Héctor Alvarez PolHéctor Alvarez Pol 16 December 2002

On the Multiwire Drift On the Multiwire Drift Chambers alignment of Chambers alignment of

the HADES dilepton the HADES dilepton spectrometerspectrometer

INDEX

Part I The HADES Physics

Part II The HADES spectrometer

Part III Overview of the drift chambers alignment

Part IV Alignment using hardware methods

Part V Alignment using software algorithms

Conclusions

PART ITHE HADES PHYSICS PROGRAM

THE HADES PHYSICS PROGRAM

Heavy ion collisions at SIS energies

THE HADES PHYSICS PROGRAM

Heavy ion collisions at SIS energies

THE HADES PHYSICS PROGRAM

Heavy ion collisions at SIS energies

THE HADES PHYSICS PROGRAM

Heavy ion collisions at SIS energies

Want to know! Observables

Behavior of the High Density Phase

• Partial restoration of the chiral symmetry

In-medium change of ρ, ω, φ masses

M (MeV/c2) Γ (MeV/c2) cτ (fm)

ρ0 769.3 150.2 1.3

ω 782.6 8.4 23.4

φ 1019.4 4.5 44.4

• Equation of State (EOS)

• Astrophysics: neutron stars and inner stars structure

In-medium dilepton decays are not affected by strong interactions!

THE HADES PHYSICS PROGRAM

In-medium vector meson decay

External vector meson decay

Dilepton invariant mass spectra

THE HADES PHYSICS PROGRAM

These series of experiments, exploiting the full range of primary and secondary beams available at GSI,

are expected to make important contributions to our understanding of Quantum Chromodynamics in the

non-perturbative regime and, in particular, will provide information on the origin of hadron masses.

From The HADES Physics Program, J. Friese and V. Metag

THE HADES PHYSICS PROGRAM

PART IITHE HADES SPECTROMETER

THE HADES SPECTROMETER

HADES installation at GSI

Flat acceptance in mass and in transverse momentum

Rejection of hadronic and electromagnetic background

which could obscure the dilepton signal

Low mass materials

are chosen in all detectors and support structures to minimize the multiple scattering

A selective trigger scheme

able to accept only those events with lepton pairs, mainly those of high mass

Excellent mass resolution ( m/m 1 % (σ) at ω mass) should allow the individual

identification of the vector mesons

Capability to deal with high count rates

and large particle multiplicities

to accumulate enough significant events in a finite time

Large dilepton acceptance

(~40% for lepton pairs), required because of the tiny dilepton branching ratio, of the order of 10-5. Allows the comprehensive studies of the behavior of vector mesons

in the nuclear medium

Large dilepton acceptance

Excellent mass resolution

High count rates

Large particle multiplicities

Rejection of hadronic and em. background

Flat acceptance in mass and in mT

Low mass materials

A selective trigger scheme

THE HADES SPECTROMETER

HADES features

Large dilepton acceptance

Excellent mass resolution

High count rates

Large particle multiplicities

Rejection of hadronic and em. background

Flat acceptance in mass and in mT

Low mass materials

A selective trigger scheme

THE HADES SPECTROMETER

RICH: Ring Imaging Cherenkov Detector

RICH

THE HADES SPECTROMETER

RICH: Ring Imaging Cherenkov Detector

RICH

THE HADES SPECTROMETER

RICH

MDCs: Multiwire Drift ChambersMDCs

MDCs

THE HADES SPECTROMETER

RICH

MDCs: Multiwire Drift ChambersMDCs

MDCs

THE HADES SPECTROMETER

RICH

MDCs: Multiwire Drift ChambersMDCs

MDCsMDC features:

• High position resolution

• Two track detection ability

THE HADES SPECTROMETER

• Operation on Isobutane-Helium mixture to reduce the multiple scattering

ILSE: Superconducting Toroidal Magnet

RICH

MDCs

MDCs

ILSE

THE HADES SPECTROMETER

RICH

MDCs

MDCs

ILSE

TOF: Time-of-Flight Detectors

TOF

TOF

THE HADES SPECTROMETER

Pre-Shower: Electromagnetic/Hadronic Shower Detector With Lead Converters

RICH

MDCs

MDCs

ILSE

TOF

TOF

Pre-Shower

Pre-Shower

THE HADES SPECTROMETER

RICH

MDCs

MDCs

ILSE

TOF

TOF

Pre-Shower

Pre-Shower

TOFino: lower angle Time-of-Flight

TOFino

THE HADES SPECTROMETER

PART IIIOVERVIEW OF THE DRIFT CHAMBERS ALIGNMENT

OVERVIEW OF THE DRIFT CHAMBERS ALIGNMENT

• Revision of the momentum reconstruction methods in the spectrometer

• Simulation of the misalignment effects on the reconstructed momentum

• Analysis of the architectural design and evaluation of the technical resources

• Definition of a specific alignment scheme

Steps towards the HADES alignment system

The tracking system

OVERVIEW OF THE DRIFT CHAMBERS ALIGNMENT

Opposite directions for e - and e+

Approx. linear behavior

Dependent on the misaligned MDC

OVERVIEW OF THE DRIFT CHAMBERS ALIGNMENT

• Maximum misalignment of the MDCs (according to Physics criteria):Δy ~ 50 μm along the particle magnetic kick direction

