Coordinate reconstruction algorithm for high energy

photons in the liquid krypton

calorimeter.

Contents

• LKr calorimeter for KEDR detector.

• Taking into account the geometric factor for photons in a strip layer, where the conversion of a photon into e+e- pair has taken place.

• Experimental setup for measurements of coordinate resolution for photon made with prototype.

• Algorithm for coordinate reconstruction: modified center of gravity and a method based on a neural network.

• Experimental results.

• Conclusion.

Barrel electromagnetic calorimeter for KEDR detector based on 27 tons of liquid krypton is setting into operation. Algorithm for reconstruction of photon coordinate close to conversion point and experimental results obtained with the prototype of the calorimeter will be presented.

KEDR detector

1. beam pipe2. vertex detector3. drift chamber4. time-of-flight system5. barrel LKr calorimeter6. superconductive coil7. muon system8. yoke9. endcap CsI calorimeter10.aerogel cherenkov counters

• KEDR is general purpose detector for experiments at VEPP-4M collider, 2E=2-11GeV• Assembled in March 2000• 2001-2002 experiments for precision measurements of Ψ/Ψ/ mass

LKr calorimeter for KEDR detector

φ-strips

z-strips

towers

ground

Barrel electromagnetic calorimeter based on 27 tons of liquid krypton15X0 , energy resolution 2% / √E(GeV)

- LKr calorimeter was assembled in 2001- technical run in 2002- modification of front-end electronics

• Electrode system is a set of 36 cylindrical ionization chambers with 2cm gap size between electrodes.• Electrodes are made of G10 foiled with copper (0.5mm of G10 + 2x18μm of Cu)

• 2304 towers for energy measurements• 4936 strips for coordinate measurements in both directions, grouped in 8 layers

Angular size of strips is constant: 2π/768 (6-22 mm).

Coordinate layer

Calorimeter is practically homogeneous and has small energy fluctuations in dead material.

For cathode readout the current is shared on a few strips (Swidth~H) and spatial resolution much better than Swidth/√12 can be obtained by weighting the signals from these strips

Compared to the crystal calorimeters where the space resolution is limited by the fluctuations of the shower center of gravity, in the LKr calorimeter considerably better resolution can be obtained thanks to finer granularity and possibility of measurements close to conversion point.

2-3 strips should be used for reconstruction

MIP coordinate, calculated by the center of gravity method is biased from real coordinate:precalculated correction function should be used

Coordinate measurements for MIP

MIP energy loss ~14MeV(3.5 MeV/cm for LKr)

Noise of electronics andradioactivity: σ~0.3 MeV

Tdrift=10μs, Vdrift=2mm/μsτlife=3μs

i

iicg

a

axX

mm mm mm mm

Coordinate measurements for photon (simple model)

For photon geometric factor exist: relative strip amplitudes depends on Z-coordinate of conversion.

In the case of center of gravity method it is difficult to parametrize correction functions. For 2 and 3 strips they have jumps and strongly depend on Z-coordinate

32131

213

31

322 , aaa

aa

aaX

aa

aaXXg

“Generalized” center of gravity (GCG) is suggested. It’s a linear combination of centers of gravity calculated by 2 and 3 strips. The correction function is smooth and continuous, and passes through the center and the edges of the strip.

Correction functions for GCG for real photon (Monte Carlo).

Dependence of Xcg from real photon coordinate and energy deposition in the gap. Noise on strips is added.

Eγ=1000MeV, conversion point distributed uniformly over the gap.

Two area is distinguished: Egap<10MeV (blue points, conversion at the end of the gap),Egap>10MeV (green points, conversion at the beginning of the gap)

In next analysis we use a set of correction functions

MeVEXbbX

MeVEXaaX

gaprealcg

gaprealcg

10),tan(

10),arctan(

21

21

Set of functions used to remove bias in the centerof gravity for several photon energies.

Experimental setup

• Experiment was performed at the ROKK-1M facility of the VEPP-4M collider. • High energy photons produced in the backward Compton scattering of the laser photons on the electron beam. Photon energy range used is 50-1700MeV. • The scattered photons move in the direction of the electron beam to the calorimeter. There are collimator with 1mm split parallel to the strips and scintillating veto counters in front of the calorimeter. • The collimator was moved across the strip direction with accuracy of 0.1mm.

Prototype (400 kg LKr) of calorimeter with similar electrode structure and strip width 10mm.

1- external vessel2- copper shield3- internal vessel4- output cables5- strip electrodesL1-L3 - towers

Algorithm of coordinate reconstruction

• Photon energy is measured in calorimeter towers.• Identification of strip layer where photon conversion is occurred. Threshold on energy deposited in gap is ~1.5 MeV.• Photon coordinate is calculated using 3 strips amplitude. Two different methods were used: general center of gravity and method based on a neural network.

General center of gravity:Coordinate corrected using different correction functions, depending on photon energyand energy deposited in the gap (Egap>10MeV or Egap>10MeV). These functions are calculated from MC simulation.

Method based on a neural network:C-library from package MLPfit is used

4-12-1 network has been triedInputs: a1,a2,a3, a1+a2+a3Output: particle coordinate

Event samples: 10000 photons with energies 50-1700MeV, with Xhit randomly distributed over 3 strips, and random Zc in the gap.

MLPfit: a tool for designing and using Multi-Layer Perceptron Version 1.40Jérôme Schwindling & Bruno Mansoulié http://schwind.home.cern.ch/schwind/MLPfit.html

Photon energy: 800MeV<Eγ<1200 MeV Collimator position: Xcol=-3.6mm

Reconstructed coordinate for GCG and NN (experiment)

Coordinate of CG before (blue hist.) and after (black hist.) S-shape correction. Correction removes shift in coordinate and makes distribution symmetrical.

Coordinate reconstructed with neural network

Averaged over the strip width resolution (MC and EXP, NN and GCG)

Photon energy: 450MeV<Eγ<550 MeV

Distribution over reconstructed by two methods coordinate in MC simulation and experiment for photons with energy 450-550 MeV. X-impact point is spread over the strip width. There is no visible difference between center of gravity method and method based on a neural network.

Averaged spatial resolution as a function of photon energie.

Averaged (over the strip) spatial resolution for photon energies 50-1500 MeV.

The best spatial resolution is obtained in the layer, where the conversion of a photon into e+e- pair takes place (blue line). For photon energy > 1GeV it is determined by the noise. The resolution in the next layer (red line) is worse and is affected by multiple scattering. The results are in a good agreement with Monte-Carlo simulation.

Conclusion

• Algorithm of the photon reconstruction by conversion point in the strip structure of liquid krypton calorimeter is developed. Two method were used:

“generalized” center of gravity which is some combination of Cg2 and Cg3.4-12-1 neural network with 3 strips amplitudes and their sum on the inputs and photon coordinate on the output. MLPfit 1.40 Jérôme Schwindling & Bruno Mansoulié package was used.

• Experimental measurements of space resolution were performed at the tagged photon beam (energy range 50-1700 MeV) with the calorimeter prototype contains 400 kg of LKr and 10 mm strips. The results for layer of conversion are: σ=1.5 mm for energy 100MeV (it’s ~15% of the strip width)σ=0.7 mm for energy 1000MeV (it’s ~7% of the strip width). The results are in a good agreement with Monte-Carlo simulation.

• Both algorithms show approximately the same position resolution, but the center of gravity technique needs applying additional corrections depending on photon energy and energy deposition in the gap.

Thanks

Thanks a lot to Organizing Committee of the ACAT03 conference for support.

Thanks to Alexei Maslennikov for help in preparation.