General theory of weak processes involving neutrinos. I. Leptonic pseudoscalar-meson decays, with associated tests for, and bounds on, neutrino masses and lepton mixing

In this paper and the others in the series we present a generalized theory of weak leptonic and semileptonic decays which consistently incorporates the possibility of nonzero neutrino masses and associated lepton mixing. In the present work we give an analysis of the leptonic decays of charged pseudoscalar mesons within the generalized theory. The charged-lepton spectrum from such a decay is shown to consist not just of a single line, but instead a discrete set of lines. We state the precise meaning of neutrino-mass limits. The analysis leads to a new and very sensitive test for neutrino masses and mixing and to a corresponding proposal for new experiments on ${\pi }_{l2\mathrm{}}$ and $K_{l2\mathrm{}}$ decays. This test involves a measurement of the charged-lepton momentum or energy spectrum and is capable of yielding the mass and weak coupling coefficient, individually, for each neutrino that can occur in such a decay. The test is applied to existing data to derive correlated bounds on these quantities. The use of this test as a low-energy probe of the number of lepton generations is proposed. We also discuss an extended spectral test involving measurement of the charged-lepton polarization. Next, we give an analysis of the constraints arising from the ratios $\frac{B(M^{+}\to e^{+}{\nu }_e)}{B(M^{+}\to {\mu }^{+}{\nu }_{\mu })}$, where $M=\pi or K$, which takes proper account of the experimental cuts that are used to define $e^{+}``{\nu }_e\text{'}\text{'}$ and ${\mu }^{+}``{\nu }_{\mu }\text{'}\text{'}$ events. Finally, the general theory of the leptonic decays of heavy $0^{-}$ mesons is presented, together with tests for neutrino masses and mixing which make use of the momentum spectra, integrated $\frac{e}{\mu }$ yields, and possible decays of sufficiently heavy neutrinos.