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8. Conclusion

The pion beta decay is a transition between two members of an isospin triplet. It is thus analogous to super-allowed Fermi transitions in nuclear beta decay which can be used to test the CVC-Hypothesis and the unitarity of the CKM quark mixing-matrix. The resulting value of Vud together with the recommended values for Vus and Vub lead to a unitarity test, which is 2.2 s lower than the standard model prediction. Another independent determination of Vud comes from the decay of the neutron leading to a value 2.1 s above unitarity of the CKM-matrix. These discrepancies call for another, independent test of CKM unitarity: The pion beta decay experiment, being the most direct test of CVC, permits an independent approach to extract Vud, without the complication of nuclear corrections, screening effects and final state coulomb-interaction.

Experimentally however, the pion beta decay rate is difficult to measure with sufficient precision, due to the small branching ratio. The most precise measurement to date is in good agreement with theory but has an experimental uncertainty of 4%. Therefore a new experiment was proposed, which attempts an overall precision of 0.5%. The experimental technique is based on stopping pions and detection of the two photons from the decay of the p 0. In order to avoid the determination of absolute values for normalization factors and detection efficiencies, a measurement of the pion beta decay relative to the decay p ->e+ n e is performed. In previous rare pion-decay experiments using the stopped pion technique the decay products were detected by inorganic scintillators with excellent energy resolutions but with relatively slow light outputs. In order to avoid background from pile-up events, pions were stopped at rather low rates (about 104 p /s). It was shown that the low energy tail corrections dominated the systematic uncertainties of the experiments.

Due to the very small branching ratio of the pion beta decay, the new experiment needs to be performed at high pion stopping-rates of up to 5·106 p /s. A segmented shower calorimeter, consisting of pure CsI-crystals, is required to detect 70 MeV positrons and photons with good energy resolution and to be capable of handling high event rates. The delivered pure CsI-crystals thus have to accomplish several specifications: The fast light output of the crystals must be above 70% and the geometrical tolerances have to be within 0.3 mm. Dedicated methods were developed to determine these parameters with precision. In addition, a tomography apparatus is in operation, which allows the determination of the number of photoelectrons per MeV and the light collection non-uniformity of each crystal. The resulting values are used as inputs for Monte-Carlo-Simulations of the electromagnetic showers in the calorimeter. The observed experimental difference in the detector response to 70 MeV positrons and photons can be explained by the light collection non-uniformity of the crystals. The simulation agrees with the results obtained by directing a beam of positrons into an array of 26 pure CsI-crystals. To determine the exact amount of the energy-resolution difference needs however a more precise parametrization of the optical non-uniformity function in the simulation.

In order to measure the detector response to 70 MeV photons, a dedicated calibration experiment was carried out by stopping a beam of negative pions in a liquid hydrogen target and detecting photons from the reaction p -p-> p 0n. The simultaneous detection of the neutron and the two photons with good angular resolution allows the determination of their energies and momenta. The calculated energy can be compared to the actual energy of the photon deposited in the array of 26 CsI-crystals and allows the calculation of an energy distribution normalized to 70 MeV. The result is compared to a Monte-Carlo-Simulation of the set-up including the properties of each individual crystal, found by the cosmic ray tomography. The experimental detector response is somewhat higher than the simulated resolution. The difference arises from the imperfect matching of the individual crystal spectra. The resulting tail below a threshold of 55.5 MeV are in good agreement. (7.0±0.5 % for the simulated and 6.6±0.5% for the experimental lineshape).

