5.3 Input for the cross sections extraction
5.3.7 Number of Targets
The measured cross-section must be divided by the total number of nucleons inside the FGD1 fiducial volume (see Fig. 5.18) given by the following formula:
NnucleonsF V = NA∆XF V∆YF V
elements
X
i
ρi∆ZiAi
Mi (5.17)
where NAis the Avogadro’s number, ∆XF V and ∆YF V are the total length of the fiducial volume in X and Y axis. The index i runs over all the elements composing the FGD1 fiducial volume, Ai and Mi are the averaged number of nucleons and atomic mass per element and the product ρi∆Zi is the areal density per element in the fiducial volume, computed from the value in Tab. XXIV. The information for each element are reported in Tab. XXV and are taken from [172]. Accordingly with the quantities in Tabs. XXIV and XXV the number of nucleons inside the FGD1 fiducial volume is:
NnucleonsF V = 5.9× 1029 (5.18)
Components ∆Z(mm) ρ(g/cm3) G10 (×2) 0.232× 2 1.700 glue layer 1 (×2) 0.188 × 2 0.920 glue layer 2 0.19 0.920 XY module 9.61× 2 1.041
air 2.0 0.00129
fibers 0.0019 1.050
TABLE XXIV. Thickness and density of each component in each layer of the FGD1.
Element A Ni Natural abundance (%) Mi Ai FGD1 fraction
C 12 6 98.9
6.011 12.01078 86.10%
13 7 1.1
O
16 8 99.762
8.00438 15.99943 3.70%
17 9 0.038
18 10 0.2
H 1 0 99.985
0.00015 1.007947 7.35%
2 1 0.015
Ti
46 24 8
25.98 47.8671 1.65%
47 25 7.5
48 26 73.8
49 27 5.5
50 28 5.4
Si
28 14 92.22
14.1072 28.0855 1.01%
29 15 4.68
30 16 3.09
N 14 7 99.634
7.00366 14.00672 0.14%
15 8 0.366
TABLE XXV. Information used to compute the total number of nucleons for each element of the FGD1 FV.
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial volume from the upstream edge of the detector. If the muon candidate starts in the FGD1 fiducial volume and is set as backward-going (end position upstream of start position) the event is rejected, since most of the tracks in this case do not start in the FGD1 as we can see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between, mainly, P0D and FGD. As the timing between the two detectors is not good enough, most generally those tracks set as backwards are forward tracks starting mainly in the P0D.
In addition, we check the highest momentum track with a TPC segment in the bunch that is not the muon candidate (requiring no TPC track quality cut on this second track). If its initial position is more than 150 mm upstream from the muon track starting position (TPC Veto Delta Z), we reject the event on the grounds that there is a track in the event that probably entered the detector from the P0D or magnet region, see Fig. 5.5.
5. TPC particle identification (PID).
Given the estimated momentum of the muon candidate, the discriminator function is cal-culated for the muon, pion, and proton hypotheses. Two cuts are then applied, requiring:
L
M IP= L
µ+ L 1 L
p> 0.8 if p < 500 MeV/c (5.10)
L
µ> 0.005 (5.11)
where L is given by Eq. 5.5. The first of this cut rejects electrons at low momentum (below 500 MeV/c). The second cut removes protons and pions. Note that the PID cuts
97
116.045 mm
2x9.61 mm +33.06 mm
446.955 mm 1474.045 mm
2 x 9.61 mm + 3.044 water
15 layers z
192x2 bars/layer 192x2 bars/layer7 layers
x (mm)
Figure 5.4: Scheme of FGD1 and FGD2
than 19 hits, the e⌃ect of the quality cut is expected to be small (less than 5%), as well as the systematic error associated to it.
If there is more than one negatively charged track passing these cuts, we select the highest momentum track as the muon candidate.
4. Wrong backwards-going tracks and TPC veto.
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial
volume from the upstream edge of the detector. If the muon candidate starts in the FGD1
fiducial volume and is set as backward-going (end position upstream of start position) the
event is rejected, since most of the tracks in this case do not start in the FGD1 as we can
see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between,
mainly, P0D and FGD. As the timing between the two detectors is not good enough, most
The goal of these cuts are to remove miss-reconstructed events entering the FGD1 fiducial
volume from the upstream edge of the detector. If the muon candidate starts in the FGD1
fiducial volume and is set as backward-going (end position upstream of start position) the
event is rejected, since most of the tracks in this case do not start in the FGD1 as we can
see in Fig. 5.5. This cut removes tracks set as backward from timing di⌃erence between,
mainly, P0D and FGD. As the timing between the two detectors is not good enough, most
In document
Measurement of the antineutrino flux and cross section at the near detector of the T2K experiment
(Page 156-159)