Velo to T Alignment - ReminderGeneral StrategyGeneral Strategy Perform relative VELO-to-IT/OT alignment using Perform relative VELO-to-IT/OT alignment using X,X,Y at the center Y at the center of magnet and of magnet and XX,,Y Y (each vs X, Y).(each vs X, Y).

X, X, Y, Y, XX, , Y Y must all peak at 0 (vs X, Y, as well) for proper must all peak at 0 (vs X, Y, as well) for proper alignmentalignment With magnet OFF data the 7 relative misalignments can be determinedWith magnet OFF data the 7 relative misalignments can be determined

– 3 translations, rotation around Z axis, Shearing along X, Y, & Z scaling3 translations, rotation around Z axis, Shearing along X, Y, & Z scaling

X, X

~ 4 meter trackprojection

One bothersome Issue• Alignment first done with field OFF.• 3 translations and 3 rotations determined.• Once magnet is turned ON and T & VELO

realigned.• How do we know that we did not induce a small

kink, or rotation angle between the two systems?• Simple check:

– The effective center of the magnet should be the same for both positive & negative charge

VELO

The geometry

Can easily calculate the shift

int( )(tan tan )T V

T Station

z zMagnet

Z zMagnet

Where: Zint = intersection point of VELO and T-Station track zMagnet = 5294 = nominal center of curvature zTstation = center of T station system = 8634 tanT,V are X slopes in T-Stations and VELO

Simulate a 1 mradrotation.1000 min bias events

Separation by chargeClear separation

Peak at 1 mrad, as expected

Error on meanfor this 1K events ~ 50 rad(rough, not fit yet)

Clearly will scalewith Ntracks..

Recall single track angularresolution ~0.3 mrad

Need to check a couple of things, but seems simpleenough…