STOPPING POWER - SUMMARY

Goal of the page

Here we try to _organically_ summarize the results big grin

Simulation results:

SIM_dEdXdistr_1cm:

Here the results for 175 MEvents in 1cm-thick PbWO4.
B field is set to 3.8T.
Both collisional and irradiation processes are included.
The total energy LOST by the muon is taken into account.
Residuals are computed with respect to the <dE/dx> values reported in PDG tables.

Accordance with PDG tables is good, especially at low momentum. Geant4 seems to be overestimating the <dE/dx> at high momentum of a few % (or is it just statistical fluctuation?).

BetheBloch_1cm.png BetheBloch_residuals_1cm.png

SIM_dEdXdistr:

Here the results for 25 MEvents in a 9X9 matrix of 23cm-thick PbWO4 crystals.
B field is set to 3.8T.
Both collisional and irradiation processes are included.
The total energy LOST by the muon is taken into account.
Residuals are computed with respect to the <dE/dx> values reported in PDG tables.

<deltaE/deltax> for 23cm-thick crystals underestimates the actual <dE/dx> for low momentum muons, but the effect become negligible already at 5 GeV/c. The same overestimation at high momentum is found.

BetheBloch.png BetheBloch_residuals.png

As a further check, residuals are computed with respect to the values obtained for 1cm-thick crystals (see plots above)

BetheBloch_residuals_vs1cm.png



Here the results when the energy DEPOSITED by the muon in ECAL is taken into account.
Residuals are computed with respect to the <dE/dx> values reported in PDG tables.

The points are fitted with a function f = a (dE/dx)coll + b (dE/dx)irr (these two contributions are taken from PDG). The fit yields
a = 0.983 +/ 7.91E-05
b = 0.682 +/ 1.84E-05
chi2 / ndf = 29.7

BetheBloch_Edep.png BetheBloch_Edep_residuals.png

Finally, the <dE/dx> computed with energy deposited in ECAL is compared to the G4-predicted value for total energy lost by the muon (instead of using PDG tables).

BetheBloch_Edep_residuals_vsG4.png

SIM_dEdXdistr_noColl:

Here the results for 25 MEvents in a 9X9 matrix of 23cm-thick PbWO4 crystals.
B field is set to 3.8T.
Only irradiation processes are included.
The total energy LOST by the muon is taken into account.
Residuals are computed with respect to the <dE/dx> values reported in PDG tables.

BetheBloch_noColl.png BetheBloch_noColl_residuals.png



Here the results when the energy DEPOSITED by the muon in ECAL is taken into account.
Residuals are computed with respect to the <dE/dx> values reported in PDG tables.

The points are fitted with a function f = b (dE/dx)irr (this contribution is taken from PDG). The fit yields
b = 0.783 +/ 1.56E-03
chi2 / ndf = 94.6

BetheBloch_Edep_noColl.png BetheBloch_Edep_residuals_noColl.png

Finally, the <dE/dx> computed with energy deposited in ECAL is compared to the G4-predicted value for total energy lost by the muon (instead of using PDG tables).

BetheBloch_Edep_residuals_noColl_vsG4.png

SIM_dEdXdistr_noWorld:

Here the results for 25 MEvents in a 9X9 matrix of 23cm-thick PbWO4 crystals.
WORLD OF SIMULATION is just the dimension of crystals: therefore, everything escaping the lead tungstate block should in principle be lost. B field is set to 3.8T.
Both collisional and irradiation processes are included.
The total energy LOST by the muon is taken into account.
Residuals are computed with respect to the <dE/dx> values reported in PDG tables.

BetheBloch_noWorld.png BetheBloch_residuals_noWorld.png

As a further check, residuals are computed with respect to the values obtained for 1cm-thick crystals (see plots above)

BetheBloch_residuals_vs1cm_noWorld.png



Here the results when the energy DEPOSITED by the muon in ECAL is taken into account.
Residuals are computed with respect to the <dE/dx> values reported in PDG tables.

The points are fitted with a function f = a (dE/dx)coll + b (dE/dx)irr (these two contributions are taken from PDG). The fit yields
a = 0.981 +/ 7.15E-05
b = 0.656 +/ 1.81E-05
chi2 / ndf = 50.5

BetheBloch_Edep_noWorld.png BetheBloch_Edep_residuals_noWorld.png

Finally, the <dE/dx> computed with energy deposited in ECAL is compared to the G4-predicted value for total energy lost by the muon (instead of using PDG tables).