In order to perform the experiment at the desired beam stopping rate, efficient background suppression is essential. A common technique in many modern particle detector systems is waveform digitizing of the detector signals. A waveform digitizing system is being developed at PSI, based on the Domino Sampling Chip DSC. In 1994, the DSC version 4 was tested and the concept for a motherboard hosting several DSCs was developed. A prototype module equipped with 6 DSCs was compared to commercial ADC's and TDC's. The obtained results are very promising: The sampling frequencys of the individual DSCs can be determined with a precision of 0.2%. By analyzing the digitized waveforms, timing resolutions below 200ps are obtained. The amplitude non-linearity of the system is 1.3mV in the range of interest between 0 and 0.3V. The DSCs include the information for a powerful reduction of background from pile-up events. Although the present version of the DSC could be used in a 16 channel module, a new version of the DSC is currently being designed. The improvements concern the simplification of the entire system. The values for timing resolution and amplitude non-linearity are expected to be lower by a factor of about 2 due to the reduced noise. The readout frequency and A/D conversion will be performed at 5MHz.

It should be mentioned that the progress of the experiment has been slowed down by production problems with the pure CsI-crystals. However, it was shown, that the additional time was used to develop methods which allow a control of the quality of the pure CsI-crystals and which guarantee excellent performance of the shower calorimeter once it is assembled. The response of the calorimeter to the processes of interest are known prior the assembly and allow an efficient online-control of the accumulated data. In addition, a new waveform digitizing system is designed, which is much cheaper than commercial systems and will be a powerful tool for background subtraction.

Finally, the presented material should prove the ability of the proposed pion beta experiment to achieve a measurement of the pion beta decay rate at the level of 0.5% overall uncertainty.

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2.1: Analysis of super-allowed Fermi transitions 7

3.1: Michel spectrum 10

3.2: Kinematics of the pion beta decay 12

3.3: Experimental apparatus of the decay at rest experiment 14

3.4: Experimental apparatus of the decay in flight experiment 15

3.5: Total energy spectrum of the PSI experiment 18

4.1: Cut through the pion beta detector 23

4.2: The p E1 beam line 26

4.3: Transport calculation for the p E1 beam line 28

4.4: Active degrader ADC vs. TDC 29

4.5: Cut through the active target 30

4.6: Beam stopping distribution 31

4.7: Shower calorimeter 33

4.8: Visualization of the clustering scheme 36

4.9: Block diagram of the trigger electronics 37

5.1: Emission spectrum of a pure CsI crystal 41

5.2: CsI-pulse of a cosmic muon 42

5.3: Result of a F/T measurement 43

5.4: Definition of the sides of a HEXA crystal 45

5.5: Comparison of theoretical shape to measured shape 46

5.6: ADC spectrum and fit-result for a "LED" run 50

5.7: Cosmic ray spectrum of a HEXA crystal 51

5.8: Tomography box with 6 crystals 53

5.9: Light non-uniformity from the 2D-reconstruction 54

5.10: Parametrization of the light non-uniformity 57

5.11: Array of 26 crystals as positioned in GEANT 60

5.12: Simulation of electromagnetic shower for perfect detectors 61

5.13: Simulation including properties of real crystals 63

6.1: Schematic diagram of the charge exchange reaction 68

6.2: E g 2 and q 12 as a function of the angle q 10 69

6.3: Box containing 26 CsI crystals 71

6.4: Experimental setup for the calibration measurement 72

6.5: Neutron TDC spectrum 75

6.6: Common mode for PMT's with CERN and UVA bases 77

6.7: Pedestal and noise after software corrections 77

6.8: Mean ADC-values and temperature as a function of time 79

6.9: Gain values for five crystals 80

6.10: Resulting energy spectra of the normalized energy 82

6.11: Experimental setup as defined in GEANT 84

6.12: Energy spectrum compared to GEANT result 86

7.1: Circuit diagram of the DSC 90

7.2: Control signals for operating the DSC 91

7.3: Circuit of zero suppression part 92

7.4: Schematic layout of the DSM100 94

7.5: Schematic diagram of the test set-up electronics 95

7.6: Display of raw event 96

7.7: Pedestals of the DSC 97

7.8: Single event display of a sampling speed calibration run 99

7.9: Differences of leading edges of the 10 MHz test pulse 100

7.10: Timing linearity plot of one DSC 102

7.11: Timing resolution of the DSCs 103

7.12: Amplitude linearity plot of one DSC 105

7.13: Raw CsI-signal and linearity check for cosmic muon pulses 1073.1: Pion decay modes 9

