Effective field theory approach to lepton number violating decays $K^\pm\rightarrow \pi^\mp l^{\pm}l^{\pm}$: short-distance contribution

Understand

This is the first paper of our systematic efforts on lepton number violating (LNV) hadronic decays in the effective field theory approach.

• These decays provide information complementary to popular nuclear neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay in that they can probe LNV interactions involving heavier quarks and charged leptons.
• We may call them hadronic $0\nu\beta\beta$ decays in short, though $\beta$ refers to all charged leptons.
• In this work we investigate the decays $K^\pm\rightarrow\pi^\mp l^{\pm}l^{\pm}$ that arise from short-distance or contact interactions involving four quark fields and two charged lepton fields, which have canonical dimension nine (dim-9) at leading order in low energy effective field theory (LEFT).