state is out of CJC acceptance and the vertex is defined by the electron track alone.
Therefore the efficiency in this region rises.
The efficiency of the vertex and track link requirement is about 92%. It is shown in figure 6.9 for data and MC after correction as a function of the polar (θelec) and azimuthal (φelec) angles of the scattered electron, and in the (Q2, x) bins used for the cross section measurement in figure 6.10. The efficiency corrections are deter-mined and applied to MC separately for each helicity sub-period of the data taking to account for small time dependent effects. An uncorrelated uncertainty due to the vertex and track finding is assigned to be 3% for 2003-04 e+p and 2% for 2005 e−p data set.
The knowledge of the primary z vertex distribution is also needed for the luminosity determination. The luminosity is calculated in the same region inzvtx,|zvtx|<35 cm, as is required for the analysis event selection. For the luminosity determination it is assumed that the primary z vertex distribution is gaussian, accompanied by two satellites of gaussian form, located at z = ±70 cm. Effects like nuclear interactions or imperfections of the beam optics add non-gaussian tails. Also an event occurring within ±35 cm could be wrongly reconstructed outside ±35 cm. The uncorrelated systematic uncertainty due to imperfect knowledge of the zvtx distribution is con-servatively estimated to be 0.5%. It appears as an additional normalisation error.
This error was estimated studying migrations of events in the tails of the z vertex distribution.
cell layer 2 cell layer 1 cell layer 0
Figure 6.11: Schematic view of the BBE octant. The filled areas indicate the regions where there is no overlap with the CB1 wheel viewed along the z axis. The hatched areas in the plot corresponds to the non-instrumented part of the BBE.
polygon) structure with an inner radius of 105 cm. The z coordinate of the intersec-tion of the extrapolated track and the reference surface is called z impact position.
The well defined reference surface has the advantage, in contrast to the cluster posi-tion, to be independent of the longitudinal shower development of the electron cluster.
In case, the electrons enters the BBE through the front face of the BBE wheel, in a region where there is no overlap with the CB1 wheel (these regions are shown in figure 6.11), the z impact position corresponds to the front face of the BBE at z =−152.5 cm.
6.5.2 Alignment of the LAr Calorimeter
The precise reconstruction of the event kinematics requires the exact relative align-ment of the different detector components. Therefore, the knowledge of the relative position of the LAr calorimeter and the central tracking system is crucial. The latter measures the interaction vertex for each event and defines the H1 coordinate system.
During the assembly of the LAr calorimeter, the wheels were pushed successively into the cryostat where they reside on supporting rails without a fixed connection among each other. The cool down to LAr temperature at about 72 K causes shrinkage of the LAr calorimeter wheels, in particular, in the z direction. Since the dimensions of the LAr calorimeter have been determined at room temperature, the change of the LAr calorimeter dimensions due to the low temperatures of the liquid argon should be corrected for [103]:
zcold = 23.67 cm +(zwarm−23.67 cm )·(1−0.0027) It corresponds to a 0.7 cm shift in z in the IF region (z = 292 cm).
An alignment of the LAr calorimeter relative to the tracking system is performed using the scattered electrons in the neutral current events. The procedure is based on the comparison of the position of the scattered electron measured in the LAr calorimeter with an associated CJC track extrapolated to the electron cluster. The alignment is performed for the data only since in MC the detectors are aligned by construction.
True position
of the LAr calorimeter
LAr position
assumed in reconstruction
∆y
Figure 6.12: Illustration of the ∆φ method.
The LAr calorimeter is aligned to the central tracking system by three rotations and three translations, defined in equations 6.4-6.6 and 6.7 respectively:
Rotations
x1 =x0 y1 =y0cosα−z0sinα z1 =z0cosα+y0sinα (6.4) x2 =x1cosβ+z1sinβ y2 =y1 z2 =z1cosβ−x1sinβ (6.5) x3 =x2cosγ−y2sinγ y3 =y2cosγ+x2sinγ z3 =z2 (6.6) where the subscript 0 refers to the point position in the unaligned coordinate system, and the subscripts 1, 2 and 3 refers to the coordinates of the point after a rotation of the coordinate system around the x,y and z axises respectively. Here, α, β and γ are the angles of rotation around the x, y and z axises, respectively.