• Also allows the determination of maximum deviation in the tilt angles

Momenta between 400 and 600 MeV/c

Electrons Positrons

MDC Δp/p (%/100μm) Δp (MeV/c/100μm) Δp/p (%/100μm) Δp (MeV/c/100μm)

I -0.21 -1.1 -0.32 -2.2

II 0.13 0.7 0.19 1.3

III 0.34 1.7 0.47 3.3

IV -0.27 -1.4 -0.37 -2.6

OVERVIEW OF THE DRIFT CHAMBERS ALIGNMENT

Simulation results

After the analysis of the architectural design and the evaluation of the allowable displacements of the support structures and other constraints, the proposed and implemented alignment scheme consist of:

• Software algorithms, based on the analysis and minimization of residuals or other functions of the hits in the drift chambers, using data samples with the magnetic field off.

• Hardware sensors (RASNIK), monitoring the relative displacements of the external MDCs with respect to the inner ones, during the data taking period.

OVERVIEW OF THE DRIFT CHAMBERS ALIGNMENT

PART IVALIGNMENT USING HARDWARE

METHODS

ALIGNMENT USING HARDWARE METHODS

RASNIK: Red Alignment System from NIKHEF

Two emitters on the external MDCs frame

Camera and lenses fixed to the internal

MDCs frame

IR light path

ALIGNMENT USING HARDWARE METHODS

2. Aperture of the lens

ALIGNMENT USING HARDWARE METHODS

Parameters of the innovative setup 1. Angle between the sensor plane and the image plane

Experimental setup

ALIGNMENT USING HARDWARE METHODS

• The resolution improves for the smallest apertures

• The resolution is practically independent of the incident angle

• For α ≥ 30°, the analysis module starts to fail

Selected setupLens aperture 15 mmAngle with sensor plane 25°

Conclusions:Resolution analysis procedure

Second order polynomial fit

Binocular design

Epoxy Carbon Fiber: KT = - 0.5x10-6 K-1

ALIGNMENT USING HARDWARE METHODS

Binocular

ALIGNMENT USING HARDWARE METHODS

Optical axis adjustments Focus adjustment

Mask and LEDs supports

ALIGNMENT USING HARDWARE METHODS

IR LEDs Matrix Mask Mount

ALIGNMENT USING HARDWARE METHODS

Stable calibration terms in different parts of the mask

Stable calibration terms for different masks

Calibration

RAHAD online monitor

• Internal raw data check• ROOT graphics facilities

EPICS Operator Screen

• Distributed monitor screens• Archiver facilities

ALIGNMENT USING HARDWARE METHODS

Complete data sample

Reduced data sample

XMDC YMDC

ZMDC

Complete data sampleσ( XMDC ) = 3.86 μmσ( YMDC ) = 4.64 μm σ( Z MDC ) = 6.88 μm

Reduced data sampleσ( XMDC ) = 1.23 μmσ( YMDC ) = 1.55 μm σ( Z MDC ) = 2.5 μm

ALIGNMENT USING HARDWARE METHODS

Resolution estimation

Correlation with the magnetic field

Correlation with the temperature of the MDC frames

ALIGNMENT USING HARDWARE METHODS

Experimental results

PART VALIGNMENT USING SOFTWARE

METHODS

ALIGNMENT USING SOFTWARE METHODS

Coordinate transformations

BBB

AAA

TXRX

TXRX

MDC to Lab:

VXMX AB

MDC to MDC:

A1

B RRM

BA1

B TTRV

where

221202

211101

201000

MMM

MMM

MMM

M

and

for instance

sinsincoscoscosM00

Variables: ))y(S),x(S,y,x(X

Hit compatibility and sample selection

)X(V)X(

21

expV)2(

1)X(f 1T

2

Probability density function:

4

)y(Sy

2ySy

2)y(S

2

2y

2

2ySy)x(Sx

2xSx

2)x(S

2

2x

2

2xSx

)y(Sy2)y(Sy

11

)x(Sx2)x(Sx

11

Equiprobability volume (hyperellipsoids on α4):

ALIGNMENT USING SOFTWARE METHODS

Three MDCs alignment algorithm

Then, minimize

with:

should be zero for each track.

Tracks

Q)(sin

)(sin22

222

)y(yQ

)x(xQ

)y(yQ

)x(xQ

)y(yQ

)x(xQ

)(sin

C2

2

CC2

2

CB2

2

B

B22

BA2

2

AA2

2

A22

ba

basin

2A02z

A01y

A00x

222

xA01y

A00z

zA00x

A02yy

A02z

A01x44A

baMaMaMabbabMbMba

bMbMbabMbMbaba

2xQ

where, for instance:

a

b

BCBCBC

zyx

BABABAzyx

zz,yy,xxb,b,bb

zz,yy,xxa,a,aa

A B

C

ALIGNMENT USING SOFTWARE METHODS

If one parameter is fixed to the correct value

The problem reduces to find out a set of histograms which univocally defines thecorrect value of the fixed parameter.

