A search for associated production of a $Z$ boson with an open charm meson is presented using a data sample, corresponding to an integrated luminosity of $1.0,mathrm{fb}^{-`}$ of proton--proton collisions at a centre-of-mass energy of 7,TeV, collected by the LHCb experiment. %% Seven candidate events for associated production of a $Z$ boson with a $D^0$ meson and four candidate events for a $Z$ boson with a $D^+$ meson are observed with a combined significance of 5.1standard deviations. The production cross-sections in the forward region are measured to be $$sigma_{Zrightarrowmu^+mu^-!,D^0} = 2.50pm1.12pm0.22pb$$ $$sigma_{Zrightarrowmu^+mu^-!,D^+} = 0.44pm0.23pm0.03pb,$$ where the first uncertainty is statistical and the second systematic.
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