Measurement of the Cross-Section

The method of counting inelastic events in the HF calorimeters involved searching the data, event-by-event, for those in which an energy deposit above the energy threshold occurred. The HF data is read out in a ‘bundle’ called a recHit. These recHit contain the energy information as well as course position information in terms of η and φ. The entire data from each of the chosen runs were processed using each of the three aforementioned triggers. Only events which passed the

energy cut were counted. Table 7.2 shows the number of events counted using each of the three triggers. The number of triggers demonstrates the differences in trigger pre-scaling.

Table 7.2: The number of events in the data (all runs) selected with each of the three triggers described.

Trigger No. of Triggers 4 GeV 5 GeV Coincidence 9244011 239782 191654 Single Bunch 1097292 8883 3291

Random 27759 254 89

To account for the pre-scaling, the number of counted events from the Single Bunch and Random triggers were scaled to the number of Coincidence triggers. Table 7.3 shows these normalised number of events for each trigger.

The events that pass the Single Bunch or Random triggers as well as the HF energy threshold, have their origin in beam background and detector noise respectively.

There may also be beam background and noise present in the data collected using the Coincidence trigger. There are two beams present in the Coincidence triggered data and only one beam present in the Single Bunch triggered data. Assuming both beams to be equal, one would need to double the beam background contribu-tion found in the Single Bunch triggered sample to estimate the beam background noise that is merged with the collision data in the Coincidence sample. Table 7.3 shows that the number of normalised events from the Random trigger, which selects detector noise, is approximately equal to the number of events from the Single Bunch trigger, suggesting that the majority of background contamination in the Coincidence triggered sample originates from detector noise, rather than from beam related effects. To test this hypothesis, the activity in the inner tracker,

Table 7.3: The number of events in the data (all runs) selected with each of the three triggers described. The Single Bunch and Random values have been normalised to the number of Coincidence triggers. Statistical uncertainties

(√

N) are shown.

Trigger No. of Triggers 4 GeV 5 GeV

Coincidence 9244011 239782±490 191654±438 Single Bunch 9244011 74834 ±794 27725±483

Random 9244011 84584 ±5307 29638±3141

Inelastic Cross Section 121 during events selected with the Single Bunch trigger, was inspected. Any beam background travelling approximately parallel to the beam pipe would leave long tracks in the inner tracker. As none were found, it was concluded that the vast majority of the contribution to the background events was due to detector noise in the HF detector, which is expected to be constant, irrespective of beam presence.

Therefore, beam gas contributions were neglected and all events selected by the Single Bunch trigger were treated as being due to detector noise, thus providing a larger ‘detector noise’ dataset as well as eliminating the need to double their contribution.

The HF towers were studied individually to ensure that they all detected events at rates similar to the nearest neighbouring towers and that no one tower was over or under represented due to poorly calibrated pedestal levels. A few specific towers were found in which the number of reconstructed recHit over the energy threshold were much larger than the global average, even without beam presence. Further investigations with the HF group resulted in the conclusion that the pedestal set-tings for several towers had drifted and the worst towers should be excluded from the event counting [123]. The number of events was counted with the noisy towers included and excluded. The exclusion caused a 0.4% difference in the result, which is included in the final systematic uncertainty.

7.4.1 HF Detector Efficiency

The HF calorimeters cover a pseudo-rapidity range of 2.9< |η| <5.2 and have a minimum energy threshold of 4 GeV. Due to these limitations, not all inelastic events can be detected. In particular, many low mass (M_x ≈ M_proton) events will pass through the HF calorimeter at |η| >5.2. In addition, there was some doubt about the calibration and performance of the inner most η ring of the detector during the early operations when the data for this analysis was recorded.

Therefore, only the rings covering the η range of 2.9< |η| <4.9 were used. To get an estimate of the efficiency of detecting inelastic events, Monte Carlo models were used in conjunction with the full CMS detector simulation. The detector simulation is provided by GEANT 4 and contains an accurate geometry and tuned readout simulation of the entire CMS detector. At the time of this analysis, the Monte Carlo generators of pythia 6, pythia 8 and phojet were officially

integrated with the CMS full simulation. Figure 7.1 shows the M_x distributions from the three models. The left hand figures show the generated distributions (white) with the distributions of events detected in the HF calorimeters which are over 4 GeV (light blue patterned area) and 5 GeV (plain red shaded area). The region corresponding the ξ cut is shown as the dark shaded area and excludes the regions in the models which disagree the most. The right hand figures show the efficiencies of each energy cut along the ξ distribution.

= 7TeV

Figure 7.1: Left: Generated ξ distributions for inelastic events according to pythia 6(top),pythia 8(center),phojet(bottom), normalised to unity over the full ξ range. Events that fulfil the 4 and 5 GeV energy requirements in the HF calorimeters, using the CMS detector simulation, are represented by the coloured histograms. Right: Efficiency of the event selection, for the two thresholds of the energy deposited in the HF calorimeters. The ξ threshold at

5×10⁻⁶ is also shown.

Inelastic Cross Section 123 Table 7.4 lists the HF detector efficiencies of detecting inelastic events, estimated from each of the three Monte Carlo simulations.

Table 7.4: The ε_inel efficiency values estimated from the three full simulation models.

Energy cut pythia 6 pythia 8 phojet E>4 GeV 94.0% 94.2% 97.3%

E>5 GeV 93.8% 94.1% 97.2%

7.4.2 Detection Efficiency over the ξ cut

Table 7.4 demonstrates the differences ofε_inelbetween the three models. To reduce the dependency of the result on the variation in the models, the analysis focuses on the region in which they mostly agree. Referring to figure 7.1, a cut on log₁₀(ξ) needed to be chosen. In their analysis of the inelastic cross-section, the ATLAS collaboration had selected a ξ cut of 5×10⁻⁶ (Mx > 15.6 GeV), so the same cut was used in this analysis to give a directly comparable result.

The calculation of the efficiency of detecting events over theξ cut follows the same principle as the ε_inel estimation. The difference is that now, only the number of events over the HF energy cut and with a ξ > 5×10⁻⁶ are counted and divided by the total number of generated events above the ξ cut. Table 7.5 lists the efficiencies, εξ, for the restricted kinematic range using the pythia 6, pythia 8 and phojet models.

Table 7.5: The ε_ξ efficiency values estimated from the three full simulation models.

Energy cut pythia 6 pythia 8 phojet E>4 GeV 98.7% 99.7% 99.4%

E>5 GeV 97.5% 99.3% 99.1%

One can see that the differences in detection efficiency have been reduced, com-pared to those in table 7.4. These efficiencies are used to calculate σ_ξ>5×10⁻⁶.