A sample of 2.8 × 10$^{4}$K$^{+}$ → π$^{+}$μ$^{+}$μ$^{−}$ candidates with negligible background was collected by the NA62 experiment at the CERN SPS in 2017–2018. The model-independent branching fraction is measured to be (9.15 ± 0.08) × 10$^{−8}$, a factor three more precise than previous measurements. The decay form factor is presented as a function of the squared dimuon mass. A measurement of the form factor parameters and their uncertainties is performed using a description based on Chiral Perturbation Theory at $ \mathcal{O} $(p$^{6}$).
Reconstructed $K^+ \to \pi^+ \mu^+ \mu^-$ differential decay width. Only statistical errors are provided. The 4-body differential decay width (shown in green in Figure 3-left) is, in general, required to fit these data points; fitting the squared modulus of the form factor may therefore be preferable.
Reconstructed squared modulus of the $K^+ \to \pi^+ \mu^+ \mu^-$ form factor. Only statistical errors are provided.
A sample of 3120 $K^\pm\to\pi^\pm\mu^+\mu^-$ decay candidates with $(3.3\pm0.7)%$ background contamination has been collected by the NA48/2 experiment at the CERN SPS, allowing a detailed study of the decay properties. The branching ratio was measured to be ${\rm BR}=(9.62\pm0.25)\times 10^{-8}$. The form factor $W(z)$, where $z=(M_{\mu\mu}/M_K)^2$, was parameterized according to several models. In particular, the slope of the linear form factor $W(z)=W_0(1+\delta z)$ was measured to be $\delta=3.11\pm0.57$. Upper limits of $2.9\times 10^{-2}$ and $2.3\times 10^{-2}$ on possible charge asymmetry and forward-backward asymmetry were established at 90% CL. An upper limit ${\rm BR}(K^\pm\to\pi^\mp\mu^\pm\mu^\pm)<1.1\times 10^{-9}$ was established at 90% CL for the rate of the lepton number violating decay.
The $d\Gamma_{\pi\mu\mu}/dz$ spectrum (background subtracted, corrected for trigger efficiency). Systematic errors, notably the external one due to the branching ratios of the normalization decay mode $K^\pm\to 3\pi^\pm$ according to PDG 2010, are not included.
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