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<!StartFragment> TEPX Simulations for TWEPP2019 <!EndFragment>
Introduction:
In order to establish an understanding of the potential properties of TEPX as luminometer for Phase 2 CMS luminosity measurement, detector simulations are being carried out by the BRIL collaboration. Since for PhaseII the range of pileup values over which the vdM calibration will have to be extrapolated is large with respect to RunII, the linearity of observables accessible with TEPX as a function of pileup is of particular interest.
For this purpose, detailed detector simulations have been started using the CMSSW release 10_4_0_pre2 and the Inner Tracker geometry version 6.1.3. To generate data samples over a large range of pileup, singleneutrino events have been overlaid with a variable number of minimum bias events using the CMSSW mixing module. 100,000 events have been generated for pileup values smaller than 20 and 10,000 events have been used for all larger pileup numbers to limit computing time to reasonable values.
Figure 
Caption 

Simulated mean number of clusters as a function of pileup for Disk 1 Ring 1 of the Inner Tracker Endcap Pixel Detector (TEPX). The data points are fitted with a firstorder polynomial in the pileup interval from 0 to 2, and the extrapolation to pileup 200 is shown with a 95% confidence interval. This is done to replicate the principal approach taken with the Van der Meer calibration. 

Simulated mean number of clusters as a function of pileup for Disk 1 Ring 5 of the Inner Tracker Endcap Pixel Detector (TEPX). The data points are fitted with a firstorder polynomial in the pileup interval from 0 to 2, and the extrapolation to pileup 200 is shown with a 95% confidence interval. This is done to replicate the principal approach taken with the Van der Meer calibration. 

Simulated mean number of clusters as a function of pileup for Disk 4 Ring 1 of the Inner Tracker Endcap Pixel Detector (TEPX). The data points are fitted with a firstorder polynomial in the pileup interval from 0 to 2, and the extrapolation to pileup 200 is shown with a 95% confidence interval. This is done to replicate the principal approach taken with the Van der Meer calibration. 

Relative nonlinearity for all rings of all disks of the Inner Tracker Endcap Pixel Detector (TEPX). It is calculated as the relative difference between the data point and the value of the fit function at the respective pileup value. 

Simulated distribution of the permodule data rates for each ring of TEPX at pileup 200 and a rate of 75 kHz of zerobias triggers. The rates are calculated over all disks of TEPX, using the RD53B specific encoding and do not account for any link layer protocol. 
 AlexanderJonasRuede  20190812
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