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Update on Global Alignment Steven Blusk Syracuse University

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- The LHCb detector alignment will require several steps. A sensiblescenario is:
- Internal Alignment of the VELO (first halves, then to each other)
- Internal alignment of T-Stations (IT, OT and IT-to-OT)
- Relative alignment of VELO to T-Stations
- Alignment of TT to VELO-T Station system
- Alignment of ECAL & HCAL to tracking system
- Alignment of MUON to tracking system
- Alignment of RICH to tracking system

The internal alignment tasks are being addressed by various groups.

Here, I present a plan and details for Step 3.

Simulations consistent of 5000 event samples of min bias usingGauss v22r1, Boole v10r3, Brunel v28r2

- After internal alignment of each, there are in principle 9 global transformations between the two systems:
- 3 translations (X,Y,Z)
- 3 rotations (a,b,g)
- 3 scale factors (Xscale, Yscale, Zscale )

- In practice, Xscale, Yscale are highly constrained by the interwire/strip spacing. Therefore there are realistically 7 global parameters between the two systems.
- Align the VELO to the T-Stations by matching segments at the center of the magnet (Zmag).. Pattern recognition done independently in each system.
- They can all be measured using MAGNET OFF data:
- DX: Mean of XVELO-XT at Zmag.
- DY: Mean of YVELO-YT at Zmag.
- DZ: Mean of (XVELO-XT)/tanqXVELO at Zmag.
- Da: Mean of tanqYVELO-tanqYT.
- Db: Mean of tanqXVELO-tanqXT
- Dg: Mean difference in azimuthal angle fVELO-fT at Zmag.
- Zscale: Mean of (tanqXVELO-tanqXT) / tanqXVELO

- We use a single kick approximation to the field, where the kickoccurs at the effective center of the magnet (Zmag).
- This is only an approximation, and in general Zmag is a function of the track’s X,Y slopes and momentum.
- To minimize dependence, we can require high momentum, low angle trackssince we are only seeking global alignment parameters. We require:
- p > 20 GeV/c (no p cut for B=0, for the moment)
- VELO angles < 100 mrad
- TX-seed angle < 200 mrad (Ty–seed constrained since Py ~unchanged)

- Zmag is determined using simulation, with “perfect geometry” and field045.cdf. We map out using the straight line intersection of T-seed and VELO tracks:
- Zmag = 526.7 cm, and has a mild dependence on X angle.
- We correct for it, but it’s not critical to determine global offsets.

- Correction to Y-slope in T-Station for change in Pz.

- Zmag = 526.7 cm, and has a mild dependence on X angle.

No Zmag,since nobending

DSlopeY

Zmag

All meansare consistentwith zero !

DX at Zmag

DY at Zmag

DZ

Dg at Zmag

No Zmag,since nobending

DSlopeY

Zmag

<DX>=(942±31) mm

DX at Zmag

DY at Zmag

All other meansconsistentwith zero !

DZ

Dg at Zmag

DSlopeY

Zmag

<DY>=(4981±55) mm

DX at Zmag

DY at Zmag

All other meansconsistentwith zero !

DZ

Dg at Zmag

All other meansconsistentwith zero !

DSlopeY

Zmag

DX at Zmag

DY at Zmag

<DZ>=(1.25±0.12) cm

DZ

Dg at Zmag

All other meansconsistentwith zero !

DSlopeY

Zmag

DX at Zmag

DY at Zmag

<Dg>=(2.03±0.16) mrad

DZ

Dg at Zmag

DSlopeY

Zmag

DX at Zmag

DY at Zmag

<Dg>=(0.47±0.31) mrad

All meansconsistentwith zero !

DZ

Dg at Zmag

DSlopeY

Zmag

<DX>=(1036±23)mm

DX at Zmag

DY at Zmag

All other meansconsistentwith zero !

DZ

Dg at Zmag

DSlopeY

Zmag

<DY>=(5049±71) mm

DX at Zmag

DY at Zmag

All other meansconsistentwith zero !

DZ

Dg at Zmag

All other meansconsistentwith zero !

DSlopeY

Zmag

DX at Zmag

DY at Zmag

<DZ>=(1.07±0.11) cm

DZ

Dg at Zmag

All other meansconsistentwith zero !

DSlopeY

Zmag

DX at Zmag

DY at Zmag

<Dg>=(2.56±0.30) mrad

DZ

Dg at Zmag

DSlopeY

Zmag

In: DX= - 250 mm

Out: DX= - (249±23)mm

In: DY= 250 mm

Out: DY= (188±50)mm

DX at Zmag

DY at Zmag

In: Dg = 2 mrad

Out: Dg = (2.38±0.33)mm

In: DZ = 4 mm

Out: DZ = (3.1±1.1) mm

DZ

Dg at Zmag

Still need to check rotations around X,Y axes and Z-scale but don’t expect any surprises

- Matching at the center of magnet appears to provide robustestimate of relative alignment between VELO and T-Stations.
- 5000 min bias events gives reasonably good precision on offsets(Scale by 1/N to get a given precision)
- Still need to check Da and Db and Z-scale, but don’t expectany surprises.
- Document in progress. Full description of LHCb alignment needsto be put together. This is one piece of it.
- Migrate (PAW) code to ROOT-based GaudiAlgorithm.

Many thanks again to Matt , Eduardo, Juan and Marco Cattaneo for lots of help with software issues…