The analysis outlined in this chapter is complementary to the measurement of the visible part of the inelastic cross section based on pile-up counting [119] as the acceptance of the two analyses is very different. In each analysis, there are possible events which can escape detection. Most single and double diffractive events are detected by the HF calorimeter but fail to hit the pixel tracker region. Similarly, central exclusive events, pp→ppX in which the two protons exit the detector in the very forward direction and the system X interacts with the pixel tracker but not with the forward calorimeters, as shown in figure 7.10.
Figure 7.10: When counting events, the topology of those events can lead to counting inefficiencies. (Left) In the case of low pT diffractive events, only the forward detectors register a hit. (Right) In central exclusive events, the incident protons remain intact, losing a small fraction of their longitudinal momentum.
A central system is produced and detected by the CMS tracker (shown as the parallel lines). Because the outgoing protons remain close to the beam pipe, the
forward calorimeters do not see such events.
The extrapolations of these two analyses to the value of the total inelastic cross section differs both numerically and in the nature of events. The recent measure-ment of the total, elastic and inelastic cross section by the TOTEM collaboration [130] and the results presented here may indicate that the invisible part of the inelastic cross section is underestimated by a wide range of models. However, im-provements to epos lhc and qgsjetII-4 which place more emphasis on central diffractive events, show substantial improvements in their dNdξ evolution, compared to their predecessors.
7.9 Conclusions
A measurement of the inelastic cross section for pp collisions at √
s = 7 TeV has been made with CMS using the Hadronic Forward Calorimeters (HF). The inelastic
events were counted requiring the detection of one particle above the 4 GeV or 5 GeV energy threshold in at least one side of the HF. The efficiencies for inelastic events using this counting mode were estimated by Monte Carlo simulations using pythia 6(D6T tune),pythia 8andphojet. To mitigate the model dependence, a selection ofξ >5×10−6 was used in determining the detection efficiency values.
This value was specifically chosen to give a visible inelastic cross-section result which would be directly comparable to that of the ATLAS collaboration.
Over 9.2 million events were processed in the dataset with low pile-up data, corre-sponding to an integrated effective luminosity of 2.76µb−1. Data from runs with pile-up ranging from∼7% to∼12% were processed with the corresponding pile-up correction factors applied.
The value of the ppcross section was calculated as the result of the analysis using the selection ξ > 5×10−6 and a 5 GeV HF energy threshold. An extrapolation was carried out to determine the total inelastic cross section using additional gen-erator level Monte Carlo models. The final results are in good agreement with the results independently obtained recently by CMS (via event pileup counting) [119]
and ATLAS [122], and follow the ln2(s) increasing trend established by previous measurements at lower energies.
The results presented here improve upon those of the original paper qcd-11-001 by the use of updated Monte Carlo generators, particularly epos lhc and qgsjetII-4. As most models over-estimated the number of events detected in the forward calorimeters above the ξ cut, it is possible that Centrally Diffractive events play a more important role in the total cross section at higher √
s. This is predicted in theory [131] but not accounted for in most of the MC models. This would result in a greater number of MC events with particle trajectories in the central, tracker region. Alternatively, if the Monte Carlo modelled Mx distribu-tions err towards larger masses, the result would be a greater number of simulated events passing the ξ cut, as well as the pT cut in the analysis of fwd-11-001. Figure 7.11 shows the η distribution of the number of particles per event. One can see that the models with a tendancy to scatter at higher η (stemming from smaller producedMx particles) have a better agreement with the measurement of σ(ξ<5×10−6), shown in 7.7.
Inelastic Cross Section 145
Figure 7.11: The η distribution of single diffractive events from each of the Monte Carlo models used in the analysis. The models with the more forward (higherη trends have a closer agreement with the restricted cross section
mea-surement.
The recently modified epos lhc model gives excellent results for the prediction in the central region analysis of fwd-11-001 and gives the best agreement with the current analysis. The modifications to the diffractive mass distributions of epos lhc resulted in lower mass, more forward going partons, compared to the other models. It is hoped that the combination of this analysis with that of fwd-11-001 and TOTEM will provide an important tool for tuning the topologies, event fractions and mass distributions of soft hadronic collisions in Monte Carlo models. Although, currently this does not provide a true theoretical understanding of the phenomonolgy unpinning such events, Monte Carlo models which are able to predict the evolution of hadronic cross sections with increased collision energy will be vital in designing detector upgrades to LHC experiments and future, higher energy colliders.