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Register a new userPion, muon decays and weak interaction symmetries
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We review the recent measurements of the rare pion decays: Pi+ -> Pi0 e+ Nu [pion beta, Pi_(e3), or Pi_beta decay], radiative decay Pi+ -> e+ Nu Gamma [Pi_(e2Gamma) or RPD], and Pi+ -> e+ Nu [Pi_(e2)] decay, as well as the radiative muon decay, Mu -> e Nu Nu-bar Gamma, their theoretical implications, and prospects for further improvement.
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The combination of simple dynamics, small number of available decay channels, and extremely well controlled radiative and loop corrections, make charged pion decays a sensitive means for testing the underlying symmetries and the universality of weak fermion couplings, as well as for improving our understanding of pion structure and chiral dynamics. This paper reviews the current state of experimental study of the allowed rare decays of charged pions: (a) leptonic, $pi^+ to e^+ u_e$, or $pi_{e2}$, (b) radiative, $pi^+ to e^+ u_egamma$, or $pi_{e2gamma}$, and $pi^+ to e^+ u_e e^+e^-$, or $pi_{e2ee}$, and (c) semileptonic, $pi^+to pi^0 e^+ u$, or $pi_{e3}$. Taken together, the combined data set presents an internally consistent picture that also agrees well with standard model predictions. The internal consistency is illustrated well by the $pi_{e2}$ branching ratio of $(R_{e/mu}^pi)^{rm PIBETA} = (1.2366 pm 0.0064) times 10^{-4}$ extracted in this work from the PIBETA measurement of the $pi_{e3}$ decay and the current best value for the CKM matrix element $V_{ud}$. However, even after the great progress of the recent decades, experimental precision is lagging far behind that of the theoretical description for all above processes. We review the implications of the present state of knowledge and prospects for further improvement in the near term.
The Michel parameter xi has been determined from a measurement of the longitudinal polarization of positrons emitted in the decay of polarized and depolarized muons. The result, xi = 0.981 +- 0.045stat +- 0.003syst, is consistent with the Standard Model prediction of unity, and provides an order of magnitude improvement in the relative precision of this parameter. This value sets new constraints on exotic couplings beyond the dominant V-A description of the leptonic weak interaction.
Building on the rare pion and muon decay results of the PIBETA experiment, the PEN collaboration has undertaken a precise measurement of B_{pi e2} = R^pi_{e/mu}, the pi^+ -> e^+ u(gamma) decay branching ratio, at the Paul Scherrer Institute, to reduce the present 40times experimental precision lag behind theory to ~ 6-7times. Because of large helicity suppression, R^pi_{e/mu} is uniquely sensitive to contributions from non-(V-A) physics, making this decay a particularly suitable subject of study. Even at current precision, the experimental value of B_{pi e2} provides the most accurate test of lepton universality available. During runs in 2008-10, PEN has accumulated over 2times 10^7 pi_{e2} events; a comprehensive maximum-likelihood analysis is currently under way. The new data will also lead to improved precision of the earlier PIBETA results on radiative pi and mu decays.
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 result 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.
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