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)⁺→h^±ℓ⁺ℓ(′)^∓, where h^± is a pion or kaon and ℓ^(′)± is an electron or muon. The measurements are performed using proton-proton collision data, corresponding to an integrated luminosity of 1.6 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 1.4 × 10⁻⁸ and 6.4 × 10⁻⁶. In most cases, these results represent an improvement on existing limits by one to two orders of magnitude.