7.4.3 ‘Contamination’ Factor correction
7.6 Extrapolation to σ inel
The measurement of the inelastic cross-section within theξ cut was an important step and provided a measurement which could be directly compared with the re-sult from ATLAS [122] (60.3 mb ±0.5 (stat.) ± 0.5 (syst.)) However, σinel is the important physical quantity one wishes to derive. To achieve this, Monte Carlo models must again be employed to extrapolate over the invisible region where the CMS detector was unable to measure†.
Additional Monte Carlo models were used for the extrapolation from the restricted ξrange to the total inelastic cross section. As the models were not able to be com-bined with the full CMS detector simulation, the extrapolation was made by using the models at the generator level to determine theirξdistribution and acceptance.
This has already been shown in table 7.8 to be an acceptable compromise as the differences between the full simulation and generator level efficiencies were within 2%.
Six additional models were considered: pythia 8[105],phojet[102], sibyll 2.1 [124], epos 1.99, epos lhc [125], and qgsjet-II 4 [103, 126]. The models use various phenomenology and tunings for the hard parton-parton and for the diffractive scattering cross sections [127], and can be considered to be aimed at modelling either collider physics processes (Pythia, Phojet) or high-energy cos-mic ray interactions (sibyll, qgsJetII).epos claims to be capable of modelling
†The TOTEM and CASTOR detectors are located at higherη than the HF. However, ac-quiring their data in the CMS framework was not possible.
Inelastic Cross Section 131 both scenarios.
The diffractive mass distribution in epos 1.99 was known to be too large. This has been corrected in epos lhc [114]. qgsjet-II 4 has been shown to predict the data from TOTEM quite closely[128]. pythia 8 is one of the recommended generators for LHC physics. The other generators have not been tuned to data at LHC energies but have been included in order to provide a broad sample of varying models. Figure 7.3 shows the predictions of the visible cross section from the six Monte Carlo generators employed in this analysis. Also shown are the measurement results and model predictions of those results, from the CMS paper fwd-11-001 [119], in which the inner tracker (|η|<2.4) was used to count tracks with pT >200 MeV/c, shown as the red squares.
The predicted results of this analysis are shown as the left-most points (upper plot) and were calculated by counting generated events over theξand energy cuts. The same correction factors as used in reaching the measured σξ>5×10−6 result were calculated from each of the generators and applied in the same way. The remain-ing points are taken from fwd-11-001. The lower plot shows each Monte Carlo predicted value normalized to the relative measurement value. As clearly shown, epos lhc (blue crosses) gives the closest predictions to the CMS data. For this reason, epos lhchas been chosen as the primary model in this analysis.
In section 7.4, aξ cut was applied to the data to reduce the effects of the variations seen between the Monte Carlo models. The equation used for calculating the ξ value was: In the alternative CMS measurement of the pp inelastic cross-section ( fwd-11-001), the calculation ofξ was made by equation 7.17.
ξ= (ΣE+ Σpz)
√s (7.17)
In order to be sure one can compare the MC predictions and results of fwd-11-001and the MC predictions and result of the current analysis, bothξ calculations were made and compared for equivalency. The ξ distributions of inelastic events
0 1 2 3 4 5 6
Figure 7.3: (Top) Monte Carlo model predictions of the σ(ξ>5×10−6) measure-ment in this analysis and the track counting analysis detailed in fwd-11-001 [119]. (Bottom) Each Monte Carlo prediction normalised to its repective
mea-surement result.
Inelastic Cross Section 133 from the generator level calculations are shown in figures 7.5 - 7.6. An example of the direct comparison of the results from the two ξ methods is shown in fig-ure 7.4. The two distributions agree very closely with only a small deviation at very low masses (ξ <6). The comparisons for all models are shown in Appendix C.
0
Figure 7.4: An example from epos lhc of the conformity between the two possible ξ calculations. The choice of calculation has a 0.1% effect on the
outcome of the extrapolation prediction of each model.
