1. Steven Blusk, Syracuse University -- 1 Update on Global Alignment Steven Blusk Syracuse University

2. Steven Blusk, Syracuse University -- 2 Preface The LHCb detector alignment will require several steps. A sensible scenario is: 1)Internal Alignment of the VELO (first halves, then to each other) 2)Internal alignment of T-Stations (IT, OT and IT-to-OT) 3)Relative alignment of VELO to T-Stations 4)Alignment of TT to VELO-T Station system 5)Alignment of ECAL & HCAL to tracking system 6)Alignment of MUON to tracking system 7)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 using Gauss v22r1, Boole v10r3, Brunel v28r2

3. Steven Blusk, Syracuse University -- 3 Relative VELO-to-T-Station Alignment  After internal alignment of each, there are in principle 9 global transformations between the two systems:  3 translations (X,Y,Z)  3 rotations (  )  3 scale factors (X scale, Y scale, Z scale )  In practice, X scale, Y scale 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 (Z mag ).. Pattern recognition done independently in each system.  They can all be measured using MAGNET OFF data:   X: Mean of X VELO -X T at Z mag.   Y: Mean of Y VELO -Y T at Z mag.   Z: Mean of (X VELO -X T )/tan  X VELO at Z mag.   : Mean of tan  Y VELO - tan  Y T.   : Mean of tan  X VELO - tan  X T   : Mean difference in azimuthal angle  VELO -  T at Z mag.  Z scale : Mean of (tan  X VELO - tan  X T ) / tan  X VELO

4. Steven Blusk, Syracuse University -- 4 Method Details  We use a single kick approximation to the field, where the kick occurs at the effective center of the magnet (Z mag ).  This is only an approximation, and in general Z mag is a function of the track’s X,Y slopes and momentum.  To minimize dependence, we can require high momentum, low angle tracks since we are only seeking global alignment parameters. We require: o p > 20 GeV/c (no p cut for B=0, for the moment) o VELO angles < 100 mrad o T X -seed angle < 200 mrad (T y –seed constrained since P y ~unchanged)  Z mag is determined using simulation, with “perfect geometry” and field045.cdf. We map out using the straight line intersection of T-seed and VELO tracks:  Z mag = 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 P z.

5. Steven Blusk, Syracuse University -- 5 Results with Perfect Geometry: B=0 No Z mag, since no bending Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ All means are consistent with zero !

6. Steven Blusk, Syracuse University -- 6 1 mm X Shift of VELO: B=0 No Z mag, since no bending Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(942±31)  m All other means consistent with zero !

7. Steven Blusk, Syracuse University -- 7 5 mm Y Shift of VELO: B=0 Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(4981±55)  m All other means consistent with zero !

8. Steven Blusk, Syracuse University -- 8 1 cm Z Shift of VELO: B=0 Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(1.25±0.12) cm All other means consistent with zero !

9. Steven Blusk, Syracuse University -- 9 2 mrad Z-Rotation  VELO: B=0 Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(2.03±0.16) mrad All other means consistent with zero !

10. Steven Blusk, Syracuse University -- 10 Results with Perfect Geometry: B=Nom Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ All means consistent with zero ! =(0.47±0.31) mrad

11. Steven Blusk, Syracuse University -- 11 1 mm X Shift of VELO: B=Nom Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(1036±23)  m All other means consistent with zero !

12. Steven Blusk, Syracuse University -- 12 5 mm Y Shift of VELO: B=Nom Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(5049±71)  m All other means consistent with zero !

13. Steven Blusk, Syracuse University -- 13 1 cm Z Shift of VELO: B=Nom Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(1.07±0.11) cm All other means consistent with zero !

14. Steven Blusk, Syracuse University -- 14 2 mrad Z-Rotation  VELO: B=Nom Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ =(2.56±0.30) mrad All other means consistent with zero !

15. Steven Blusk, Syracuse University -- 15 Several Shifts  VELO: B=Nom Z mag  Slope Y  X at Z mag  Y at Z mag  at Z mag ZZ In  X= - 250  m Out:  X= - (249±23)  m In  Y= 250  m Out:  Y= (188±50)  m In  = 2 mrad Out:  = (2.38±0.33)  m In  Z = 4 mm Out:  Z = (3.1±1.1) mm

16. Steven Blusk, Syracuse University -- 16 Summarizing Parameter Varied Input Value B=0 Rec. value B=Nom Rec. value X1 mm ( 0.94±0.04 ) mm( 1.04±0.02 ) mm Y5 mm ( 4.98±0.05 ) mm( 5.05±0.08 ) mm Z1 cm ( 1.25±0.12 ) mm( 1.07±0.11 ) mm  2 mrad ( 2.03±0.16 ) mrad( 2.56±0.30 ) mrad XYZXYZ -0.25 mm +0.25 mm 4.0 mm 2 mrad - ( 0.25 ±0.23 ) mm ( 0.19 ±0.05 ) mm ( 3.1 ± 1.1 ) mm ( 2.38±0.33 ) mrad Still need to check rotations around X,Y axes and Z-scale but don’t expect any surprises

17. Steven Blusk, Syracuse University -- 17 Conclusions  Matching at the center of magnet appears to provide robust estimate 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  and  and Z-scale, but don’t expect any surprises.  Document in progress. Full description of LHCb alignment needs to 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…