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The NA48/2 experiment at CERN collected a large sample of charged kaon decaysto final states with multiple charged particles in 2003--2004. A new upperlimit on the rate of the lepton number violating decay$K^{\pm}\to\pi^{\mp}\mu^{\pm}\mu^{\pm}$ 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 $X$ in $K^{\pm}\to\pi\mu\mu$ decays (suchas heavy neutral leptons $N_4$ and inflatons $\chi$) are also presented. In theabsence of signals, upper limits are set on the products of branching fractions$\mathcal{B}(K^{\pm}\to\mu^{\pm}N_4)\mathcal{B}(N_4\to\pi\mu)$ and$\mathcal{B}(K^{\pm}\to\pi^{\pm}X)\mathcal{B}(X\to\mu^+\mu^-)$ for ranges ofassumed resonance masses and lifetimes. The limits are in the$(10^{-11},10^{-9})$ range for resonance lifetimes below 100 ps.

Searches for Lepton Number Violation and Resonances in $K^{\pm}\to\pi\mu\mu$ Decays