Measurement of diffractive dissociation cross sections in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$

Measurements of diffractive dissociation cross sections in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ are presented in kinematic regions defined by the masses $M_X$ and $M_Y$ 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 ${\xi }_X=M_X^2/s$ in the region $-5.5<{\log }_{10}{\xi }_X<-2.5$, for ${\log }_{10}{M}_Y<0.5$, dominated by single dissociation (SD), and $0.5<{\log }_{10}{M}_Y<1.1$, dominated by double dissociation (DD), where $M_X$ and $M_Y$ are given in GeV. The inclusive $pp$ cross section is also measured as a function of the width of the central pseudorapidity gap $\mathrm{\Delta }\eta$ for $\mathrm{\Delta }\eta >3$, ${\log }_{10}{M}_X>1.1$, and ${\log }_{10}{M}_Y>1.1$, a region dominated by DD. The cross sections integrated over these regions are found to be, respectively, $2.99\pm 0.02{(\text{stat})}_{-0.29}^{+0.32}(\text{syst})\mathrm{mb}$, $1.18\pm 0.02(\text{stat})\pm 0.13(\text{syst})\mathrm{mb}$, and $0.58\pm 0.01{(\text{stat})}_{-0.11}^{+0.13}(\text{syst})\mathrm{mb}$, and are used to extract extrapolated total SD and DD cross sections. In addition, the inclusive differential cross section, $d\sigma /d\mathrm{\Delta }{\eta }^{\mathrm{F}}$, for events with a pseudorapidity gap adjacent to the edge of the detector, is measured over $\mathrm{\Delta }{\eta }^{\mathrm{F}}=8.4$ 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.

Figure 1

Schematic diagrams of (a) nondiffractive, $pp\to X$, and diffractive processes with (b) single dissociation, $pp\to Xp$ or $pp\to pY$, (c) double dissociation, $pp\to XY$, and (d) central diffraction, $pp\to pXp$; $X(Y)$ represents a dissociated proton or a centrally produced hadronic system.

Figure 2

Detector-level distributions of the energy of PF objects in four pseudorapidity intervals: $|{\eta }_{\mathrm{PF}}|<1.4$, $1.4<|{\eta }_{\mathrm{PF}}|<2.6$, $2.6<|{\eta }_{\mathrm{PF}}|<3.2$, and $|{\eta }_{\mathrm{PF}}|>3.2$, corresponding to the barrel, end-cap, end-cap-forward transition, and forward detector regions (columns), for five particle candidate types: charged hadrons (tracks), photons, neutral hadrons, and two types that yield electromagnetic or hadronic energy deposits in HF (rows). Electron and muon candidates constitute less than 0.1% of the PF objects reconstructed in the $|{\eta }_{\mathrm{PF}}|<2.6$ region, and are not shown. The data are compared to the predictions of the pythia 8 MBR simulation, normalized to the integrated luminosity of the data sample. The contribution of each of the generated processes is shown separately.

Figure 3

Event topologies in final-state particle $\eta$ space. Detector level: nondiffractive events (ND), diffractive events with a forward pseudorapidity gap on the positive (FG1) or negative (FG2) $\eta$ side of the detector, or with a central pseudorapidity gap (CG). Generator level: (a) ND, $pp\to X$, (b) SD1, $pp\to Xp$, (d) SD2, $pp\to pY$, and (c, e, f) DD, $pp\to \mathrm{XY}$, events. The empty box represents the central CMS detector ($|\eta |\lesssim 4.7$), filled full boxes indicate final-state hadronic systems or a proton—the vertical thin bar at the right/left end of sketch (b)/(d). The dotted empty boxes in (d) and (e) represent the CASTOR calorimeter ($-6.6<\eta <-5.2$).

Figure 4

Detector-level distributions for the (a) ${\eta }_{\max }$, (b) ${\eta }_{\min }$, and (c) $\mathrm{\Delta }{\eta }^0={\eta }_{\max }^0-{\eta }_{\min }^0$ variables measured in the minimum bias sample (with only statistical errors shown), compared to predictions of the pythia 8 MBR simulation normalized to the integrated luminosity of the data sample. Contributions from each of the MC-generated processes, and simulated events with at least two overlapping interactions of any type (pileup), are shown separately. The dashed vertical lines indicate the boundaries for the ${\eta }_{\max }<1$, ${\eta }_{\min }>-1$, and $\mathrm{\Delta }{\eta }^0>3$ selections.

Figure 5

Simulated distributions of the dissociated mass $M_X$ at stable-particle level for the SD process in the FG2 sample at successive selection stages (trigger, minimal detector activity within BSC acceptance, ${\eta }_{\min }>-1$) for pythia 8 MBR (left) and pythia 8 4C (right). The MC samples are normalized to the luminosity of the data sample.

Figure 6

Simulated (pythia 8 MBR) event selection efficiency in the $M_X$ vs. $M_Y$ plane for true DD events after (a) the trigger selection, and (b) the FG2 selection with a CASTOR tag or (c) the CG selection (Fig. 3). The regions delimited by the solid (red) lines in (b) and (c) are those of the cross section measurements; the dashed (red) box in (b) corresponds to the enlarged region for which the cross section is given (Sec. 9), assuming the same dependence on $M_X$ and $M_Y$; the dashed (blue) line in (c) marks the region of $\mathrm{\Delta }\eta >3$.

Figure 7

Two-dimensional distribution of reconstructed ${\xi }_X^{+}$ vs. generated ${\xi }_X$ values for the events in the SD2 sample obtained with the pythia 8 MBR simulation. The solid red line represents the condition ${\log }_{10}{\xi }_X^{+}={\log }_{10}{\xi }_X$.

