A dedicated sample of Large Hadron Collider proton-proton collision data at centre-of-mass energy $\sqrt{s}=8$ TeV is used to study inclusive single diffractive dissociation, $pp \rightarrow Xp$. The intact final-state proton is reconstructed in the ATLAS ALFA forward spectrometer, while charged particles from the dissociated system $X$ are measured in the central detector components. The fiducial range of the measurement is $-4.0 < \log_{10} \xi < -1.6$ and $0.016 < |t| < 0.43 \ {\rm GeV^2}$, where $\xi$ is the proton fractional energy loss and $t$ is the squared four-momentum transfer. The total cross section integrated across the fiducial range is $1.59 \pm 0.13 \ {\rm mb}$. Cross sections are also measured differentially as functions of $\xi$, $t$, and $\Delta \eta$, a variable that characterises the rapidity gap separating the proton and the system $X$. The data are consistent with an exponential $t$ dependence, ${\rm d} \sigma / {\rm d} t \propto \text{e}^{Bt}$ with slope parameter $B = 7.65 \pm 0.34 \ {\rm GeV^{-2}}$. Interpreted in the framework of triple Regge phenomenology, the $\xi$ dependence leads to a pomeron intercept of $\alpha(0) = 1.07 \pm 0.09$.
The production of two prompt $J/\psi$ mesons, each with transverse momenta $p_{\mathrm{T}}>8.5$ GeV and rapidity $|y| < 2.1$, is studied using a sample of proton-proton collisions at $\sqrt{s} = 8$ TeV, corresponding to an integrated luminosity of 11.4 fb$^{-1}$ collected in 2012 with the ATLAS detector at the LHC. The differential cross-section, assuming unpolarised $J/\psi$ production, is measured as a function of the transverse momentum of the lower-$p_{\mathrm{T}}$ $J/\psi$ meson, di-$J/\psi$ $p_{\mathrm{T}}$ and mass, the difference in rapidity between the two $J/\psi$ mesons, and the azimuthal angle between the two $J/\psi$ mesons. The fraction of prompt pair events due to double parton scattering is determined by studying kinematic correlations between the two $J/\psi$ mesons. The total and double parton scattering cross-sections are compared with predictions. The effective cross-section of double parton scattering is measured to be $\sigma_{\mathrm{eff}} = 6.3 \pm 1.6 \mathrm{(stat)} \pm 1.0 \mathrm{(syst)}$ mb.
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