Simple dynamics, few available decay channels, and highly controlled radiative and loop corrections, make pion and muon decays a sensitive means of exploring details of the underlying symmetries. We review the current status of the rare decays: pi+ -
> e+ nu, pi+ -> e+ nu gamma, pi+ -> pi0 e+ nu, and mu+ -> e+ nu nu-bar gamma. For the latter we report new preliminary values for the branching ratio B(E_gamma >10 MeV, theta_(e-gamma) > 30deg) = 4.365 (9)_stat (42)_syst x 10^{-3}, and the decay parameter eta-bar = 0.006 (17)_stat (18)_syst, both in excellent agreement with standard model predictions. We review recent measurements, particularly by the PIBETA and PEN experiments, and near-term prospects for improvement. These and other similar precise low energy studies complement modern collider results materially.
We have measured the $pi^+to {rm e}^+ ugamma$ branching ratio over a wide region of phase space, based on a total of 65,460 events acquired using the PIBETA detector. Minimum-$chi^2$ fits to the measured $(E_{e^+},E_gamma)$ energy distributions resul
t in the weak form factor value of $F_A=0.0119(1)$ with a fixed value of $F_V=0.0259$. An unconstrained fit yields $F_V=0.0258(17)$ and $F_A=0.0117(17)$. In addition, we have measured $a=0.10(6)$ for the dependence of $F_V$ on $q^2$, the ${rm e}^{+} u$ pair invariant mass squared, parametrized as $F_V(q^2)=F_V(0)(1+acdot q^2)$. The branching ratio for the kinematic region $E_gamma > 10 $MeV and $theta_{{rm e^+}gamma} > 40^circ $ is measured to be $B^{rm exp}=73.86(54) times 10^{-8}$. Earlier deviations we reported in the high-$E_gamma$/low-$E_{{rm e}^+}$ kinematic region are resolved, and we find full compatibility with CVC and standard $V$$-$$A$ calculations without a tensor term. We also derive new values for the pion polarizability, $alpha_E = rm 2.78(10) times 10^{-4} fm^3$, and neutral pion lifetime, $tau_{pi 0} = (8.5 pm 1.1) times 10^{-17} $s.
Segmented electromagnetic calorimeters are used to determine both the total energy and direction (momentum components) of charged particles and photons. A trade off is involved in selecting the degree of segmentation of the calorimeter as the spatial
and energy resolutions are affected differently. Increased number of individual detectors reduces accidental particle pile-up per detector but introduces complications related to ADC pedestals and pedestal variations, exacerbates the effects of electronic noise and ground loops, and requires summing and discrimination of multiple analog signals. Moreover, electromagnetic showers initiated by individual ionizing particles spread over several detectors. This complicates the precise gain-matching of the detector elements which requires an iterative procedure. The PIBETA calorimeter is a 240-module pure CsI non-magnetic detector optimized for detection of photons and electrons in the energy range 5-100 MeV. We present the computer-controlled, automatic, in situ gain-matching procedure that we developed and used routinely in several rare pion and muon decay experiments with the PIBETA detector.
