Impact of Secondary Acceleration in Gamma-Ray Bursts

We discuss the acceleration of secondary muons, pions, and kaons in gamma-ray bursts within the internal shock scenario, and their impact on the neutrino fluxes. We introduce a two-zone model consisting of an acceleration zone (the shocks) and a radiation zone (the plasma downstream the shocks). The acceleration in the shocks, which is an unavoidable consequence of the efficient proton acceleration, requires efficient transport from the radiation back to the acceleration zone. On the other hand, stochastic acceleration in the radiation zone can enhance the secondary spectra of muons and kaons significantly if there is a sufficiently large turbulent region. Overall, it is plausible that neutrino spectra can be enhanced by up to a factor of two at the peak by stochastic acceleration, that an additional spectral peaks appears from shock acceleration of the secondary muons and pions, and that the neutrino production from kaon decays is enhanced. Depending on the GRB parameters, the general conclusions concerning the limits to the internal shock scenario obtained by recent IceCube and ANTARES analyses may be affected by up to a factor of two by secondary acceleration. Most of the changes occur at energies above 10^7 GeV, so the effects for next-generation radio-detection experiments will be more pronounced. In the future, however, if GRBs are detected as high-energy neutrino sources, the detection of one or several pronounced peaks around 10^6 GeV or higher energies could help to derive the basic properties of the magnetic field strength in the GRB.Comment: 10 pages, 5 figures, 1 tabl

Testing for Time Dependence in Parameters

This paper proposes a new test based on a Fourier series expansion to approximate the unknown functional form of a nonlinear time-series model. The test specifically allows for structural breaks, seasonal parameters and time-varying parameters. The test is shown to have evry good size and power properties. However, it is not especially good in detecting nonlinearity in variables. As such, the test can help determine whether an observed rejection of the joint null hypothesis of linearity and time invariant parameters is due to time-varying coefficients of a nonliearity in variables.time varying parameters; fourier-series; nuisance parameters

Reflection positivity in higher derivative scalar theories

Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to their Lorentzian signature counterparts. In this work we rigorously prove the violation of reflection positivity in a large class of free scalar fields with a rational propagator. This covers in particular higher-derivative theories where the propagator admits a partial fraction decomposition as well as degenerate cases including e.g. p^4 -type propagators.Comment: 9 pages, 1 figur