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See paper for full list of authors ; The pt-differential production cross sections of the prompt (B feed-down subtracted) charmed mesons D0, D+, and D*+ in the rapidity range |y|<0.5, and for transverse momentum 1< pt 12 GeV/c, were measured in proton-proton collisions at sqrt(s) = 2.76 TeV with the ALICE detector at the Large Hadron Collider. The analysis exploited the hadronic decays D0 -> K pi, D+ -> K pi pi, D*+ -> D0 pi, and their charge conjugates, and was performed on a L_{int} = 1.35 nb^{-1} event sample collected in 2011 with a minimum-bias trigger. The total charm production cross section at sqrt(s) = 2.76 TeV and at 7 TeV was evaluated by extrapolating to the full phase space the pt-differential production cross sections at sqrt(s) = 2.76 TeV and our previous measurements at sqrt(s) = 7 TeV. The results were compared to existing measurements and to perturbative-QCD calculations. The fraction of cubar D mesons produced in a vector state was also determined.
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