We report a search for the doubly charmed baryon $Xi_{cc}^{+}$ through the decay $Xi_{cc}^{+} to Lambda_{c}^{+} K^{-} pi^{+}$, using a data sample corresponding to an integrated luminosity of $0.65~mathrm{pb^{-1}}$ of $pp$ collisions at $mathrm{sqrt{s}} = 7~mathrm{TeV}$. In the mass range 3300-3800$~mathrm{MeV}/c^{2}$ no significant signal is observed. Upper limits at $95%$ confidence level are set on $R$, the ratio of the production cross section of the $Xi_{cc}^{+}$ times the relevant branching fraction over the $Lambda_{c}^{+}$ cross section, as a function of the $Xi_{cc}^{+}$ mass and lifetime. The largest upper limits on $R$ over the investigated mass range are $R<1.5times10^{-2}$ for a lifetime of $100~mathrm{fs}$ and $R<3.9times10^{-4}$ for a lifetime of $400~mathrm{fs}$.
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