Translations
xf =x3−∆x, yf =y3−∆y, zf =z3−∆z, (6.7) where ∆x, ∆y and ∆z are translations in x, y and z directions.
In thexandydirection these three rotations and translations of the LAr calorimeter with respect to the CJC are seen as z dependent shifts in ϕ of the cluster position with respect to the expected position defined from the tracker, as shown in figure 6.12.
These shifts are studied by looking at ∆φ=ϕtrack−ϕcluster as function ofϕin slices of zLAr (so-called “∆φ-method”), which in case of misalignment has a sinusoidal form, as it is illustrated at the figure 6.13. The ∆φ distributions for the slices are then simultaneously fitted and the alignment constants are extracted.
The ∆φ-method is not sensitive to translations in the z direction. Therefore such translations are studied looking at ∆θ = θtrack −θcluster (“∆θ-method”) as function
< -80) / rad (-100 < z
Larϕ
-2Tr 0 2/ mrad
Clϕ -
Trϕ
-20 -15 -10 -5
< -80) / rad (-100 < z
Larϕ
-2Tr 0 2/ mrad
Clϕ -
Trϕ
-20 -15 -10 -5
Figure 6.13: Illustration of the
∆ϕ-method. ∆ϕ = ϕtrack − ϕcluster, as a function of ϕof the track for the z slice −100 cm <
zLAr <−80 cm, shown for data (full points). The curve repre-sents results of the alignment fit.
of ϕin slices of zLAr in a similar way as for the ∆φ-method.
The applied alignment constants are listed in table 6.2.
rotations:
α= +0.0 mrad around x β =−0.9 mrad around y γ = +0.0 mrad aroundz translations:
∆x=−0.14 cm inx
∆y= +0.40 cm iny
∆z = +0.00 cm in z
Table 6.2: The alignment parameters of the LAr calorimeter.
.
In figure 6.14 the effect of the alignment of the LAr calorimeter is shown. The figure shows that after alignment the ∆x, ∆y and ∆z differences between the position of the cluster and the entrance of the track to the LAr are very close to zero, and well described by MC which is intrinsically aligned.
The CJC and LAr measurements of the scattered electron polar angle θe are com-pared after alignment in figure 6.15, as a function of ϕ and the electron z impact position in the LAr calorimeter. They are in reasonable agreement. The remaining differences of the LAr to the CTD angle measurements are described by MC well within the quoted systematic uncertainty of 3 mrad. These differences may be at-tributed to the lack of precise z measurement from CJC. CIP and COZ are presently unable to improve the precision of the θ determination.
6.5.3 Azimuthal and Polar Electron Angles
The most accurate measurement of the azimuthal angle ϕe is provided by the CJC which is optimised for r−ϕmeasurements. Therefore, if a DTRA track is matched with the scattered electron, ϕe is taken from the track. When no track is associated to the scattered electron, the azimuthal angle is determined using the position of the
/ cm zLar
-100 0 100
) / cmφ∆ x ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmφ∆ x ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmφ∆ x ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmφ∆ x ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmφ∆ y ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmφ∆ y ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmφ∆ y ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmφ∆ y ( ∆
-1 -0.5 0 0.5 1
/ cm zLar
-100 0 100
) / cmθ∆ z ( ∆
-2 0 2 4
/ cm zLar
-100 0 100
) / cmθ∆ z ( ∆
-2 0 2 4
/ cm zLar
-100 0 100
) / cmθ∆ z ( ∆
-2 0 2 4
/ cm zLar
-100 0 100
) / cmθ∆ z ( ∆
-2 0 2 4
Figure 6.14: Track cluster matching before (left) and after (right) alignment for data (full points), compared to the simulation (open points). The shifts ∆x and
∆y, determined using the ∆φ-method, and ∆z, using the ∆θ-method, are shown as function of the z impact position of the scattered electron in the LAr calorimeter.
cluster in the LAr calorimeter and the interaction vertex.
The z information provided by the CJC is poor due to the inferior z resolution.
Therefore, the polar angle measurement θe is taken from the LAr clusters.
Electron tracks entering the Forward Track Detector are difficult to control. Elec-trons tend to shower in the dead material between CJC and FTD. Therefore, in the forward region, θe <30◦, the calorimeter cluster is used both for the azimuthal and polar angle measurements.
/ 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
.