ALIGNMENT USING SOFTWARE METHODS

Convergence inside the allowable error

Below 50 μm

Simulation results

How to fix the angular parameter

ALIGNMENT USING SOFTWARE METHODS

b b

a

b

c c

c

a a8.6x10-5

2.06x10-3

-1.93x10-3

Abscissa for y=0-6.6x10-5

November 2001 alignment: three MDCs algorithm

ALIGNMENT USING SOFTWARE METHODS

• The uncertainties in the calibration procedures and hit fitting tasks lead to hits with incompatible slopes on the MDCs.• As a consequence, the uncertainty intervals for the alignment results in Nov01 are slightly larger than expected (~100 μm for MDCs I-II, ~300 μm for MDCs II-III).

Differences in mrad

Two MDCs alignment

ALIGNMENT USING SOFTWARE METHODS

Minimization of the residuals:

2

)y(xS

2

)y(yS

2

)x(xS

Tracks

2

)y(S

2

)x(S

2

y

2

x

2

)y(SxW

2)y(Sy

W2

)x(SxW

2

)y(SW

1)x(S

W1

yW1

xW1

Q

Analytical minimization with respect to the components of the

translation vector:

0W

)y(S2W

)y(S2W

)x(S2Wy2

Wx2

VQ

0W

)y(S2W

y2VQ

0W

)y(S2W

)x(S2W

x2VQ

i )y(xS

xii

)y(yS

yii

)x(xS

xii

y

yii

x

xii

2

2

i )y(yS

i

y

i

1

2

i )y(xS

i

)x(xS

i

x

i

0

2

The solution is the relative translation

vector V=(V0,V1,V2)

ALIGNMENT USING SOFTWARE METHODS

Geometrical determination of the relative rotations,

for instance, in-plane rotations:

Two MDCs alignment

cosysinx'y

sinycosx'x

θ

ALIGNMENT USING SOFTWARE METHODS

Two MDCs alignment

Iterative approach to the solution:

1. Sample selection2. Analytical minimization of the

translation (vector V)3. Geometrical correction of the

rotation (rotation matrix M)

Below 50 μm

Simulation results

Convergence inside the allowable error

ALIGNMENT USING SOFTWARE METHODS

The Target Finder algorithm1. Analytical minimization of:

2. Iterative approach to the solution using bi-squared Tukey

weights

)z,y,x(dwQ ttt2i

ii

2

ALIGNMENT USING SOFTWARE METHODS

November 2001 alignment: two MDCs algorithm

Mean:-7.8x10-3

Mean:-4.5x10-3

ALIGNMENT USING SOFTWARE METHODS

Beam line reconstruction after alignment

Beam line (Z)

Track

ρ

θ

ALIGNMENT USING SOFTWARE METHODS

November 2002 “Last minute” result

Double target reconstruction

20mm

Very preliminary alignment

CONCLUSIONS

In this work, several tools and methods have been developed to obtain the relative alignment of the Multiwire Drift Chambers (MDCs), the main tracking detectors in the

HADES spectrometer.

• In a first step, the requirements on the resolution in the reconstructed momentum and the invariant mass of the lepton pair, have been expressed as maximum deviations in the knowledge of the relative displacements and rotations of the MDCs.

• A set of RASNIK devices has been considered as optimal solution for the hardware monitoring and a specific RASNIK configuration has been developed.

The influence on the resolution of both the light incidence angle onto the camera and the lens aperture have been studied.

CONCLUSIONS(1)

• The implementation of the RASNIK devices in the spectrometer has required the design of custom-made pieces. This task has been accomplished from the mechanical design of all pieces up to the final installation in the spectrometer.

•A complete monitoring program (RAHAD) has been developed. It performs a data calibration and transformation, according to the coordinate systems of the MDCs, as well as the interface with the EPICS “HADES Slow Control System”.

• Once the RASNIK setup was installed on the spectrometer, its performances below the requirements were confirmed.

The RASNIK results have been successfully correlated with temperature changes and with the magnetic field forces. The RASNIK monitoring results have been used to correct the alignment parameters obtained by software methods.

CONCLUSIONS(2)

• Regarding the software methods, several iterative algorithms have been developed in order to obtain the relative alignment parameters between MDCs.

Two different algorithms has been developed, for those sectors with three or two MDCs.

The use of the “Two MDCs algorithm” includes the determination of the target position, implemented in the so-called “Target Finder” algorithm. The “Three MDCs algorithm” has been chosen as the main method to obtain the position parameters.

• The different algorithms have been first tested under simulation, checking their convergence to the correct parameters. The errors have been estimated and the resolution in the determination of the relative alignment parameters fulfils the requirements.

• A set of data has been analyzed (Carbon beam at 1 GeV on a Carbon target, November 2001 run) using the alignment algorithms. The alignment parameters have been estimated, including their uncertainty intervals.

CONCLUSIONS(3)