3.2: Muon and p 0 decay modes 9

4.1: Beam parameters at the focal point F 32

4.2: The 9 module types composing the shower calorimeter 32

5.1: Some properties of pure CsI 40

5.2: Data sheet from distance measurements of a HEXA crystal 47

5.3 Compilation of distance measurements of 25 crystals 48

5.4: Peak values for cosmic muon spectra 52

5.5: Parameters for 26 CsI crystals 59

7.1: DSC performance under experimental conditions 108 Herzlich danken möchte ich meinem Doktorvater Herrn Prof. Dr. R. Engfer, welcher mir die Ausarbeitung dieser Dissertation ermöglicht hat und Herrn PD Dr. R. Frosch für seine Hilfe während dem Abfassen der Arbeit.

Grosser Dank geht an Manfred Daum der mit seinem stets wohlwollenden "ätzenden Saft der Kritik" zu meiner Arbeit beigetragen hat.

Roland Horisberger hat mir "seinen" Domino Sampling Chip zur Weiterentwicklung überlassen und mit vielen wertvollen Tips dem Projekt zum Erfolg verholfen.

Peter Kettle half bei der kritischen Überarbeitung des Kapitels über den DSC.

Mein ganz spezieller Dank gilt meinem Bürogenossen Stefan Ritt, der mich in die Welt der PC's eingeführt hat und mit seinem breiten Wissen in allen Bereichen dieser Arbeit geholfen hat.

Roger Schnyder hat mit der Realisierung des DSM100 ausgezeichnete Arbeit geleistet.

A very special thank to Dinko Pocanic from UVA. I appreciate his enthusiasm in leading the experiment and in attacking and solving all the problems that are occurring when performing experimental measurements. His knowledge and experience was of high importance for this work.

Many thanks to Emil Frlez (It was a great time in Virginia, Emil), Ketevi Assamagan, Cole Smith, Steven Bruch and all the others from UVA who participate the pion beta experiment.

Zum Schluss möchte ich meiner Frau Barbara ganz herzlich für Ihre Liebe und Kraft danken, die sie während der Dissertationszeit für mich und unsere Kinder aufbrachte. Vielen Dank auch für die Hilfe beim Zeichnen der Bilder.

Villigen, im April 1996

Curriculum Vitae

Brönnimann Christian

Kirchweg 8

5422 Oberehrendingen (AG)

Geboren am 6.9.1966 in Wettingen (AG).

Aus Zimmerwald (BE).

Verheiratet seit dem 18. Mai 1990 mit Barbara Brönnimann, geb. Stammbach.

Drei Kinder: David (1990), Tabea (1992) und Julian (1995).

1973 - 1978 Primarschule in Wettingen.

1978 - 1982 Bezirksschule in Baden.

1982 - 1985 Realgymnasium der Kantonsschule Baden (Matura Typus C).

1985 - 1992 Physikstudium an der Universität Zürich, Diplom in Experimentalphysik am Paul Scherrer Institut (PSI), Villigen, bei Prof. Dr. R. Engfer.

1992 - 1996 Assistent an der Universität Zürich. Doktorand für das Pion Beta Decay Experiment am Paul Scherrer Institut (PSI), Villigen, unter der Leitung von Prof. Dr. R. E. Engfer.

Verzeichnis der Dozenten:

C. Amsler, A.O. Benz, D. Brinkmann, R.E. Engfer, H. Gross, P. Hess, H. Jarchov, H.H. Keller, W. Kündig, P.F. Meier, H. Nussbaumer, G. Rasche, G. Scharf, J.O. Stenflo, N. Straumann, A. Thellung, P. Truöl.

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