Distributions of the three-body invariant mass for the $ D ^+_{(s)} \rightarrow \left(\phi \rightarrow \ell^-\ell^+ \right)$ $\pi ^+$ candidates used for normalisation and calibration. The final states are specified in the mass label. The $ D ^+$ ( $ D ^+_ s $ ) signal component is shown as a dashed orange (green) line, peaking backgrounds are denoted by the solid (hashed) regions and the non-peaking background is denoted by the blue dotted line.

Distributions of the three-body invariant mass in the signal regions for decays with two muons. The final states are specified in the mass label. The left (right) fit with the signal-plus-background (background-only) hypothesis is overlaid with the peaking backgrounds denoted by dashed lines and the non-peaking background is denoted by the blue dotted line.

Distributions of the three-body invariant mass in the signal regions for decays with two electrons. The final states are specified in the mass label. The left (right) fit with the signal-plus-background (background-only) hypothesis is overlaid with the peaking backgrounds denoted by dashed lines and the non-peaking background is denoted by the blue dotted line.

Distributions of the three-body invariant mass in the signal regions for decays with an oppositely charged electron and muon. The final states are specified in the mass label. The left (right) fit with the signal-plus-background (background-only) hypothesis is overlaid with the peaking backgrounds denoted by dashed lines and the non-peaking background is denoted by the blue dotted line.

Distributions of the three-body invariant mass in the signal regions for decays with an electron and a muon with matching charge. The final states are specified in the mass label. The left (right) fit with the signal-plus-background (background-only) hypothesis is overlaid with the peaking backgrounds denoted by dashed lines and the non-peaking background is denoted by the blue dotted line.

Upper limits at \SI{90}{\percent} confidence level on the $ D ^+_{(s)}$ signal channels. The median (orange), $\pm1\sigma$ and $\pm2\sigma$ expected limits are shown as box plots and the observed limit is given by a black cross. The green line shows the previous world's best limit for each channel where the solid, dotted and dashed lines correspond to BaBar, CLEO and LHCb \cite{Lees:2011hb,Rubin:2010cq,LHCB-PAPER-2012-051}.

Animated gif made out of all figures.

Reference branching fractions ($\mathcal{B}$) used for the resonant channels alongside signal yields.

Summary of systematic uncertainties for each signal decay. The " $\phi \rightarrow \mu ^- \mu ^+ $ yield" column represents the combination of the statistical uncertainty from the $ D ^+_{(s)} \rightarrow \left(\phi \rightarrow \mu ^- \mu ^+ \right)$ $\pi ^+$ dataset with the systematic uncertainty from the modelling of the $ D ^+_{(s)} \rightarrow \pi ^+ \pi ^+ \pi ^- $ backgrounds. A further \SI{7.6}{\percent} uncertainty from the branching fraction of $ D ^+_{(s)} \rightarrow \left(\phi \rightarrow \mu ^- \mu ^+ \right)$ $\pi ^+$ and a \SI{1.0}{\percent} uncertainty from the finite size of the simulated $ D ^+_{(s)} \rightarrow \left(\phi \rightarrow \mu ^- \mu ^+ \right)$ $\pi ^+$ sample apply to all channels. The electron efficiency correction, described at the end of Section ???, is denoted by $\epsilon_{\text{electron}}$. All values are given in percent as a fractional uncertainty on the signal yield.

The single event sensitivities (SES), and upper limits on the branching fractions obtained using the CL$_s$ method, for each signal decay channel.