STOPPING POWER - SUMMARY

Goal of the page

Here we try to _organically_ summarize the results

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?).

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.

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

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

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).

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.

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

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).

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.

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

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

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).

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.

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.

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 .

File legend:

* When label "no correction" is found, it means that no correction is applied
* 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

• output_1.txt
  
  
• BetheBloch_noCorrections_1.png
• residuals_noCorrections_1.png
  
  
• BetheBloch_irrCorrections_1.png
• residuals_irrCorrections_1.png
  
  
• BetheBloch_collIrrCorrections_1.png
• residuals_collIrrCorrections_1.png

# 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

• output_2.txt
  
  
• BetheBloch_noCorrections_2.png
• residuals_noCorrections_2.png
  
  
• BetheBloch_irrCorrections_2.png
• residuals_irrCorrections_2.png
  
  
• BetheBloch_collIrrCorrections_2.png
• residuals_collIrrCorrections_2.png

# 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

• output_3.txt
  
  
• BetheBloch_noCorrections_3.png
• residuals_noCorrections_3.png
  
  
• BetheBloch_irrCorrections_3.png
• residuals_irrCorrections_3.png
  
  
• BetheBloch_collIrrCorrections_3.png
• residuals_collIrrCorrections_3.png

# 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

• output_4.txt
  
  
• BetheBloch_noCorrections_4.png
• residuals_noCorrections_4.png
  
  
• BetheBloch_irrCorrections_4.png
• residuals_irrCorrections_4.png
  
  
• BetheBloch_collIrrCorrections_4.png
• residuals_collIrrCorrections_4.png

# 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

• output_5.txt
  
  
• BetheBloch_noCorrections_5.png
• residuals_noCorrections_5.png
  
  
• BetheBloch_irrCorrections_5.png
• residuals_irrCorrections_5.png
  
  
• BetheBloch_collIrrCorrections_5.png
• residuals_collIrrCorrections_5.png

# 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

• output_6.txt
  
  
• BetheBloch_noCorrections_6.png
• residuals_noCorrections_6.png
  
  
• BetheBloch_irrCorrections_6.png
• residuals_irrCorrections_6.png
  
  
• BetheBloch_collIrrCorrections_6.png
• residuals_collIrrCorrections_6.png

# 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

• output_7.txt
  
  
• BetheBloch_noCorrections_7.png
• residuals_noCorrections_7.png
  
  
• BetheBloch_irrCorrections_7.png
• residuals_irrCorrections_7.png
  
  
• BetheBloch_collIrrCorrections_7.png
• residuals_collIrrCorrections_7.png

# 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

• output_8.txt
  
  
• output_Tk10-40_8.txt
  
  
• output_curvedM_8.txt
  
  
• output_curvedM_Tk10-40_8.txt
  
  

• BetheBloch_noCorrections_8.png
• residuals_noCorrections_8.png
  
  

• BetheBloch_irrCorrections_8.png
• residuals_irrCorrections_8.png
  
  
• BetheBloch_irrCorrections_Tk10-40_8.png
• residuals_irrCorrections_Tk10-40_8.png
  
  
• BetheBloch_irrCorrections_curvedM_8.png
• residuals_irrCorrections_curvedM_8.png
  
  
• BetheBloch_irrCorrections_curvedM_Tk10-40_8.png
• residuals_irrCorrections_curvedM_Tk10-40_8.png
  
  

• BetheBloch_2o3-irrCorrections_8.png
• residuals_2o3irrCorrections_8.png
  
  
• BetheBloch_collIrrCorrections_8.png
• residuals_collIrrCorrections_8.png

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

• output_9.txt
  
  
• BetheBloch_noCorrections_9.png
• residuals_noCorrections_9.png
  
  
• BetheBloch_irrCorrections_9.png
• residuals_irrCorrections_9.png
  
  
• BetheBloch_collIrrCorrections_9.png
• residuals_collIrrCorrections_9.png

# 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

• output_10.txt
  
  
• BetheBloch_irrCorrections_10.png
• residuals_irrCorrections_10.png
  
  

# 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

• output_11.txt
  
  
• BetheBloch_irrCorrections_11.png
• residuals_irrCorrections_11.png
  
  

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

• output_12.txt
• BB_visi.pdf
• BB_residui_visi.pdf
  
  

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)

the same distributions with 10000 toy experiments follow:

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

Energy = 110.104; Momentum = 192.676

Energy = 137.868; Momentum = 160.232

Energy = 274.547; Momentum = 272.21