Reconstructed mass for $ K ^0_{\mathrm{ \scriptscriptstyle S}} \rightarrow \pi^+\pi^-$ decays in trigger-unbiased events, computed assuming the muon (dashed red line) or pion (solid blue line) mass for the final-state tracks. Candidates satisfy the selection criteria described in the text.

Fits to the reconstructed kaon mass distributions, for the two most sensitive $\text{BDT}_{\rm cb}$ bins in the two trigger categories, TOS $ _{\mu}$ and TOS $ _{\mu\mu}$ . The fitted model is shown as the solid blue line, while the combinatorial background and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \rightarrow \pi^+\pi^-$ double misidentification are overlaid with dotted red and dashed green lines, respectively. For each fit, the pulls are shown on the lower smaller plots.

Confidence level of exclusion for each value of the $ K ^0_{\mathrm{ \scriptscriptstyle S}} \rightarrow \mu^+\mu^-$ branching fraction. The regions corresponding to $90\%$ and $95\%$ CL are emphasised in green (dark shading) and yellow (light shading), respectively.

Animated gif made out of all figures.

Values of the single candidate sensitivity $\alpha_{ij}$ and the number of candidates $N^{K}_{ij}$ compatible with the $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ mass (reconstructed mass in the range $[492,504] {\mathrm{ Me V /}c^2} $), for each $\text{BDT}_{\rm cb}$ bin $i$ and trigger category $j$. Only statistical uncertainties are given. The first uncertainty is uncorrelated, while the second is fully correlated among the $\text{BDT}_{\rm cb}$ bins of the same trigger category.

Relevant systematic uncertainties on the branching fraction. They are separated, using horizontal lines, into relative uncertainties on (i) $\alpha_{ij}$, (ii) on the signal yield from the signal model used in the mass fit, and (iii) on the branching fraction, obtained combining the two categories, from the background model.