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A search is performed for rare and forbidden charm decays of the form$D_{(s)}^+ \to h^\pm \ell^+ \ell^{(\prime)\mp}$, where $h^\pm$ is a pion orkaon and $\ell^{(')\pm}$ is an electron or muon. The measurements are performedusing proton-proton collision data, corresponding to an integrated luminosityof $1.6\text{fb}^{-1}$, collected by the LHCb experiment in 2016. No evidenceis observed for the 25 decay modes that are investigated and $90\%$ confidencelevel limits on the branching fractions are set between $1.4\times10^{-8}$ and$6.4\times10^{-6}$. In most cases, these results represent an improvement onexisting limits by one to two orders of magnitude.

Searches for 25 rare and forbidden decays of $D^+$ and $D_s^+$ mesons