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

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 or kaon and $ell^{()pm}$ is an electron or muon. The measurements are performed using proton-proton collision data, corresponding to an integrated luminosity of $1.6text{fb}^{-1}$, collected by the LHCb experiment in 2016. No evidence is observed for the 25 decay modes that are investigated and $90%$ confidence level limits on the branching fractions are set between $1.4times10^{-8}$ and $6.4times10^{-6}$. In most cases, these results represent an improvement on existing limits by one to two orders of magnitude.