BetheBloch_Edep_residuals_vsG4_noWorld.png

Momentum-bin distribution:

Here some distributions of dE/dx for single events, shown for 4 different momentum bins. Total energy LOST by the muon taken into account.

BetheBloch_pBin_9.png BetheBloch_pBin_15.png BetheBloch_pBin_20.png BetheBloch_pBin_25.png

Correction Factor:

Correction for energy leakage is computed as the average value taken from two opposite simulations: nothing in front of ECAL and all the tracker material just before the ECAL crystals. Here in the plot there is plotted the quantity ((dE/dx)_corrected - (dE/dx)_measured) / (dE/dx)_corrected.

correction_factor.png

Experimental results:

Here follow a number of different trials: the different cut and correction conditions are REPORTED IN THE TABLE.

Common selections:

  • Number of momentum bins: 25
  • SuperCluster energy rescaled by 0.97
  • SuperCluster phi between 0 and -3.14
  • only bottom leg muons contribute to the final plot
  • muon momentum taken between 5 and 1000 GeV/c

Cut summary:

* nMuons: number of muon legs reconstructed. If =2, only one leg reconstructed in the upper part and only one in the lower part;
* nAssociated muons: a reconstructed SuperCluster is required for each muon;
* veto: an event is rejected if the muon leg in the upper ECAL part is associated to a SClusterEnergy>Eveto;
* sigmaPoP max: the error on the momentum measurement is required smaller than the bin width (sigmaPoP is the ratio between the momentum bin centre and the bin width and is constant all over the momentum range);
* EoP max: sanity check;
* angle max:
* angular correction: the <dE/dx> vs alpha in the momentum range 5-10 GeV/c is fitted in the two different regions to be
- plateau (alpha < 0.2) = 1.806742
- decreasing region (alpha > 0.2) = - alpha*0.4116948 + 1.868352
The correction consists in normalizing each off-plateau dE/dx to the plateau value, by adding the dE/dx difference (it's not a multiplicative correction factor);
* ZS(SR): the contribution of noise fluctuations to the SuperCluster energy has been estimated with a MC at the level of 17.5 MeV. (at gain 200 the SR threshold is 170MeV);

Statistical errors / 68%CL region:

The green band on the plot is obtained by sampling Nev times the single-event dE/dx distribution of each momentum bin and repeating this toy experiment 1000 times. Nev is taken approximately as the number of events of each bin of the experimental BetheBloch curve. The result of each toy is stored in a histogram. The 68% CL is the region where 680 results of toy experiments is contained. The upper and lower limits of this region define the upper and lower limit of the green band.
N.B. To sample Nev times the dE/dx distribution, a binned histogram is used. Result may then suffer from the finite binning, but to do otherwise is computationally too difficult for us smile .

File legend:

* When label "no correction" is found, it means that no correction is applied smile
* When label "collIrrCorrections" is found, it means that a correction for both collisional and irradiation energy loss is applied, together with a correction for the fraction of photoNuc
* When label "irrCorrections" is found, it means that a correction is applied, based on the sole energy lost via irradiation and estimated with the Geant4. A correction for the fraction of photoNuc is still applied
* When label "2o3irrCorrections" is found, it means that the correction applied to the only energy lost via irradiation is 2/3 wrt the one from the Geant4. A correction for the fraction of photoNuc is still applied

Trial results:

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
1 <=2 <= 2 NO N.P. 0.275 1. inf NO NO

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
2 = 2 <= 2 NO N.P. 0.275 1. inf NO NO

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
3 = 2 = 2 NO N.P. 0.275 1. inf NO NO

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
4 = 2 = 2 NO N.P. 0.275 1. 0.5 NO NO

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
5 = 2 = 2 YES 0.5 GeV 0.275 1. 0.5 NO NO

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
6 = 2 = 2 YES 0.5 0.275 1. 0.5 YES NO

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
7 = 2 = 2 YES 0.5 0.275 1. 0.5 YES YES

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
8 = 2 = 2 YES 0.5 0.275 NO 0.5 YES YES

Stability checks:

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
9 = 2 = 2 YES 0.5 0.2 NO 0.5 YES YES

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
10 = 2 = 2 YES 0.5 0.275 NO 0.7 YES YES

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
11 = 2 = 2 YES 0.5 0.275 NO 0.3 YES YES

Final selection cuts (as in the final version of the paper)

# of trial # of mu # associated mu veto Eveto sigmaP/P MAX EoP MAX angle MAX angular correction ZS correction
12 = 2 = 2 YES 0.5 0.275 YES 0.5 YES YES

Low statistic momentum-bin distribution from MC toy:

Here the distributions of dE/dx for 5 highest momentum bins, from toy MC and the same statistic available with data. (1000 toy experiment)

Bin_21.png Bin_22.png Bin_23.png Bin_24.png Bin_25.png

the same distributions with 10000 toy experiments follow:

skew_bin22.png skew_bin23.png skew_bin24.png skew_bin25.png

blue vertical line = average; black vertical line = experimantal point from energy loss curve (see Final selection)

High energy deposits:

The ieta-iphi maps of the crystals belonging to the super clusters with an energy above 100 GeV are reported.

