The most precise measurement of the pion beta decay rate to date [McF-85] was carried with an in-flight decay technique. The decay in flight method measures the pion beta decay rate fairly directly by detecting a certain number of pions in a known amount of pion proper time. Moreover, although high pion beam intensity is required, the average raw rates in the detectors are lower by about two orders of magnitude than in the stopped pion experiment. However, important drawbacks to the in-flight technique limit possible improvements of the set-ups of previous experiments and dictate the choice of the experimental method for this precision measurement. The drawbacks to the in-flight technique are discussed below.
Firstly, the in-flight method requires an absolute counting of beam pions as well as an absolute determination of the detector acceptance, efficiency, and pion proper time in the decay region. No scheme has been demonstrated to date to achieve an accuracy significantly better than a percent in counting beam pions at intensities of and momenta greater than 400 MeV/c. A way around the problem of absolute normalization, is to do a relative normalization using a well measured decay channel of the pion. The only option is .
Figure: Radial dependence of the in-flight detector acceptances for and assuming 3 m decay path and a beam momentum of 450 MeV/c. The dashed line shows the change in acceptance corresponding to extending the detector inward radially by 5 cm at the center.
However a precise knowledge of the acceptances and conversion efficiencies for both decays is still required. As shown in figure , the acceptances for both decays differ by a factor of 2 for reasonable geometries so that the uncertainties do not cancel out in the ratio.
Secondly, the absolute determination of the effective acceptance of a detector at the desired level of accuracy is difficult due to edge effects. The edge effects arise from the opening to let the beam and the Michel positrons through. However, the edge region contributes most significantly to the total acceptance as shown in figure for a set-up with three meters decay region. A radial uncertainty of 1 cm in fiducial area translates into a uncertainty in total acceptance.
Thirdly, the triggers: the pion decays occur over an extended decay region. As a result, there is no unique correlation between the shower and the coordinates of the conversion point. In a relative measurement, an energy-angle cut is necessary for the identification of events. The energy-angle cut requires the placement of a tracking detector in front of the calorimeter. In a realistic experimental situation, the tracking accuracy and thus the energy-angle cut efficiency is limited by beam size, divergence and momentum distribution. Moreover, the energy resolution in the calorimeter is important in isolating the and decays from the background. In an in-flight technique involving more energetic showers, it is more difficult to resolve the separation of about 30 MeV.
Fourthly, rate limitations: due to the high kinematic boost of all events, their energy separation in the detector is difficult. Particularly troublesome are the radiative decays and . The effective duty factor for in-flight measurement is , given the PSI beam structure. This exacerbates the suppression of accidentally coincident background events like . In order to suppress them by a time-of-flight cut, a long beam line is needed, which reduces the total available beam pions. Enlarging the shower detector does not work beyond a certain point because the size of the opening determines the total acceptance for pion beta events, not the outer boundary (see figure ).
and cost of the detector: figure gives a good indication of
the size requirements for an in-flight decay detector. For a calorimeter in
CsI like in the stopped experiment, the volume would be
and the cost about . This is
more than four times the volume of a corresponding shower calorimeter in the
stopped experiment (see section 5.4).