Infinite matrices may violate the associative law

The momentum operator for a particle in a box is represented by an infinite order Hermitian matrix $P$. Its square $P^2$ is well defined (and diagonal), but its cube $P^3$ is ill defined, because $P P^2\neq P^2 P$. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.Comment: final version in J. Phys. A28 (1995) 1765-177

Revising Limits on Neutrino-Majoron Couplings

Any theory that have a global spontaneously broken symmetry will imply the existence of very light neutral bosons or massless bosons (sometimes called Majorons). For most of these models we have neutrino-Majoron couplings, that appear as additional branching ratios in decays of mesons and leptons. Here we present an updated limits on the couplings between the electron, muon and tau neutrinos and Majorons. For such we analyze the possible effects of Majoron emission in both meson and lepton decays. In the latter we also include an analysis of the muon decay spectrum. Our results are $|g_{e\alpha}|^{2}<5.5x10^{-6}$, $|g_{\mu\alpha}|^{2}<4.5x10^{-5}$ and $|g_{\tau\alpha}|^{2}<5.5x10^{-2}$ at 90 % C. L., where $\alpha=e,\mu,\tau$.Comment: 12 pages, 5 figure

Atmospheric neutrinos: LMA oscillations, Ue3 induced interference and CP-violation

We consider oscillations of the low energy (sub-GeV sample) atmospheric neutrinos in the three neutrino context. We present the semi-analytic study of the neutrino evolution and calculate characteristics of the e-like events (total number, energy spectra and zenith angle distributions) in the presence of oscillations. At low energies there are three different contributions to the number of events: the LMA contribution (from electron-neutrino oscillations driven by the solar oscillation parameters), the Ue3-contribution proportional to s13**2, and the Ue3 - induced interference of the two amplitudes driven by the solar oscillation parameters. The interference term is sensitive to the CP-violation phase. We describe in details properties of these contributions. We find that the LMA, the interference and Ue3 contributions can reach 5 - 6%, 2 - 3% and 1 - 2 % correspondingly. An existence of the significant (> 3 - 5 %) excess of the e-like events in the sub-GeV sample and the absence of the excess in the multi-GeV range testifies for deviation of the 2-3 mixing from maximum. We consider a possibility to measure the deviation as well as the CP- violation phase in future atmospheric neutrino studies.Comment: 30 pages, RevTeX4.0, 11 figures; improved figure

Constraints on neutrino decay lifetime using long-baseline charged and neutral current data

We investigate the status of a scenario involving oscillations and decay for charged and neutral current data from the MINOS and T2K experiments. We first present an analysis of charged current neutrino and anti-neutrino data from MINOS in the framework of oscillation with decay and obtain a best fit for non-zero decay parameter $\alpha_3$. The MINOS charged and neutral current data analysis results in the best fit for $|\Delta m_{32}^2| = 2.34\times 10^{-3}$~eV$^2$, $\sin^2 \theta_{23} = 0.60$ and zero decay parameter, which corresponds to the limit for standard oscillations. Our combined MINOS and T2K analysis reports a constraint at the 90\% confidence level for the neutrino decay lifetime $\tau_3/m_3 > 2.8 \times 10^{-12}$~s/eV. This is the best limit based only on accelerator produced neutrinos