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VELO Mechanical Constraints

1. The context

We have to consider two different types of misalignments: In each cases we have 6 possible sources of misalignment: 3 translations and 3 rotations. These parameters are defined in the figure shown below.

1. Definition of the 6 degrees of freedom

<XYZ> is the VELO reference frame, where Z axis is related to the beam direction. VELO movements during the experiment are possible. During each LHC fill, the two halves are retracted by 3cm along the X axis, in order to protect the sensors. Apart from these movements, precise translations along X and Y axis are possible in order to align transversely the halves with the beam.

Other movements, in particular those concerning individual sensors, couldn't be corrected mechanically. These positions will be very precisely measured before the start of the experiment, and then they will be corrected only by the alignment software.

However, small movements during the runs are still possible, and if we want to develop a proper correction algorithm, the scale of those potential movements should be small and evaluated.

These scales are presented and discussed in the next parts. The effects of these misalignments are presented on a specific page.

2. Half-box misalignments scales (NIKHEF)

2.1 Translations

Alignment of the detector halves is expected to be done with a 0.5mm accuracy at the installation. However, as we said in the previous part, detector halves could be mechanically translated on x and y axis. The scale of these translations is +/- 5mm with an expected precision of 5 micrometers.

We then have the following misalignment scales for the translations: 50 to 100 micrometers.

Nevertheless, these are expected values, and measurements should be performed in order to confirm these assumptions. One would find up-to-date information about the expected accuracies by looking at HenkJan Bulten's presentation at the last LHCb tracking & alignment workshop.

2.2 Rotations

Rotations are more critical, since they couldn't be corrected mechanically when VELO is on operation. In particular, rotations around X and Y axis will lead to bad vertex fit efficiency. Rotation around Z seems less annoying "a priori", however its effect (on overlap tracks for example) should be estimated.

So far, only Y axis rotation scale is referenced. A 0.05mrad mechanical accuracy is expected. As a first approximation, we could expect the same scale for X and Z axis. However, as for the translations, detector halves potential rotations had to be precisely measured.

3. Sensor misalignments scales (LIVERPOOL)

3.1 Translations

According to VELO TDR, a 20 micrometers alignment of each individual modules within an half box is required. Then, the sensors are expected to be aligned to the module base with a 10 micrometers accuracy, and alignment between R and Phi sensor could be obtained by construction with a precision better than 5 micrometers.

A raw estimation thus lead to the following mechanical misalignment scales for individual translations in X, Y, and Z: 40 micrometers.

But, as in the half detector case, this values had to be experimentally confirmed. In particular, thermal effects and sensor mechanical deformations (when the sensor is on hybrid) should be extensively studied.

3.2 Rotations

Precise informations concerning individual sensors rotations are missing. However, individual sensors misalignment study shows clearly that if rotations around X and Y axis are not to worrying for physics measurements, rotations around Z axis could have a large effect. A 5mrad Z rotation will lead to a track efficiency reduction of 30%.

But we need to know the mechanical accuracy which is expected for rotation parameters.

4. Conclusion

Mechanical constraints on misalignments parameters should be measured. Even if we could use the expected values for misalignment effects studies, precise estimations will be useful for alignment algorithm development, and in order to dertermine the relevant parameters.