of which the first element Vud ~ 0.974 [PDG98], the cosine of the
Cabibbo angle, is the largest contribution; Vud is accessible
through beta decay.
In order to achieve a highly precise measurement of Vud, and thus a
test of the standard model, the Pion Beta Decay experiment (PiBeta) at the Paul
Scherrer Institute (PSI), Villigen, Switzerland investigates the rare
semileptonic decay
p +-> p 0e+ n e
( p b ). This process is an exact analogy to the b + decay
of a nucleus, but lacks the necessity of nuclear corrections. The decay
probability of this super-allowed Fermi decay is calculable to 0.2% precision.
A measurement of similar precision therefore is essential, but difficult due
the branching ratio of (1.025±0.002)*10-8. With the prospected
measurement precision of 0.5%, the conserved vector current (CVC) hypothesis
and radiative corrections due to quantumelectrodynamics can be proved, as well.
An even higher precision of about 0.3% could be achieved after a remeasurement
of the p +->e+ n e decay rate and then
also the universality of the weak interaction would be tested. Competitive
measurements to prove the unitarity of the CKM matrix have either shown
ambiguous results or were consistent but lacked the desired precision. The
currently most accurate measurement of the pion beta decay branching ratio has
an error of 3.8% [Dep68].Several considerations led to the present form of the Pion Beta decay experiment in order to provide the desired accuracy. A p + beam of high intensity will be stopped in an active target and the pair of photons from the nearly instantaneous (10-16s) decay p 0-> g g then provides a clear signature of a p b event. Rather than an absolute measurement of the decay rate, a relative measurement is desirable because of a lower systematical error. This will be achieved by the normalization to the decay p +->e+ n e. In order to obtain similarly high efficiencies for the positrons from p +->e+ n e and the p b -photons, which are of similar energy, a spherical shower calorimeter with good energy resolution and fast response was built. Therefor 240 hexagonal and pentagonal CsI crystals form a sphere that covers 80% of the 4 p sr solid angle. It provides good energy resolution, fast response and a high granularity. Using the concept of a self supporting structure only little non-sensitive material is used. CsI was chosen as the scintillating material because it delivers relatively high light yield with a fast response. Furthermore it provides the best stopping power and shortest radiation length compared to similar materials.
In order to achieve a good energy resolution the light yield of the scintillators has to be maximized. Additionally the quality of each CsI crystal that went into the calorimeter was reviewed carefully. For a good energy resolution also a uniform response of light over nearly the entire crystal volume is necessary. The surface treatment of the crystals therefore was optimized. It was found that two layers of Polytetrafluor-Ethylene (PTFE) foil with an additional layer of aluminized mylar provide both good light yield and uniformity. The crystals were also painted with a layer of wavelength shifting lacquer to enhance diffuse reflection. As a result of this treatment the energy resolution for 70 MeV (beam) positrons was improved from 5.2 MeV to 4.2 MeV FWHM between the beam periods in 1996 and 1997. The results of the scintillator studies are also important parameters for the Monte Carlo simulations of the detector.
The disadvantage of a stopped pion experiment is the positron background due to the decay chain p ->µ->e with a maximum positron energy of 53 MeV. In order to discriminate background events, an efficient triggering and a good energy resolution of the calorimeter are mandatory. This background event can be identified by the timing structure of the decaying muon. Furthermore the energy resolution of 4.2 MeV for 70 MeV positrons is ample to discriminate this source of background.
The present work will report on the developments and experimental result during the production and final assembly stage of the PiBeta detector[3]. Furthermore two test beam periods that took place during the development phase with a subset of the final detector are described. These beam periods were planned for detector calibration but also led to basic physical results where one is the radiative pion decay probability and the other the so-called Panofsky ratio [Pan50].
In parallel to the evaluation of the detector parts a GEANT simulation was initiated. Results from laboratory test and beam periods went into the simulation code, such as optical non-uniformity, photon statistics and electronic noise. Having reached consistency between data and simulation of the calorimeter response [Bro96], several studies became possible. With this, the comparison of shower developments of positrons and photons within the calorimeter was of large interest. On top of that a track reconstruction and cluster finding algorithm was developed. With the use of track reconstruction the angular resolution was determined with the simulation to be 3.6°±0.2° for 70 MeV positrons. A comparison to 70 MeV beam positrons could confirm this result. The angular resolution further depends on energy and particle type because of differently developing showers. In general, one obtains from simulations that positrons start to shower earlier than photons due to their charge with a slightly wider cone. With higher energies the shower penetrates deeper into the calorimeter (for both positrons and photons) while the transverse shower spread becomes smaller. For example 70 MeV photons have a mean shower depth of 7.6 cm at a cone radius of 2.6 cm. This proves that the uniform response of the first half of a crystal is crucial.
Another problem to be addressed is untypical development of electromagnetic showers that show some widespread depositions of small fractions of the particle energy within the calorimeter. The overall shower distribution within the PiBeta calorimeter could be modelled using a threshold function which requires that at least 98% of the shower energy are contained within the area under the graph of that function. This threshold function can be used twofold when implemented in a track finding algorithm. I) It offers a clustering routine in order to rebuild the deposited shower energy. II) It decides whether the deposited energy originates from one or more incoming particles. With the help of the algorithm the probability to find the radiative decay p +->e+ n e g with a photon energy exceeding 5 MeV was obtained to be (2.9±1.2)*10-6. This agrees well with the theoretical value of 2.7*10-6. At lower photon energies the radiative decay mostly emerges from inner bremsstrahlung, while higher photon energies - which occur with lower probability - give access to the ratio g of the pion form factors. This ratio can be remeasured with high statistics using the complete PiBeta detector.
The 1997 beam time was foreseen for calorimeter calibration with both 70 MeV positrons and photons. In order to generate the photons a liquid hydrogen target was used to stop negative pions. The charge exchange reaction then delivers photons from 55 MeV up to 83 MeV due to the p 0 decay into a pair of photons within 10-16s. With the use of a NaI detector array to tag one of the photons the desired photon energy was chosen. As a competitive reaction also radiative capture occurs, where the intermediate pionic hydrogen transforms into a 8.9 MeV neutron and a 129.4 MeV photon. The ratio of both possible reactions can be obtained with a calorimeter of good energy resolution. This measurement was carried out using an CsI-array of 44 crystals. The so-called Panofsky ratio P is directly proportional to the pion-nucleon scattering length b1. With the obtained value of 1.546±0.010 for P, b1 becomes (-0.085±0.002) in units of inverse pion masses.