Yair Mahalalel, Feb. 17th MMX

Complementary to optical/mechanical alignment.

Advantages – 6D alignment Generated from experimental dataDisadvantages – Module alignment is only relative to other

modules (only option for most modules) Requires available tracks, ideally a working

collider

Relies on /Tracking/TrkAlignment , a generic reimplementation of the inner detector toolset which has been developed for many years

Provides all the necessary services, database interfaces etc. out of the box

Uses ATHENA reconstruction and tracking for state of the art handling of data

Minimization of Where V is the covariance matrix and are the residuals Requires calculating

either analytically or numerically.

tracks

T rVr 12

kaemr iiiˆ)),((

0000 da

dr

a

r

da

dr

Is implicit in the analytical derivative calculation. Incorrect when large non-uniformity exists along

a chamber, e.g. in the MDTs. Can neither be used when aligning compound

modules (e.g. wheels). In these cases the derivatives are calculated

numerically by shifting and rotating the module and refitting the track. Adds computation complexity and non-trivial parameter dependence.

Currently a software design flaw prevents chamber shifting because TGC hits are combined to form a CompetingRIOsOnTrack measurement, generating a new surface which is the average of individual hit surfaces.

The new surface is not connected to the module so the shifting the module doesn’t move the hit.

A new approach is currently being tested.

Implementation complete – Level 3 (single chamber) align modules Using analytical derivatives Geometry transformations Debug ntuples Alignment DB I/O

AMDB geometry description difference between TGC and MDTs

Various enhancements to generic tools to support 2D chambers and second coordinate measurements

Off by 2 chamber phi indexing

Found in AnalyticalDerivCalcTool by CSC aligners

Triggers when a single chamber has one 1D measurement (wires) and one 2D (strips)

Might explain strange behavior when running 6D alignment

Patch received a few days ago. Will be validated by us.

GeoModel support for aligning individual endcap TGC modules doesn’t exist yet – no code to read chamber eta index.

A fix should be comitted in a couple of weeks by Stefania Spagnolo.

Typical A-line in ASZT file –W Stat jff jzz job Translations RotationsA T1E 1 2 0 1.234 1.234 1.234 0.00123 0.00123 0.00123

Convergence slow and erratic, and to the wrong point.

Implementation complete but validation is proving more confusing and slow than expected

Currently known problems are in external services (but are being fixed)

Hopefully once we finish validating these fixes we’ll start seeing more reasonable results

Then – more serious validation of our code using MC and real data

Backup slides

Corrections to nominal chamber locations are collected from various sources –

Optical sensors Resistive sensors Track based alignmentThe corrections specific for every run are

applied by GeoModel at ATHENA initialization.

Huge problem – thousands of modules to align

Many approaches – Robust method – fits distributions to

tracks Local fit – needs many iterations Global fit – few iterations, but

potentially huge memory requirement.Algorithms also vary by their ability to

handle magnetic fields (curved tracks), multiple Coulomb scattering, etc.

22

Main methodology – minimization of global error

Where V is the covariance matrix and the

Are the measurement residuals, defined as the distance between measurements and intersection of track with the sensor plane.

tracks

T rVr 12

kaemr iiiˆ)),((

The intersection of the extrapolated track with the sensor plane depends on two parameter sets –

The track parameters

The align parameters

}/),(cot,,,{ 000 Tpqanza

},,,,,{ ZYXZYX RRRTTTa

Should be diagonal, or at least block diagonal within the module but rarely is because of –

Multiple Coulomb scattering Additional constraints (event main

vertex)

The equation which needs to be solved is

In order to solve it we need to calculate the full derivative

Under the linearity assumption that for small enough changes.

02

a

0000 da

dr

a

r

da

dr

02

ji

r

The linear expansion around the original yields the equation

With the solution

0

0)),((0

01

0

r

arVrT

),( 01

0

1

0

1

000 arV

rrV

r TT

We can look at this expression for as function of and use its derivative to rewrite the full derivative as

Where

a

0

111

0

))(1(a

rVEEVEE

da

dr TT

0

r

E

Similarly to our track parameter treatment, we can write the equation for the align parameter derivative –

Where

tracks

T

tracks a

T

arVda

dra

da

drV

da

dr0),( 00

1

0

1

0

tracks

T

tracks

T

aWra

r

a

rW

a

ra ),( 00

0

1

00

111111 )(ˆ VEEVEEVVWVW TT

We define the unit vectors crossing the strips,

along the strips and perpendicular to the sensor plane. The two residuals are then

And their derivatives with respect to a

general parameter are

X

Y Z

Yemres

Xemres

Y

X

ˆ)(

ˆ)(

Ydp

ed

p

res

Xdp

ed

p

res

Y

X

ˆ

ˆ

The intersection of the path length with the detector plane, , is given by the equation

Which is solved iteratively. Can now be written as .

Since is an implicit function of ,

intl0ˆ)( Zme

dp

ed

dp

dl

l

e

p

e

dp

ed int

int

intl p

int

int

)ˆ(

)ˆ(

lZe

pZe

dp

dl

The residual derivatives can now be written as

where

Or using local track direction of ,

Zlele

p

e

p

res

ˆ

ˆ

ˆ

int

int

YX ,

),(

ZYp

e

p

res

ZXp

e

p

res

Y

X

ˆ)tan()sin(ˆ

ˆ)tan()cos(ˆ