ \mid {V}_{ts}{V}_{td}\sin \left(\beta +{\beta}_s\right)\mid \approx \mid {A}^2{\lambda}^5\overline{\eta}\mid $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∣</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>ts</mml:mi></mml:msub><mml:msub><mml:mi>V</mml:mi><mml:mi>td</mml:mi></mml:msub><mml:mo>sin</mml:mo><mml:mfenced><mml:mrow><mml:mi>β</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>∣</mml:mo><mml:mo>≈</mml:mo><mml:mo>∣</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>λ</mml:mi><mml:mn>5</mml:mn></mml:msup><mml:mover><mml:mi>η</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo>∣</mml:mo></mml:math> with hadronic uncertainties below 1%.