The detection efficiency to inelastic events (εinel), the efficiency to detecting events above theξcuts (εξ) and the fraction of selected events below threshold, (fξ), were calculated from each model and together, provided six extrapolation factors which are shown in table 7.10.
Extrapolation Factor=ξ/(1 − fξ)inel
The extrapolated cross-sections from each model are also shown in table 7.10. Di-viding the σineltotal cross-section of each model by the extrapolation factor gives the σ(ξ>5×10−6) value as predicted by the models. Figure 7.7 shows these values with the σ(ξ>5×10−6) measurement made in this analysis (red dot).
ξ
(a) epos 1.99 Calculation based on Eq. 7.15.
ξ
(b)epos 1.99 Calculation based on Eq. 7.17.
-10 -8 -6 -4 -2 0 ξ
(c)epos LHC Calculation based on Eq. 7.15.
-10 -8 -6 -4 -2 0 ξ
(d) epos LHC Calculation based on Eq. 7.17.
ξ
(e)Qgsjetii-4 Calculation based on Eq. 7.15.
ξ
(f)Qgsjetii-4 Calculation based on Eq. 7.17.
Figure 7.5: Generator level ξ distributions of inelastic events in the different models used for extrapolation.
Table 7.10: Efficiency and ‘contamination’ correction factors and the extrap-olation factor derived from each Monte Carlo generator. The differences in the results from ξ calculation of FWD-11-001 (Eq. 7.15) and from Eq. 7.17 are negligible (0.1%). Numbers are calculated from 200,000 events from each MC
generator.
Model σtotalinel [mb] εinel±0.2% εξ±0.2% f ±0.2% extr. factor σinelextr.[mb]
EPOS 67.9 0.955 0.995 0.0052 1.047 63.0
EPOS LHC 71.32 0.897 0.988 0.027 1.131 68.1
Phojet 77.52 0.972 0.996 0.009 1.035 62.3
Pythia 8 71.5 0.929 0.991 0.019 1.087 65.4
QGSJetII-04 73.11 0.904 0.992 0.021 1.121 67.5
Sibyll 79.61 0.959 0.998 0.012 1.054 63.5
Inelastic Cross Section 135
(a) Phojet Calculation based on Eq. 7.15.
ξ
(b) Phojet Calculation based on Eq. 7.17.
-10 -8 -6 -4 -2 0 ξ
(c)Pythia Calculation based on Eq. 7.15.
-10 -8 -6 -4 -2 0 ξ
(d) Pythia Calculation based on Eq. 7.17.
ξ
(e)Sibyll Calculation based on Eq. 7.15.
ξ
(f) Sibyll Calculation based on Eq. 7.17.
Figure 7.6: Generator level ξ distributions of inelastic events in the different models used for extrapolation (continued).
0 2 4 6 8 10
[mb]σ
50 55 60 65 70 75 80 85
90 SYBILL 2.1 PHOJET
QGSJET II 4 EPOS LHC
EPOS 1.99 PYTHIA 8
CMS - Trk Based CMS - HF Based
Ext. Result σinel
-6)
>5x10 ξ
CMS( N>2 N>3 N>4
Figure 7.7: Comparison between the Monte Carlo model predictions of theσξ and σ(N tracks) measurements done in this analysis and fwd-11-001. The left-most points show the extrapolation from each model based on the σ(ξ>5×10−6) measurement of 60.2 mb. Note that the values fromfwd-11-001have not been
recalculated in this analysis.
Inelastic Cross Section 137 The primary model of epos lhc gives and extrapolation factor of 1.131 and an extrapolated cross section result of 68.1 mb±0.5 mb (stat). When combined with the systematic uncertainties of the restricted cross section measurement and the 4% uncertainty in the luminosity, one obtains the inelastic ppcross section result, based on theepos lhc generator:
σinel = 68.1mb±0.5mb(stat.)±2.4mb(syst.)±2.7 mb(lumi)