Theoretical cross sections

The cross sections of the R-hadron simulated samples are calculated at NLO+NLL level, i.e. at next-to-leading order in the strong cou- pling constant αS and soft gluon emissions are resummed at next- to-leading-logarithmic accuracy [321–323]. The procedure to esti- mate the uncertainty is described in [324]. It results from a com- parison of different cross-section predictions obtained by using var- ious sets of parton distribution functions following the 68% con- fidence limit ranges of the MSTW2 0 0 8 [325] and CTEQ6.6 [326] pdf sets and incorporating different factorisation and renormalisa- tion scales. The resulting uncertainties are listed next to the calcu- lated cross sections in table5.1. For gluinos they range from 14% at m(g˜) = 400 GeV to 57% at m(g˜) = 3000 GeV and for squarks from 13% atm(b˜/˜t) =600 GeV to 23% form(b˜/˜t) =1400 GeV.

For stau and chargino samples the cross sections are calculated at NLO in αS. Uncertainties are obtained by evaluation of the 68% confidence level (CL) ranges of the underlying pdfs and variation of the factorisation and renormalisation scales by factors 0.5 and 2.0. Following the recommendations in [327], the quoted cross sections are taken as the central value of the enveloping functions, the un- certainty is taken as half the spread. The assigned uncertainties are listed in table 5.3 (table 5.2) for stau (chargino) samples and range from 6% at m(τ˜) = 287 GeV to 10% at m(τ˜) = 911 GeV

(6% at m(χ˜₁±) = 250 GeV to 10% at m(χ˜±₁) = 1500 GeV for the

˜

χ±₁χ˜₁± production channel and 4% at m(χ˜₁±) = 300 GeV to 8% at

m(χ˜±₁) =1500 GeV for ˜χ±₁χ˜0₁).

A summary of systematic uncertainties due to theoretical cross- section predictions can be found in table5.13.

particle sys. unc. Gluinos 14%–57% Sbottom 13%–23% Stops 13%–23% Staus 6%–10% Charginos ˜χ±₁χ˜±₁ 6%–10% Charginos ˜χ±₁χ˜0₁ 4%–8%

Table5.13: List of systematic uncertain- ties assigned to all particle types due to the uncertainty on the theoretical cross- section prediction.

5.8.2

E

T

trigger efficiency

The missing transverse energy which the Emiss

T triggers are sensi- tive to is calculated exclusively from clusters of deposited energy in the calorimeters. Since muons do not cause extensive showering in the calorimeters the Emiss_T trigger is blind to them and muons thus provide a possibility to access systematic uncertainties regarding the trigger efficiency.

Events are selected via the lowest unprescaled single-muon trigger and undergo a basic Z → µµselection22. TheE_Tmisstrigger onset is

22

This includes event quality conditions and exactly two muons with tracks in the ID and the MS with pT >10 GeV that have opposite charge and combine to an invariant mass within 10 GeV of theZ-boson mass

studied in data and simulatedZ→µµevents. An error function of the form ε(Emiss_T ) = A 2 " 1+erf E miss T_√ −B 2C !# (5.5)

can be used to fit the trigger onset, where the parameterAdescribes the maximal trigger efficiency and is fixed to 1.0, parameterBcorre- sponds to the Emiss_T value at 50% efficiency and thus constitutes an effective threshold and parameterC, which represents the resolution as the width of a Gaussian that cumulatively models the slope of the fit. Figure5.30shows the fitted trigger efficiency onset as function of the reconstructed offlineE_Tmissfor two exemplary triggers.

Figure5.30:Emiss

T trigger onsets in data and MC with an appliedZ → µµ se-

lection for the employed triggers with the lowest (70 GeV) and the largest (110 GeV) trigger threshold. Fitted er- ror functions to the onset are drawn as solid lines. The corresponding plots for the remaining twoEmiss

T triggers with thresholds of 90 GeV and 100 GeV are given in figure E.2 _{in Appendix E.}1_. The offlineEmiss_T used here is based on calorimeter clusters without receiving

corrections from the MS. miss _[GeV]

T Offline E 0 50 100 150 200 250 300 350 400 Trigger efficiency 0 0.2 0.4 0.6 0.8 1 1.2 1.4 data MC µ µ → Z =13 TeV s , -1 L dt = 3.2 fb

