/ rad ϕTr
-2 0 2
/ mradClθ-Trθ
-5 0 5 10
/ rad ϕTr
-2 0 2
/ mradClθ-Trθ
-5 0 5 10
(a)
/ cm ZLAr
-200 -100 0 100 200
/ mradClθ-Trθ
-5 0 5
/ cm ZLAr
-200 -100 0 100 200
/ mradClθ-Trθ
-5 0
5 (b)
Figure 6.15: The track-cluster θe difference as a function of ϕe (a) and as a function of z impact position (b), shown for data (full points) and simulation (open) points.
Beam Tilt Correction
The ep beam axis does not exactly coincide with the z-axis of the H1 coordinate system. The beam has a small inclination in the xand y directions (see figure 6.16), the so-called “beam tilt”.
Run number
406647411489414322421808425199429918433746436085
Slope X / mrad
-1 -0.9 -0.8 -0.7
Run number
406647411489414322421808425199429918433746436085
Slope X / mrad
-1 -0.9 -0.8 -0.7
(a)
Run number
406647411489414322421808425199429918433746436085
Slope Y / mrad
0.7 0.8 0.9 1
Run number
406647411489414322421808425199429918433746436085
Slope Y / mrad
0.7 0.8 0.9 1
(b)
Figure 6.16: Beam tilt: the inclination of the beam with respect to the H1 coordinate system in the x−z (a) and they−z (b) plane.
For the final calculation of the polar and azimuthal angles of the election this differ-ence between beam axis and the H1 coordinate system is taken into account. For this purpose a tilted coordinate system (x0, y0, z0) is defined with thez0-axis in the direc-tion of beam. The posidirec-tion of the electron cluster (xe, ye, ze) in the original (X, Y, Z) coordinate system is then projected into tilted coordinate system (x0e, ye0, z0e) and the final angles are determined as θe =arctg
z0e
√x0e2+y0e2
and ϕe=arctg
y0e x0e
.
angles of the scattered electron and of the hadronic final state, together with the precisely known beam energies, can be used to predict the energy of the scattered electron, using equation (5.20), and to perform a calibration of the calorimeter re-sponse.
The absolute calibration of the electron energy measurement is done separately for the data and MC in order to account for possible biases in the reconstruction.
6.6.1 Electron Energy Calibration
For the electron calibration the cluster energy in the LAr calorimeter is compared to the electron energy calculated using the double angle method (equation (5.20)).
The energy calibration is studied using a sub-sample of the inclusive selection given in section 7.3. Additional criteria are applied to ensure sufficient precision of the DA method:
• Ee0 >14 GeV.
• yΣ <0.3 (0.5) forzimpact ≤20 cm (20 < zimpact<100 cm) ensures an accurate estimation of the EDA (hadronic final state is well measured).
• 44< E−Pz <66 GeV reduces effects of initial state radiation.
• γh > 10◦ ensures that the hadronic final state is contained in the detector acceptance and therefore well measured.
• The regions near the ϕand z cracks, where the electrons are poorly measured, are excluded from the analysis.
The calibration is performed comparing the calorimetric energy with the DA-prediction as a function of thezimpact position of the electron in the calorimeter. The main geo-metrical structures of the LAr calorimeter arez-dependent wheel and theϕ-dependent octant structures (see section 3.6.1).
Calibration factors are obtained from the mean of the ratio Ee/EDA. In order to reduce the influence of tails in the distributions only events with 0.85 < Ee/EDA <
1.15 are considered in the averaging. The calibration is done iteratively in a two stage process:
• The wheel- and octant-wise calibration. The first calibration step is per-formed octant-wise for each of the BBE, CB1, CB2 and CB3 wheels. The regions are enumerated byNstack = 8·Nwheel+Noctant. Here,Noctant = 0−7 for ϕ= 0−360◦, and the wheels are enumerated by Nwheel = 0−3 for BBE, CB1, CB2, CB3. Because of the limited statistics, for the wheels FB1 and FB2 only one calibration factor per wheel is determined. Figure 6.17 shows the inverse calibration factors as a function of the stack number.
