Following similar approaches in the past, the Schrödinger equation for three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2×2 ...matrices. The final result for the oscillation probabilities is obtained directly in the conventional parametric form as in the vacuum but with explicit simple modification of two mixing angles (θ12 and θ13) and mass eigenvalues. In this form, the analytical results provide excellent approximation to numerical calculations and allow for simple qualitative understanding of the matter effects.
A
bstract
Flavour oscillations of sub-GeV atmospheric neutrinos and antineutrinos, traversing different distances inside the Earth, are a promising source of information on the leptonic CP phase
δ
. ...In that energy range, the oscillations are very fast, far beyond the resolution of modern neutrino detectors. However, the necessary averaging over the experimentally typical energy and azimuthal angle bins does not wash out the CP violation effects. In this paper we derive very accurate analytic compact expressions for the averaged oscillations probabilities. Assuming spherically symmetric Earth, the averaged oscillation probabilities are described in terms of two analytically calculable effective parameters. Based on those expressions, we estimate maximal magnitude of CP-violation effects in such measurements and propose optimal observables best suited to determine the value of the CP phase in the PMNS mixing matrix.
We explore oscillations of the solar B8 neutrinos in the Earth in detail. The relative excess of night νe events (the day-night asymmetry) is computed as function of the neutrino energy and the nadir ...angle η of its trajectory. The finite energy resolution of the detector causes an important attenuation effect, while the layer-like structure of the Earth density leads to an interesting parametric suppression of the oscillations. Different features of the η− dependence encode information about the structure (such as density jumps) of the Earth density profile; thus measuring the η distribution allows the scanning of the interior of the Earth. We estimate the sensitivity of the DUNE experiment to such measurements. About 75 neutrino events are expected per day in 40 kt. For high values of Δm212 and Eν>11 MeV, the corresponding D-N asymmetry is about 4% and can be measured with 15% accuracy after 5 years of data taking. The difference of the D-N asymmetry between high and low values of Δm212 can be measured at the 4σ level. The relative excess of the νe signal varies with the nadir angle up to 50%. DUNE may establish the existence of the dip in the η− distribution at the (2–3)σ level.
The ideas and formulas presented in the article will help to bring together the theoretical predictions for the anomalous magnetic moment of muon and the results of the "Muon g-2" experiment. In ...doing so, we are discussing the new effect exclusively within the Standard Model. In quantum physics a state with spin perpendicular to a magnetic field can be expressed as a superposition of energy eigenstates with spins parallel and antiparallel to the field: the resultant spin precession is due to the energy difference between the two eigenstates. If the state, like the muon, is unstable and can decay, it will have a natural energy spread. As a result the frequency of the spin precession can vary. For a constant magnetic field the measured spin precession velocity will be spread according to the Lorentzian distribution with width \(\left(\gamma\tau\right)^{-1}\), for Lorentz gamma factor \(\gamma=E/ m\), and particle lifetime \(\tau\). Although the true mean and variance of a Lorentzian distribution is undefined, the latter can be estimated by the maximum likelihood method to be \({2 \over N (\gamma \tau)^2}\), twice that of a normal distribution. Thus, the statistical error on the anomalous magnetic moment in reality should turn out to be wider than with \(\chi^2\) analysis of the experiment.
Following similar approaches in the past, the Schrodinger equation for three
neutrino propagation in matter of constant density is solved analytically by
two successive diagonalizations of 2x2 ...matrices. The final result for the
oscillation probabilities is obtained directly in the conventional parametric
form as in the vacuum but with explicit simple modification of two mixing
angles ($\theta_{12}$ and $\theta_{13}$) and mass eigenvalues.
Following similar approaches in the past, the Schrodinger equation for three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2x2 ...matrices. The final result for the oscillation probabilities is obtained directly in the conventional parametric form as in the vacuum but with explicit simple modification of two mixing angles (\(\theta_{12}\) and \(\theta_{13}\)) and mass eigenvalues.
We present the results of a new analysis of the data of the MiniBooNE experiment taking into account the additional background of photons. MiniBooNE normalises the rate of photon production to the ...measured \(\pi^0\) production rate. We study neutral current (NC) neutrino-induced \(\pi^0\)/photon production (\(\nu_\mu + A \to \nu_\mu +1\pi^0 / \gamma + X\)) on carbon nucleus (A=12). Our conclusion is based on experimental data for photon-nucleus interactions from the A2 collaboration at the Mainz MAMI accelerator. We work in the approximation that decays of the intermediate states (non-resonant N, \(\Delta\) resonance, higher resonances) unaffected by its production channel, via photon or Z boson. \(1\pi^0+X\) production scales as A\(^{2/3}\), the surface area of the nucleus. Meanwhile the photons incoherently created in intermediate states decays will leave the nucleus, and that cross section will be proportional to the atomic number of the nucleus. We also took into account the coherent emission of photons. We show that the new photon background can explain part of the MiniBooNE low-energy excess, thus significantly lowering the number of unexplained MiniBooNE electron-like events from \(5.1\sigma\) to \(3.6\sigma\).
PDF
