3. Rare Pion-Decay Experiments

The intention of the proposed pion beta decay experiment is a precise determination of the decay rate p ⁺-> p ^₀e⁺ n _e relative to the rate for the decay p ⁺->e⁺ n _e as will be discussed in section 4.1. In order to deal with the occurring experimental difficulties, a precise knowledge of the experimental technique and the calibration methods of previous experiments on both of the two pion decay modes is required. The presentation of previous experiments includes thus a discussion of their calibration methods (see 3.1.1) and low energy tail corrections (see 3.2), since some of these calibration methods are a central subject of the present work.

An overview of the decay channels of pions, muons and p ^₀'s is given in tables 3.1 and 3.2.

Process
R = /[Gamma]

p ⁺->µ⁺ n _µ
(99.98770±0.00004)%

p ⁺->µ⁺ n _µ g
(1.24±0.25)·10^-4

p ⁺->e⁺ n _e
(1.230±0.004)·10^-4

p ⁺->e⁺ n _e g
(1.61±0.23)·10^-7

p ⁺-> p ^₀e⁺ n _e
(1.025±0.034)·10^-8

Table 3.1: Pion decay modes [PDG 94]

Process	R =/[Gamma]	Process	R = /[Gamma]
µ⁺->e⁺ n _eµ	(98.6±0.4)%	p ^₀-> g g	(98.798±0.032)%
µ⁺->e⁺ n _eµ g	(1.4±0.4)%	p ^₀->e⁺e^- g	(1.198±0.032)%
µ⁺->e⁺ n _eµ e⁺e^-	(3.4±0.4)·10^-5

Table 3.2: Muon and p ^₀ decay modes [PDG 94]

Figure 3.1: Michel spectrum of positrons from muon decays at rest. The main decay of the pion ( p ⁺->µ⁺ n _µ) produces a monoenergetic µ⁺ which decays with a lifetime of [tau]_µ [congruent] 2.2µs mainly into µ⁺->e⁺ n _e
µ ( p µe chain). For stopped pion decay experiments where the pion is assumed to be at rest before decaying, the muon has a kinetic energy of T_µ [congruent] 4.12 MeV. Since the range of the µ⁺ is very small ( about 1mm in scintillator material) the µ⁺ is also stopped in the target and the muon decay occurs at rest too. The energy spectrum of the e⁺ from the decay is the Michel spectrum, shown in Fig. 3.1, with a maximum energy of 52.83 MeV. Positrons from the p µe chain are the main background for all stopped pion decay experiments.

	Process	R = /[Gamma]
	p ⁺->µ⁺ n _µ	(99.98770±0.00004)%
	p ⁺->µ⁺ n _µ g	(1.24±0.25)·10^-4
	p ⁺->e⁺ n _e	(1.230±0.004)·10^-4
	p ⁺->e⁺ n _e g	(1.61±0.23)·10^-7
	*p ⁺-> p ^₀e⁺ n _e*	(1.025±0.034)·10^-8