Analysis at Detector Level

Abstract

In this chapter, the analysis is described at the level of the detector, i.e. without correcting the measurement from the artefacts of the detector. The selection is discussed, as well as several calibrations and their associated systematic uncertainties. At the end of this chapter, a global picture of the content of the sample at detector level is drawn.

Appendices

7.A Missing Transverse Energy

The missing transverse momentum corresponds to the momentum vector imbalance in the perpendicular plane (xy) to the beam axis (z):

$$\begin{aligned} \mathbf {p}_T^\text {miss} = - \sum _\text {jets} \mathbf {p}_T^\text {jet} \end{aligned}$$

(7.26)

The Missing Transverse Energy (MET) is the magnitude of the missing transverse momentum:

$$\begin{aligned} E_T^\text {miss} = |\mathbf {p}_T^\text {miss}| \end{aligned}$$

(7.27)

Some physics processes or detector effects may cause it to be significant. In this section, we check these effects in the inclusive jet and inclusive b-tagged jet reconstructed spectra, first at generator level, then at detector level.

1.1 7.A.1 Detector Studies

General effects have already been studied in the inclusive jet measurements at CMS at 7 and 8$\,{\text {TeV}}$ [19, 20]. In the CMS publication at 8$\,{\text {TeV}}$ [21], a cut-off on the fraction of MET is applied in order to reduce the contribution from event suffering from significant detector effects with the least effect on physics processes. However, such a cut-off is not applied in the inclusive-jet analysis at 13$\,{\text {TeV}}$with 2015 data [22], nor in the inclusive-b-jet analysis at 7$\,{\text {TeV}}$ [23]. The cut-off is very much dependent on the condition of data taking and needs to be checked on a case-by-base basis.

1.1.1 7.A.1.1 MET Variables

We first check three variables:

• the MET itself,

• the fraction of MET with respect to the total transverse energy;

• and the azimuthal angle of the MET.

The ratio of MC samples with data is shown in Fig. 7.18. Three series of curves, corresponding to the three rows, are investigated:

• 1. the three usual MC samples,

• 2. the inclusive and tagged samples in Pythia  8,

• 3. and the inclusive sample in Pythia  8 with different cut-offs on the fraction of MET (0.2, 0.3, 0.4).

In the first row, Herwig++ shows a slightly different behaviour while Pythia  8 and Madgraph are very similar, which is most likely related to the respective simulations of the detector (as we said in Sect. 7.2, the simulation of the CMS detector is older for Herwig++ ). The dependence on the azimuthal angle of the MET shows a phase, which is likely due to the simulation of the position of the interaction point; since the final measurement does not depend on the azimuthal angle, this phase is not relevant. The second row shows that the tagging behaves similarly for data and MC, therefore the same agreement is seen. Finally, the different cut-offs act the same way for data and MC. The conclusion is that in general, the MET is well simulated in MC, since the agreement with data does not change.

Fig. 7.18

Ratios of MC with data for MET, fraction of MET and azimuthal direction of MET are shown (in the columns) for different scenarios (rows)

1.1.2 7.A.1.2 Spectrum of Reconstructed Transverse Momentum

The effect of the cut-off on the fraction of MET for the inclusive jet and inclusive b-tagged jet sample is shown in Figs. 7.19 and 7.20. In general, an effect starts being visible, though very small, above $1.5\,{\text {TeV}}$. Since the final measurement will be limited to the region where the calibration of b-tagging discrimination is available, it turns out that the cut-off does not seem relevant for this analysis. However, the effect of the cut-off on different physics processes still needs to be checked.

Fig. 7.19

The ratios of different samples after and before applying the different values of cut-off on the MET fraction are shown for MC and data. For the inclusive jet selection, an effect may be seen starting from $1.5\,{\text {TeV}}$

Fig. 7.20

The ratios of different samples after and before applying the different values of cut-off on the MET fraction are shown for MC and data. For the inclusive b-tagged jet selection, there is no effect up to 1$\,{\text {TeV}}$

1.2 7.A.2 Generator Studies

The effect of the standard cut-off is also investigated at generator level in MC studies with Pythia  8; it is shown in Fig. 7.21, but the same conclusions may be drawn from other bins, including the contribution of other SM processes: $t\bar{t}$, $W+\text {jet}$ or $Z+\text {jet}$ a.k.a. DY. Effects are only found at low transverse momentum.