Figure 8

Detector-level distributions of the reconstructed and calibrated ${\xi }_X$ for (a) the entire FG2 sample, and the FG2 subsamples with (b) no CASTOR tag, and (c) a CASTOR tag (statistical errors only). The data are compared to the predictions of the pythia 8 MBR (top three plots) and pythia 8 4C (bottom three plots) simulations, which are normalized to the integrated luminosity of the data sample. The contribution of each of the generated processes is shown separately.

Figure 9

Cross sections $d\sigma /d{\log }_{10}{\xi }_X$ for (a,b) ${\log }_{10}{M}_Y<0.5$ (SD dominated) and (c,d) $0.5<{\log }_{10}{M}_Y<1.1$ (DD dominated) compared to MC predictions: (a,c) pythia 8 MBR, pythia 8 4C, pythia 6 Z2*, and (b,d) phojet, qgsjet-ii 03, qgsjet-ii 04, epos. Error bars are dominated by systematic uncertainties (discussed in Sec. 11).

Figure 10

Detector-level distributions of reconstructed and calibrated $\mathrm{\Delta }{\eta }^0$ values for the measured CG sample with a central LRG. The data are compared to predictions of (a) pythia 8 MBR, and (b) pythia 8 4C simulations normalized to the integrated luminosity of the data sample. Contributions for each of the generated processes are shown separately.

Figure 11

The central pseudorapidity-gap cross section $d\sigma /d\mathrm{\Delta }\eta$ (DD dominated) compared to MC predictions: (a) pythia 8 MBR, pythia 8 4C, and pythia 6 Z2*, and (b) phojet, qgsjet-ii 03, qgsjet-ii 04, and epos. Error bars are dominated by systematic uncertainties, which are discussed in Sec. 11.

Figure 12

Diffractive cross sections as a function of collision energy measured in $pp$ and $p\overline{p}$ collisions [3, 31, 32, 33, 34, 35, 39] compared to pythia 8 MBR ($ϵ=0.08$, 0.104) and other model predictions [36, 37, 38]: (a) total SD cross section for $\xi <0.05$, and (b) total DD cross section for $\mathrm{\Delta }\eta >3$. The inner (outer) error bars of the CMS data points correspond to the statistical and systematic (and the additional extrapolation) uncertainties added in quadrature.

Figure 13

Uncorrected $\mathrm{\Delta }{\eta }^{\mathrm{F}}$ distribution compared to various detector-level MC predictions.

Figure 14

Differential cross section $d\sigma /d\mathrm{\Delta }{\eta }^{\mathrm{F}}$ for stable particles with $p_{\mathrm{T}}>200\mathrm{MeV}$ in the region $|\eta |<4.7$ compared to the corresponding predictions of (a) pythia 8 MBR ($ϵ=0.08$), (b) pythia 8 MBR ($ϵ=0.104$), (c) pythia 8 tune 4C, and (d) pythia 6 tune Z2*. The band around the data points represents the total systematic uncertainty, which is discussed in Sec. 11.

Figure 15

Differential cross section $d\sigma /d\mathrm{\Delta }{\eta }^{\mathrm{F}}$ for stable particles with $p_{\mathrm{T}}>200\mathrm{MeV}$ in the region $|\eta |<4.7$ compared to the ATLAS result [4]: distributions (top) and ratio to the CMS measurement (bottom). The band represents the total systematic uncertainty in the CMS measurement, while the uncertainty in the ATLAS measurement is shown by the error bars. The stable-particle level definitions of the two measurements are not exactly identical: CMS measures the forward pseudorapidity gap size starting from $\eta =\pm 4.7$, whereas the ATLAS limit is $\eta =\pm 4.9$.

Figure 16

Generator-level SD cross section as a function of ${\xi }_X=M_X^2/s$ for ${\xi }_X<0.05$, shown for pythia 8 4C, pythia 6 Z2*, phojet, qgsjet-ii 03, qgsjet-ii 04, epos MC, and pythia 8 MBR with the parameters of the Pomeron trajectory changed from the nominal values (${\alpha }^{\prime }=0.25{\mathrm{GeV}}^{-2}$, $ϵ=0.08$) to ${\alpha }^{\prime }=0.125{\mathrm{GeV}}^{-2}$, $ϵ=0.104$, and $ϵ=0.07$ (one parameter changed at a time). The nominal pythia 8 MBR simulation is presented in each plot for the two regions of ${\xi }_X$, $-5.5<{\log }_{10}{\xi }_X<-2.5$ (dashed yellow) and ${\xi }_X<0.05$ (solid khaki), used to extrapolate the measured SD cross section (from the dashed (yellow) to the solid (khaki) regions).

Figure 17

Charged-particle multiplicity ($N_{\mathrm{ch}}$) distributions (area-normalized) in the pythia 8 MBR, pythia 8 4C, pythia 6 Z2*, phojet, qgsjet-ii 03, qgsjet-ii 04, and epos MC simulations (rows) in three bins of $M_X$ (columns) in SD collisions, compared to a reference hadronization model (dashed line), which describes the available data at $\sqrt{s}\le 1800\mathrm{GeV}$ [41, 46].

Figure 18

Transverse-momentum ($p_{\mathrm{T}}$) distributions (area-normalized) in the pythia 8 MBR, pythia 8 4C, pythia 6 Z2*, phojet, qgsjet-ii 03, qgsjet-ii 04, epos MC simulations (rows) in three bins of $M_X$ (columns) in SD collisions, compared to a reference hadronization model (dashed line), which describes the available data at $\sqrt{s}\le 1800\mathrm{GeV}$ [41, 46].