Measurements of diffractive dissociation cross sections in pp collisions at $\sqrt{s}=7$ TeV are presented in kinematic regions defined by the masses $M_{\mathrm{X}}$ and $M_{\mathrm{Y}}$ of the two final-state hadronic systems separated by the largest rapidity gap in the event. Differential cross sections are measured as a function of $\xi_{\mathrm{X}}= M^2_{\mathrm{X}}/s$ in the region $-5.5<\log_{10}\xi_{\mathrm{X}}<-2.5$, for $\log_{10}M_{\mathrm{Y}}<0.5$, dominated by single dissociation (SD), and $0.5<\log_{10}M_{\mathrm{Y}}<1.1$, dominated by double dissociation (DD), where $M_{\mathrm{X}}$ and $M_{\mathrm{Y}}$ are given in GeV. The inclusive pp cross section is also measured as a function of the width of the central pseudorapidity gap $\Delta\eta$ for $\Delta\eta>3$, $\log_{10}M_{\mathrm{X}}>1.1$, and $\log_{10}M_{\mathrm{Y}}>1.1$, a region dominated by DD. The cross sections integrated over these regions are used to extract the total SD and DD cross sections. In addition, the inclusive differential cross section, $\mathrm{d}\sigma / \mathrm{d}\Delta\eta^\mathrm{F}$, for events with a pseudorapidity gap adjacent to the edge of the detector, is measured over $\Delta\eta^\mathrm{F}$ = 8.4 units of pseudorapidity. The results are compared to those of other experiments and to theoretical predictions, and found compatible with slowly-rising diffractive cross sections as a function of center-of-mass energy.
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