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~$\mathcal{B}(K^{\pm} \to \mu^{\pm} N_{4})\mathcal{B}(N_{4} \to \pi^{\mp}\mu^{\pm})$ 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.