1. Introduction to the pb Experiment - 3.2 Pion Decay into Positron and Neutrino

3.2 Pion Decay into Positron and Neutrino

According to the V-A theory, the decay ( p e n ) is suppressed with respect to the normal pion decay by a factor of

, (3.8)

because the positron is emitted in the "wrong" helicity state. The kinetic energy of the positrons from this decay is

. (3.9)

Results of two experiments on this decay mode have been published recently, each of them reached an overall precision of ~0.4%. One experiment [Cza 93] was carried out at PSI the other at TRIUMPH [Bri 94]. In order to avoid pile-up, i.e. several decay products for one trigger event, low beam intensities were used (7·10⁴/s for the TRIUMF experiment and 5·10³/s for the PSI experiment). Due to the low rate, inorganic scintillators with excellent energy resolution but slow decay times [tau]_d could be used ( p a g [Iota]3[tau] d ">[tau]_d~ 300 ns for BGO and [tau]_d~250 ns for NaI(Tl) ).

The main systematic errors for both experiments came from tail corrections, i.e. from the estimation of the number of events from p ->e⁺ n _e decay below the edge of the Michel spectrum. The tail can be seen in Figure 3.5, which shows the recorded total energy spectrum for p ->e⁺ n _eevents. In the PSI experiment this tail occurred because of photo-nuclear absorption with neutron emission and could be estimated only by a Monte Carlo Simulation. In case of the TRIUMF experiment the tail was due mostly to the response function of the NaI(Tl) crystal. The response function of the crystal was measured directly in a positron beam. The result was convoluted with the response function obtained from Monte Carlo calculations.

Figure 3.5: The total energy spectrum[3] (after applying cuts) of the PSI experiment [Cza 93]. The peak at 90 MeV results from the decay p ->e⁺ n _e . The two vertical lines mark the window used to calculate the branching ratio. The dashed line shows the contributions from the p µe background, the dotted line is the pion strong interaction background (SIB). To determine the final branching ratio, the number of p ->e⁺ n _e events below the p µe background edge had to be estimated.

[3] In this experiment, for each incoming pion the total energy was measured, i.e. the kinetic energy of the pion (20MeV) and the energy of all the charged decay products in the target and the calorimeter.