∫

Online threshold: 70 GeV

[GeV] miss T Offline E 0 50 100 150 200 250 300 350 400 Trigger efficiency 0 0.2 0.4 0.6 0.8 1 1.2 1.4 data MC µ µ → Z =13 TeV s , -1 L dt = 20.3 fb

∫

Online threshold: 110 GeV

The effect of the trigger efficiency on the signal yield can be quan- tified via a bin-by-bin multiplication of theE_Tmissspectrum in signal MC with the fitted trigger onset. Since the same detector response models have been used for signal MC and Z → µµ MC, the onset

derived from the latter is also valid in signal MC23

. Four individ-

23

In fact,Z→ µµMC is only used to characterise the behaviour of the trig- ger onset in simulation and assess the difference from data.

ual components are considered to contribute to the total associated uncertainty:

• the relative difference between the signal yields derived by folding the signal MC Emiss_T distributions with the onsets from data and MC,

• the relative effect of a 10% variation in scale of the signal MCEmiss_T , • the relative signal yield differences from independent ±1.0σvari-

ations of the fit parametersBandCin the fit on data, and • the same variations for the fit on MC.

[%] C−1σ C C+1σ

B−1σ 0.3352 0.3565 0.3775

B 0.0217 0.0000 0.0216 B+1σ 0.3780 0.3557 0.3336

Table5.14: Given is the relative change in signal yield for a 2000 GeV gluino R-hadron sample with respect to the central fit values under independent 1σ

variations of the fit parameters Band Cof the fit in data for anEmiss

T trigger with a threshold of 110 GeV.

As an example, the relative changes in signal yield through vari- ation of fit parameters are given in table5.14for the fit in data and table5.15for the fit in MC. In both cases a 2000 GeV gluinoR-hadron sample and anEmiss_T trigger with an online threshold of 110 GeV has been considered. The largest individual relative change is taken as the contribution from the parameter variation.

The absolute uncertainty for each trigger and signal mass point is calculated by adding all four contributions in quadrature. This pro- cedure has been applied to all signal MC samples and allEmiss_T trig- gers. Estimates from the different triggers are combined by weight- ing the estimate according to the fraction of integrated luminosity during which the trigger was actively used. As an example, fig- ure5.31shows the individual uncertainties for all trigger and signal mass points of gluino R-hadrons and stable staus, as well as the lu- minosity weighted average. A full overview over all signal samples is given in figure E.3in Appendix E.1.

[%] C−1σ C C+1σ

B−1σ 0.3947 0.4161 0.4374 B 0.0222 0.0000 0.0220 B+1σ 0.4379 0.4151 0.3924

Table5.15: Given is the relative change in signal yield for a 2000 GeV gluino R-hadron sample with respect to the central fit values under independent 1σ

variations of the fit parametersBandC of the fit in MC for anEmiss

T trigger with a threshold of 110 GeV. 500 1000 1500 2000 2500 3000 mass [GeV] g ~ 0.005 0.01 0.015 0.02 0.025 0.03 Uncertainty HLT_xe70_mht HLT_xe90_mht_L1XE50 HLT_xe100_mht_L1XE50 HLT_xe110_mht_L1XE50 Luminosity weighted 300 400 500 600 700 800 900 mass [GeV] τ∼ 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Uncertainty HLT_xe70_mht HLT_xe90_mht_L1XE50 HLT_xe100_mht_L1XE50 HLT_xe110_mht_L1XE50 Luminosity weighted

Figure 5.31: Estimated systematic un- certainties of theEmiss

T trigger efficiency evaluated for gluino R-hadrons and stable staus. The uncertainties de- rived from the onset for individual trig- gers are shown with coloured markers, while the solid black line indicates the luminosity-weighted average of all trig- gers. The variation in scale between samples is generally small and the ap- proach of a flat uncertainty indicated by the dashed red line is well justified.

For simplicity and since the variation in between samples is small, a flat systematic uncertainty is assigned to each particle hypothesis. The resulting uncertainties are listed in table5.16.

particle sys. unc. Gluinos 1.7% Sbottoms 1.5%

Stops 1.5%

Staus 2.0%

Charginos 2.4%

Table5_.16_{: List of systematic uncertain-} ties assigned to all particle types due to

Emiss

T trigger efficiency.