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 Tracker Endcap Pixel Detector (TEPX). The figure shows the linear behaviour of the mean number of clusters over the full pileup range from 0 to 200. 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 Tracker Endcap Pixel Detector (TEPX). The figure shows the linear behaviour of the mean number of clusters over the full pileup range from 0 to 200. 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 Tracker Endcap Pixel Detector (TEPX). The figure shows the linear behaviour of the mean number of clusters over the full pileup range from 0 to 200. 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 each disk of the Tracker Endcap Pixel Detector (TEPX). The deviation is calculated as the relative difference between the data point and the value of the fit function at the respective pileup value. For each disk, the size of the box is determined by taking the minimum and maximum deviations across all rings. For clusters, this deviation is smaller than 1% over a pileup range from 0 to 200.  
Simulated mean data rates per module for each ring of all Tracker Endcap Pixel Detector (TEPX) disks at pileup 200 and a rate of 75 kHz of zerobias triggers. The mean rates are shown with their standard deviation, accounting only for the RD53B specific encoding and do not include overhead of any link layer protocol. 
 AlexanderJonasRuede  20190812
I  Attachment  History  Action  Size  Date  Who  Comment 

png  deviation_lin.png  r1  manage  143.2 K  20190821  15:56  AlexanderJonasRuede  
png  disk_rates.png  r1  manage  203.9 K  20190821  15:56  AlexanderJonasRuede  
png  linD1R1.png  r1  manage  192.7 K  20190821  15:56  AlexanderJonasRuede  
png  linD1R5.png  r1  manage  196.7 K  20190821  15:56  AlexanderJonasRuede  
png  linD4R1.png  r1  manage  195.1 K  20190821  15:56  AlexanderJonasRuede 