Energy = 114.798; Momentum = 160.829 mapSC_000.png mapSC_000_lego.png

Energy = 110.104; Momentum = 192.676 mapSC_001.png mapSC_001_lego.png

Energy = 137.868; Momentum = 160.232 mapSC_002.png mapSC_002_lego.png

Energy = 274.547; Momentum = 272.21 mapSC_003.png mapSC_003_lego.png

Topic attachments
I Attachment History Action Size Date Who Comment
PNGpng 10k_bin_22.png r1 manage 9.3 K 2009-10-21 - 18:45 FedericoDeGuio  
PNGpng 10k_bin_23.png r1 manage 10.3 K 2009-10-21 - 18:45 FedericoDeGuio  
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PNGpng 10k_bin_25.png r1 manage 9.8 K 2009-10-21 - 18:46 FedericoDeGuio  
PDFpdf BB_residui_visi.pdf r1 manage 139.4 K 2009-10-07 - 17:51 FedericoDeGuio  
PDFpdf BB_visi.pdf r1 manage 130.1 K 2009-10-07 - 17:51 FedericoDeGuio  
PNGpng BetheBloch.png r1 manage 11.8 K 2009-07-12 - 16:35 AndreaBenaglia  
PNGpng BetheBloch_1cm.png r1 manage 12.2 K 2009-07-12 - 14:36 AndreaBenaglia  
PNGpng BetheBloch_2o3-irrCorrections_8.png r1 manage 12.0 K 2009-07-14 - 17:12 ArabellaMartelli  
PNGpng BetheBloch_Edep.png r1 manage 12.0 K 2009-07-12 - 16:33 AndreaBenaglia  
PNGpng BetheBloch_Edep_noColl.png r1 manage 11.3 K 2009-07-12 - 19:04 AndreaBenaglia  
PNGpng BetheBloch_Edep_noWorld.png r1 manage 11.8 K 2009-07-15 - 02:20 AndreaBenaglia  
PNGpng BetheBloch_Edep_residuals.png r1 manage 12.4 K 2009-07-12 - 18:10 AndreaBenaglia  
PNGpng BetheBloch_Edep_residuals_noColl.png r1 manage 12.7 K 2009-07-12 - 19:04 AndreaBenaglia  
PNGpng BetheBloch_Edep_residuals_noColl_vsG4.png r1 manage 13.0 K 2009-07-12 - 19:05 AndreaBenaglia  
PNGpng BetheBloch_Edep_residuals_noWorld.png r1 manage 12.4 K 2009-07-15 - 02:20 AndreaBenaglia  
PNGpng BetheBloch_Edep_residuals_vsG4.png r1 manage 11.6 K 2009-07-12 - 18:31 AndreaBenaglia  
PNGpng BetheBloch_Edep_residuals_vsG4_noWorld.png r1 manage 11.6 K 2009-07-15 - 02:20 AndreaBenaglia  
PNGpng BetheBloch_collIrrCorrection_1.png r1 manage 11.3 K 2009-07-13 - 00:31 AndreaBenaglia  
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PNGpng BetheBloch_irrCorrection_1.png r2 r1 manage 12.1 K 2009-07-13 - 19:35 ArabellaMartelli  
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PNGpng BetheBloch_irrCorrections_4.png r3 r2 r1 manage 12.0 K 2009-07-13 - 18:44 ArabellaMartelli  
PNGpng BetheBloch_irrCorrections_5.png r3 r2 r1 manage 12.0 K 2009-07-13 - 18:43 ArabellaMartelli  
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PNGpng BetheBloch_irrCorrections_7.png r1 manage 12.0 K 2009-07-13 - 15:08 ArabellaMartelli  
PNGpng BetheBloch_irrCorrections_8.png r1 manage 11.9 K 2009-07-13 - 19:40 ArabellaMartelli  
PNGpng BetheBloch_irrCorrections_9.png r1 manage 11.9 K 2009-07-13 - 19:57 ArabellaMartelli  
PNGpng BetheBloch_irrCorrections_Tk10-40_8.png r2 r1 manage 11.9 K 2009-07-17 - 16:34 ArabellaMartelli  
PNGpng BetheBloch_irrCorrections_curvedM_8.png r1 manage 12.0 K 2009-07-17 - 16:21 ArabellaMartelli  
