Cosmic rays hitting the solar atmosphere generate neutrinos that interact and oscillate in the Sun and oscillate on the way to Earth. These neutrinos could potentially be detected with neutrino telescopes and will be a background for searches for neutrinos from dark matter annihilation in the Sun. We calculate the flux of neutrinos from these cosmic ray interactions in the Sun and also investigate the interactions near a detector on Earth that give rise to muons. We compare this background with both regular Earth-atmospheric neutrinos and signals from dark matter annihilation in the Sun. Our calculation is performed with an event-based Monte Carlo approach that should be suitable as a simulation tool for experimental collaborations. Our program package is released publicly along with this paper.

The combination of data from long-baseline and reactor oscillation experiments leads to a preference of the leptonic CP phase δ CP in the range between π and 2π. We study the statistical significance of this hint by performing a Monte Carlo simulation of the relevant data. We find that the distribution of the standard test statistic used to derive confidence intervals for δ CP is highly non-Gaussian and depends on the unknown true values of θ 23 and the neutrino mass ordering. Values of δ CP around π/2 are disfavored at between 2σ and 3σ, depending on the unknown true values of θ 23 and the mass ordering. Typically the standard χ 2 approximation leads to over-coverage of the confidence intervals for δ CP . For the 2-dimensional confidence region in the (δ CP , θ 23 ) plane the usual χ 2 approximation is better justified. The 2-dimensional region does not include the value δ CP = π/2 up to the 86.3% (89.2%) CL assuming a true normal (inverted) mass ordering. Furthermore, we study the sensitivity to δ CP and θ 23 of an increased exposure of the T2K experiment, roughly a factor 12 larger than the current exposure and including also anti-neutrino data. Also in this case deviations from Gaussianity may be significant, especially if the mass ordering is unknown.

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Cosmic rays hitting the outer parts of the Sun result in showers of high energy particles. The shower particles propagate through the solar atmosphere and interact further or decay. Among the shower particles are high energy neutrinos, after production these oscillate between flavours and interact with the solar material while propagating out of the Sun to the Earth. The result is a high energy neutrino flux at the Earth that may be detectable by modern neutrino detectors such as IceCube. Such a neutrino flux will furthermore act as a background in searches for neutrinos coming from annihilations of weakly interacting massive particles, often suggested to be the dark matter in the Universe. We perform an updated calculation of the solar atmospheric neutrino flux using the code MCEq for the cascade evolution in the solar atmosphere and WimpSim for the propagation of the neutrinos from the Sun to the detector on Earth, including full three-flavour treatment of neutrino oscillations and interactions in the Sun.