• The z-wise calibration. Further calibration factors are determined as func-tion of the z position of the electron impact point in the LAr calorimeter
Stack
10 20 30 40
Ee / Eda
0.96 0.98 1 1.02
1.04 BBE CB1 CB2 CB3 FB1 FB2
MC Data
Figure 6.17: Mean values of the ratio Ee/EDA as a function of the stack number for data (full circles) and MC (open circles) before calibration.
Z bin
50 100 150 200
Ee / Eda
0.96 0.98 1 1.02
1.04 BBE CB1 CB2
MC Data
Figure 6.18: Mean values of the ratioEe/EDA as a function of the z position of the electron impact point for data (full circles) and MC (open circles) before calibration. Bin zero corresponds to z =−190 cm.
zLAr. The factors are determined in 1 cm bins for zLAr < 0, 10 cm bins for 0 ≤ zLAr < 90 cm, 20 cm bins for 90 ≤ zLAr < 110 cm and 50 cm bins for zLAr ≥110 cm. The increasing bin size is related to the decreasing statistics of the NC events (increasingQ2). The calibration factors are shown as a function of zbin in figure 6.18.
• The two steps procedure is iteratively repeated with narrowing of the averaging window for Ee/EDA to 0.9< Ee/EDA <1.1.
After applying these calibration factors, the ratio Ee/EDA is shown in figure 6.19.
The ratio is everywhere close to unity, with only small deviations (less then 1%) near the cracks and in BBE. A good agreement, well within 1%, between data and simu-lation is observed.
The total uncertainty on the electron energy scale is estimated to be:
- forzLAr ≤20 cm 1%;
- for 20 cm < zLAr ≤110 cm 2%;
- forzLAr >110 cm 3%;
The correlated part of the total uncertainty comes mainly from possible biases of the calibration method and is estimated to be 0.5% throughout the LAr calorimeter.
N stack
10 20 30 40
DA / EeE
0.96 0.98 1 1.02
1.04 BBE CB1 CB2 CB3 FB1 FB2
MC Data
(a)
Z bin
50 100 150 200
DA / EeE
0.96 0.98 1 1.02
1.04 BBE CB1 CB2
MC Data
(b)
/ deg
oct, BBE
-20 -10 0 ϕ10 20
DA / EeE
0.9 0.95 1 1.05 1.1
/ deg
oct, BBE
-20 -10 0 ϕ10 20
DA / EeE
0.9 0.95 1 1.05 1.1
(c)
/ deg
oct, CB
-20 -10 0 10ϕ 20
DA / EeE
0.9 0.95 1 1.05 1.1
/ deg
oct, CB
-20 -10 0 10ϕ 20
DA / EeE
0.9 0.95 1 1.05 1.1
(d)
Figure 6.19: Electron energy measurement after calibration for the data from 2004-05. The mean values of the ratioEe/EDAas a function of the stack number (see text) (a) and the z position of electron impact point (b). The ratio Ee/EDA as a function of the ϕangle between the electron impact point and closestϕ-crack for BBE (c) and CB1-CB3 (d).
Z bin
50 100 150 200
Resolution
0 0.02 0.04 0.06 0.08
BBE CB1 CB2
MC Data
Figure 6.20: The resolution of the electron energy measurement as a function of the z-position of the impact point before calibration for data (full circles) and MC (open circles).
Z bin
50 100 150 200
Resolution
0 0.02 0.04 0.06 0.08
BBE CB1 CB2
MC Data
Figure 6.21: The resolution of the electron energy measurement as a function of the z-position of the impact point after calibration and a gaussian smearing of the energy in simulation.
6.6.2 Electron Energy Resolution
The energy resolution of the LAr for electromagnetic deposits has been studied with the test beams at CERN [104] and was found to be
σ(E)/E = 12%/p
E/GeV⊗1%.
The electron energy resolution in the LAr calorimeter as function of z impact deter-mined using a root mean square of the ratio Ee/EDA is shown in figure 6.20. For the given event selection it is typically between four and six percent. The resolution is significantly worse near the z-cracks, at z ' −65 cm and z ' −150 cm. To improve the description of the resolution by the simulation, additional energy smearing in MC is applied using a Gaussian function with σsmear = p
σ2Data−σM C2 . This difference is determined for each z bin used in the z-wise calibration. Figure 6.21 shows that, after this additional smearing the MC describes the data almost perfectly.