PNGpng BetheBloch_irrCorrections_curvedM_Tk10-40_8.png r1 manage 12.0 K 2009-07-17 - 16:22 ArabellaMartelli  
PNGpng BetheBloch_noColl.png r1 manage 11.0 K 2009-07-12 - 18:54 AndreaBenaglia  
PNGpng BetheBloch_noColl_residuals.png r1 manage 12.3 K 2009-07-12 - 18:55 AndreaBenaglia  
PNGpng BetheBloch_noCorrection_1.png r1 manage 11.4 K 2009-07-13 - 00:26 AndreaBenaglia  
PNGpng BetheBloch_noCorrections_2.png r1 manage 11.4 K 2009-07-13 - 00:36 AndreaBenaglia  
PNGpng BetheBloch_noCorrections_3.png r1 manage 11.4 K 2009-07-13 - 00:50 AndreaBenaglia  
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PNGpng BetheBloch_noCorrections_5.png r1 manage 11.3 K 2009-07-13 - 01:19 AndreaBenaglia  
PNGpng BetheBloch_noCorrections_6.png r1 manage 12.0 K 2009-07-13 - 14:51 ArabellaMartelli  
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PNGpng BetheBloch_noCorrections_8.png r1 manage 11.9 K 2009-07-13 - 19:40 ArabellaMartelli  
PNGpng BetheBloch_noCorrections_9.png r1 manage 11.9 K 2009-07-13 - 19:56 ArabellaMartelli  
PNGpng BetheBloch_noWorld.png r1 manage 11.9 K 2009-07-15 - 02:20 AndreaBenaglia  
PNGpng BetheBloch_pBin_15.png r1 manage 9.1 K 2009-07-12 - 19:39 AndreaBenaglia  
PNGpng BetheBloch_pBin_20.png r1 manage 9.0 K 2009-07-12 - 19:39 AndreaBenaglia  
PNGpng BetheBloch_pBin_25.png r1 manage 8.9 K 2009-07-12 - 19:39 AndreaBenaglia  
PNGpng BetheBloch_pBin_9.png r1 manage 9.1 K 2009-07-12 - 19:38 AndreaBenaglia  
PNGpng BetheBloch_residuals.png r1 manage 12.1 K 2009-07-12 - 16:11 AndreaBenaglia  
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PNGpng correction_factor.png r2 r1 manage 13.2 K 2009-11-10 - 12:45 AndreaBenaglia  
PNGpng mapSC_000.png r1 manage 6.4 K 2009-08-04 - 17:04 FedericoDeGuio  
PNGpng mapSC_000_lego.png r1 manage 18.2 K 2009-08-04 - 17:07 FedericoDeGuio  
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PNGpng mapSC_001_lego.png r1 manage 18.4 K 2009-08-04 - 17:07 FedericoDeGuio  
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PNGpng mapSC_003_lego.png r1 manage 20.4 K 2009-08-04 - 17:09 FedericoDeGuio  
Texttxt output_1.txt r1 manage 3.2 K 2009-07-13 - 01:12 AndreaBenaglia  
Texttxt output_10.txt r1 manage 3.2 K 2009-07-14 - 10:13 ArabellaMartelli  
Texttxt output_11.txt r1 manage 3.2 K 2009-07-14 - 10:16 ArabellaMartelli  
Texttxt output_12.txt r1 manage 3.8 K 2009-10-07 - 17:25 FedericoDeGuio  
Texttxt output_2.txt r1 manage 3.2 K 2009-07-13 - 01:13 AndreaBenaglia  
Texttxt output_3.txt r1 manage 3.2 K 2009-07-13 - 01:13 AndreaBenaglia  
Texttxt output_4.txt r1 manage 3.2 K 2009-07-13 - 01:13 AndreaBenaglia  
Texttxt output_5.txt r1 manage 3.2 K 2009-07-13 - 01:13 AndreaBenaglia  
Texttxt output_6.txt r1 manage 3.2 K 2009-07-13 - 14:50 ArabellaMartelli  
Texttxt output_7.txt r1 manage 3.2 K 2009-07-13 - 15:07 ArabellaMartelli  
Texttxt output_8.txt r1 manage 3.2 K 2009-07-13 - 19:39 ArabellaMartelli  
