Searches for Lepton Number Violation and resonances in the $K^{\pm }\to \pi \mu \mu$ decays at the NA48/2 experiment

The NA48/2 experiment at CERN collected a large sample of charged kaon decays into final states with multiple charged particles in 2003–2004. A new upper limit on the rate of the lepton number violating decay $K^{\pm }\to {\pi }^{\mp }{\mu }^{\pm }{\mu }^{\pm }$ obtained from this sample is reported: $\mathcal{B}(K^{\pm }\to {\pi }^{\mp }{\mu }^{\pm }{\mu }^{\pm })<8.6\times {10}^{-11}$ at 90% CL. Searches for two-body resonances in the $K^{\pm }\to \pi \mu \mu$ decays (including heavy neutral leptons~$N_4$ and inflatons~$\chi$) in the accessible range of masses and lifetimes are also presented. In the absence of a signal, upper limits are set on the products of branching ratios~$\mathcal{B}(K^{\pm }\to {\mu }^{\pm }{N}_4)\mathcal{B}(N_4\to \pi \mu )$ and $\mathcal{B}(K^{\pm }\to {\pi }^{\pm }\chi )\mathcal{B}(\chi \to {\mu }^{+}{\mu }^{-})$ as functions of the resonance mass and lifetime. These limits are in the ${10}^{-10}-{10}^{-9}$ range for resonance lifetimes below 100~ps.