Fig. 7.21

Effect of the cut-off on the fraction of MET for the four main signals, shown for the four main contributions in the SM

7.B Details of Trigger Efficiency

Tables for turn-on values. In Sect. 7.1.1.1, while presenting the determination of the trigger efficiencies, we presented the emulation and the Tag and Probe methods; they are given in Table 7.3 for each trigger, per era and per rapidity bin.

Representation of the subdivision of the phase space. In Sect. 7.1.1.2, the final choice of the turn-on values was described. In Fig. 7.22, one can visualise the subdivision of the phase space. In complement, the number of events per trigger is given in Table 7.4 per era and per rapidity bin.

Table 7.3 Turn-on points for trigger efficiency in bins of rapidity per trigger and era, shown for the two methods

Fig. 7.22

The different contributions from the different triggers to the total cross section are stacked in bins of rapidity and per era

Table 7.4 Number of jets per trigger and per era in rapidity bins, after the final phase space subdivision

Fig. 7.23

Run-by-run averages of the pre-scales for each of the triggers used in this analysis (the threshold is indicated on the very left). 372 runs are shown, but only a few of them can be explicitly written for readability. Black vertical lines separate the different eras and the changes of version are shown by dashed lines

Run-by-run average pre-scales. One can define the pre-scales as follows:

$$\begin{aligned} f^\text {run}_\text {trigger}=\mathcal {L}^\text {run}_\text {total}/\mathcal {L}^\text {run}_\text {trigger} \end{aligned}$$

(7.28)

Then, Eq. 7.7 can also be written as follows:

$$\begin{aligned} \sigma ^\text {run}_\text {trigger} = \frac{f^\text {run}_\text {trigger} N^\text {run}_\text {trigger}}{\mathcal {L}^\text {run}_\text {total}} \end{aligned}$$

(7.29)

The run-by-run averaged trigger pre-scales in Fig. 7.23; as it can be seen, the variations are significant. (Similarly, as it was already mentioned in Chap. 3, Fig. 3.7, the luminosity can become smaller by a factor of two during a single run, and pre-scales can be adapted on-line to compensate.) Higher instantaneous luminosity implies higher pile-up conditions, and therefore higher pre-scales. The figure shows that, along the year of 2016, the LHC has achieved better and better performances in terms of luminosity.

7.C Additional Control Plots About Jets

Angular response. The angular response of the detector for jet reconstruction is compared in data and in the simulation in Fig. 7.24; it can be seen that the imperfections of the detector are well described.

Fig. 7.24

Jet $\eta -\phi$ spectrum in data (left) and simulation (right), for inclusive jet (top) and inclusive b jet (bottom). The bins corresponds to the count of jets (not to a cross section) with arbitrary normalisation

Fig. 7.25

Resolution profiles for systematic shifts and for flavoured samples

More on binning. The following binning in considered in this analysis:

$p_T$:

43,49,56,64,74, 84, 96, 114, 133, 153, 174, 196, 220, 245, 272, 300, 330, 362, 395, 430, 468,507, 548, 592, 638, 686, 737, 790, 846, 905, 967,1032, 1101, 1172, 1248, 1327, 1410, 1497, 1588, 1684, 1784, 1890, 2000,2116, 2238, 2366, 2500, 2640, 2787, 2941

|y|:

0, 0.5, 1.0, 1.5, 2.0, 2.4

Additional checks are shown in Fig. 7.25. Most importantly, the resolution for b jets is slightly worse, especially in the forward region ($|y| > 1.5$); we will see later that during the procedure of unfolding, bins have to be merged roughly in pairs, which will cover the migrations.

7.D More on Tagging

We show in Fig. 7.26 the performance of the tagger before calibration. In this case, one can also compare to Herwip++ : the performance is extremely similar, and the discrepancy at high transverse momentum is even more pronounced.

Fig. 7.26

Performance of CSVv2 in simulation before calibration with the tight selection. Pythia  8 and Madgraph share the same tune CUETP8M1 while Herwip++ has its own tune CUETHppS1; calibration is only available for Pythia  8 and Madgraph . A significant disagreement from one in the fraction ratio can be seen for all simulations

Additional checks may be performed by comparing taggers and WPs.