Texttxt output_9.txt r1 manage 3.2 K 2009-07-13 - 19:54 ArabellaMartelli  
Texttxt output_Tk10-40_8.txt r2 r1 manage 3.2 K 2009-07-17 - 16:41 ArabellaMartelli  
Texttxt output_curvedM_8.txt r1 manage 3.2 K 2009-07-17 - 16:21 ArabellaMartelli  
Texttxt output_curvedM_Tk10-40_8.txt r1 manage 3.2 K 2009-07-17 - 16:22 ArabellaMartelli  
PNGpng residuals_2o3irrCorrections_8.png r2 r1 manage 12.4 K 2009-07-14 - 19:58 ArabellaMartelli  
PNGpng residuals_collIrrCorrections_1.png r1 manage 11.7 K 2009-07-13 - 00:16 AndreaBenaglia  
PNGpng residuals_collIrrCorrections_2.png r1 manage 11.6 K 2009-07-13 - 00:37 AndreaBenaglia  
PNGpng residuals_collIrrCorrections_3.png r1 manage 11.6 K 2009-07-13 - 00:51 AndreaBenaglia  
PNGpng residuals_irrCorrections_1.png r1 manage 11.7 K 2009-07-13 - 14:02 AndreaBenaglia  
PNGpng residuals_irrCorrections_10.png r1 manage 12.4 K 2009-07-14 - 19:50 ArabellaMartelli  
PNGpng residuals_irrCorrections_11.png r1 manage 10.9 K 2009-07-14 - 19:50 ArabellaMartelli  
PNGpng residuals_irrCorrections_2.png r1 manage 11.6 K 2009-07-13 - 14:02 AndreaBenaglia  
PNGpng residuals_irrCorrections_3.png r1 manage 11.6 K 2009-07-13 - 00:51 AndreaBenaglia  
PNGpng residuals_irrCorrections_4.png r1 manage 12.1 K 2009-07-13 - 01:02 AndreaBenaglia  
PNGpng residuals_irrCorrections_8.png r2 r1 manage 12.4 K 2009-07-14 - 19:57 ArabellaMartelli  
PNGpng residuals_irrCorrections_9.png r1 manage 12.4 K 2009-07-14 - 19:48 ArabellaMartelli  
PNGpng residuals_irrCorrections_Tk10-40_8.png r2 r1 manage 12.4 K 2009-07-17 - 16:33 ArabellaMartelli  
PNGpng residuals_irrCorrections_curvedM_8.png r1 manage 12.5 K 2009-07-17 - 16:21 ArabellaMartelli  
PNGpng residuals_irrCorrections_curvedM_Tk10-40_8.png r1 manage 12.5 K 2009-07-17 - 16:23 ArabellaMartelli  
PNGpng residuals_noCorrections_1.png r1 manage 11.7 K 2009-07-13 - 00:16 AndreaBenaglia  
PNGpng residuals_noCorrections_2.png r1 manage 11.6 K 2009-07-13 - 00:37 AndreaBenaglia  
PNGpng residuals_noCorrections_3.png r1 manage 11.6 K 2009-07-13 - 00:50 AndreaBenaglia  
PNGpng residuals_noCorrections_4.png r1 manage 11.9 K 2009-07-13 - 01:02 AndreaBenaglia  
Unknown file formateps skew_bin22.eps r1 manage 11.8 K 2009-10-22 - 11:08 FedericoDeGuio  
PNGpng skew_bin22.png r1 manage 17.5 K 2009-10-22 - 11:29 FedericoDeGuio  
Unknown file formateps skew_bin23.eps r1 manage 13.1 K 2009-10-22 - 11:09 FedericoDeGuio  
PNGpng skew_bin23.png r1 manage 21.8 K 2009-10-22 - 11:29 FedericoDeGuio  
Unknown file formateps skew_bin24.eps r1 manage 13.8 K 2009-10-22 - 11:09 FedericoDeGuio  
PNGpng skew_bin24.png r1 manage 23.0 K 2009-10-22 - 11:29 FedericoDeGuio  
Unknown file formateps skew_bin25.eps r1 manage 12.3 K 2009-10-22 - 11:09 FedericoDeGuio  
PNGpng skew_bin25.png r1 manage 22.4 K 2009-10-22 - 11:30 FedericoDeGuio  
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Topic revision: r26 - 2009-11-10 - AndreaBenaglia
 
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