The Pion Beta Decay Experiment and A Remeasurement of the Panofsky Ratio

2.2.2 Experimental Technique

The Pion Beta Decay experiment is being carried out at the p E1 channel of the Paul Scherrer Institute. Positive pions with a momentum of 116 MeV/c first pass active degrading material before coming to rest in the central part of a plastic scintillator target where they decay with 26 ns mean life time. The decay channels of main interest are the rare pion beta decay, the p ⁺->e⁺ n _e decay, which is used for the calibration of the decay rate, and the most frequent pion decay p ⁺->µ⁺ n _µ . The latter is the major source of background, since the muons of 4.2 MeV are not capable to leave the target and decay with a mean life time of 2.2 µs into positrons and neutrinos. These positrons are referred to as Michel positrons. For the position sensitive identification of the positrons, they are passing two highly efficient multiwire proportional chambers (MWPC) with low mass and a thin plastic scintillator hodoscope before they enter the calorimeter.

The goal of the Pion Beta Decay experiment is the measurement of the p b -branching ratio relative to the decay p ⁺->e⁺ n _e with a precision of 0.5%. This implies, at an external systematical error of 0.4% [Poc95], a statistical error of better than 0.3 % (or 10⁵ p b events). The key considerations for the PiBeta detector were a minimization of the systematical error and a large acceptance for the two decay photons from the p ⁰ decay, as well as for the positron from the p ⁺->e⁺ n _e decay.

Then the pion beta decay rate can be obtained by

. Thus the determination of p b events relies on the identification of two clearly separated coincident photons from p ⁰-decay[9]. Due to the low phase space for this three-body-decay the p ⁰ will only receive low kinetic energy, since the p ⁺ decays at rest. The photon energy range in dependence of which represents the relative angle between photon and pion direction calculates to

since the maximum kinetic energy T_max of the pion using is at

Here have been used.

For the participating leptons the allowed range of kinetic energy lies between 0 MeV and 4 MeV. The direction of the two photons deviates at most 3.8° from collinearity[10] .

Process
Branching Ratio
[Gamma] p ₁
p ⁺->µ⁺ n _µ( g )
0.9998770
[Gamma] p _{1 g}
radiative [Gamma] p ₁ (E_µ< 3.38 MeV)
1.24*10^-4
[Gamma] p ₂
p ⁺->e⁺ n _e( g )
1.230*10^-4
[Gamma] p _{2 g}
radiative [Gamma] p ₂ (E_g> 21 MeV)
1.61*10^-7
[Gamma] p ₃
p ⁺->e⁺ n _ee⁺e^-
3.2*10^-9
[Gamma]µ₁
µ⁺->e⁺ n _e( g )
~1
[Gamma]µ_{1 g}
radiative [Gamma]µ₁ (E_g> 10 MeV)
0.014
[Gamma]µ₂
µ⁺-> e⁺ n _e_µe⁺e^-
3.4*10^-5

Table 2-3 c 431794640"> p and µ decay modes and probabilities taken from [PDG98].

At PSI an intense pion beam with low contamination and high momentum resolution (±2%) is available. The p E1 beam line at the Paul Scherrer Institute supplies high intensity pion and muon beams up to 10⁸ particles per second, depending on the selected momentum between 10 and 500 MeV/c. Beam studies [Ass95] have found the transport of 116 MeV/c particles to be a good compromise of high rate and low e⁺ and µ⁺ contamination in the p ⁺ beam. The transport of muons and positrons into the area occurs mostly due to subsequent pion and muon decays at flight. Afore, a 4 mm carbon degrader plate located within the second dipole magnet stopped the protons and sufficiently degraded pions, muons and positrons to enable separation in the downstream dipole magnets due to different deflection angles. A lead collimator at the focal point with 10 mm circular opening finally stops the displaced positrons and muons. This way contamination can be reduced by two orders of magnitude [Bro96]. The focal point then is refocused by a quadrupole triplet over a distance of 3.625 m to the reaction centre. With this, a beam profile of ca. 1 cm r.m.s. diameter and a rate of 2*10⁶ p /s can be achieved with a momentum spread of about 2% [Ass95].

[9] The p ⁰ will decay almost instantaneously with a lifetime of 8.4*10^-17s [PDG98] into a pair of photons

[10] The minimal relative angle was obtained using

	Process	Branching Ratio
[Gamma] p ₁	p ⁺->µ⁺ n _µ( g )	0.9998770
[Gamma] p _{1 g}	radiative [Gamma] p ₁ (E_µ< 3.38 MeV)	1.24*10^-4
[Gamma] p ₂	p ⁺->e⁺ n _e( g )	1.230*10^-4
[Gamma] p _{2 g}	radiative [Gamma] p ₂ (E_g> 21 MeV)	1.61*10^-7
[Gamma] p ₃	p ⁺->e⁺ n _ee⁺e^-	3.2*10^-9
[Gamma]µ₁	µ⁺->e⁺ n _e( g )	~1
[Gamma]µ_{1 g}	radiative [Gamma]µ₁ (E_g> 10 MeV)	0.014
[Gamma]µ₂	µ⁺-> e⁺ n _e_µe⁺e^-	3.4*10^-5