1.1 7.D.1 Comparison of the Working Points

The SFs have been shown on Fig. 7.15 for the tight selection. The medium and loose WPs are also investigated, and they can be seen on Figs. 7.27 and 7.28; the effect of different WPs on the $p_T(y)$ can be seen on Fig. 7.29. Allowing larger statistics, the SFs for the mistag of light jets can be provided with rapidity dependence in addition to transverse momentum dependence in order to attempt to mitigate the disagreement, especially in the $1.0< |y| < 1.5$ region where it is the strongest. The rapidity dependence is defined in different binning schemes according to the WP:

• for the medium selection, it is done in three bins of width 0.8, i.e. 0.0, 0.8, 1.6, 2.4;

• for the loose selection, it is done in seven bins of different widths, i.e. $0.0,0.3,0.6,0.9,1.2,1.5,1.8,2.4$.

From Fig. 7.31, the fraction ratio is better described; on the other hand, the contamination from light (charm) jets reaches 60% (20%), and the purity is around $10{-}20\%$ in the whole spectrum. The improvement seen in the fraction can be explained by the presence of more n jets. Therefore, we cannot conclude any improvement from the rapidity dependence of the SFs with looser WPs. The same conclusions may be drawn with the different WPs of the different taggers (not shown here).

Fig. 7.27

SFs for the medium selection. Mistag scale factors for light jets include a rapidity dependence in 3 bins

Fig. 7.28

SFs for the loose selection for the different flavours. Mistag scale factors for light jets include a rapidity dependence in 3 bins

Fig. 7.29

Effect of the b calibration on the spectrum with different WPs. Different WPs are compared for CSVv2. The five columns correspond to the five rapidity bins. The coloured, shaded bands correspond to the uncertainties of the SFs

Fig. 7.30

Effect of the b calibration on the spectrum with different taggers. Different taggers are compared for the tight WP. The five columns correspond to the five rapidity bins. The coloured, shaded bands correspond to the uncertainties of the SFs

1.2 7.D.2 Comparison of the Taggers

The different taggers can be compared in Fig. 7.32; the effect of the calibration for the different taggers on the $p_T(y)$ can be seen D on Fig. 7.30. The uncertainties from the CSVv2 (JP) tagger are the smallest (greatest) one. However, they all show similar tendencies, and confirm that possible biases are not due to their respective performances.

Fig. 7.31

Comparison of the performance of CSVv2 of Pythia  8 with different WPs

Fig. 7.32

Comparison of the performance of CSVv2 of Pythia  8 with different taggers

7.E Jet Constituents

The content of jets and of $\hat{b}$ jets is described by two categories of variables: The energy fractions (Fig. 7.33):

• charged-hadron energy fraction

• neutral-hadron energy fraction

• charged e.m. energy fraction

• neutral e.m. energy fraction

• muon energy fraction

The multiplicities (Fig. 7.34):

• charged-hadron multiplicity

• neutral-hadron multiplicity

• electron multiplicity

• photon multiplicity

• muon multiplicity

(The figures for the energy fractions and for the multiplicities are shown opposite to one another.)

1.1 7.E.1 Jet ID

The jet ID, already addressed while describing the selection in Sect. 6.3.1, is based on these variables. In this analysis, the tight ID is used, to which the corresponding cut-off values for $|y| < 2.4$ are shown in Table 7.5.

Table 7.5 Tight jet ID definition in $|y|<2.4$

Fig. 7.33

Comparison of data and simulation of the fractions of the jet constituents

Fig. 7.34

Comparison of data and simulation of the multiplicities of the jet constituents

1.2 7.E.2 Jet Constituents in Bins of Rapidity

In order to investigate the discrepancy in the fraction ratio (Sect. 7.4), we show some elements of additional investigations on the jet constituents in bins of rapidity.

Figures 7.33 and 7.34 show the agreement with data in bins of rapidity, after the tight jet ID selection, for inclusive jet and inclusive $\hat{b}$ jet production. Statistical uncertainties are included, but systematical uncertainties have not been investigated.

Despite the different showering used, it is interesting that Pythia  8 and Madgraph on the one hand and Herwig++ and the other hand do not show any large difference on any of these variables. In general, only the variables involving neutral particles show a sensitive difference (Figs. 7.33b,d and 7.34b,d). But most importantly, the agreement is not affected by the b tagging.

This having been said, the statistics is usually low, and it is hard to conclude. To be perfectly rigorous in our investigations, the same investigations should be performed in bins of $p_T$; unfortunately, this is not possible, since the statistics are too low.