5 research outputs found

    Several explicit formulae for Bernoulli polynomials

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    We prove several explicit formulae for the nn-th Bernoulli polynomial Bn(x)B_{n}(x), in which Bn(x)B_{n}(x) is equal to an affine combination of the polynomials (x1)n(x-1)^{n}, (x2)n(x-2)^{n}, ldotsldots, (xk1)n(x-k-1)^{n}, where kk is any fixed positive integer greater or equal than nn

    Measurement of the total cross section from elastic scattering in pp collisions at s√ = 7 TeV with the ATLAS detector

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    A measurement of the total pp cross section at the LHC at √s = 7 TeV is presented. In a special run with high-β beam optics, an integrated luminosity of 80 µb−1 was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable t. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the |t| range from 0.01 GeV2 to 0.1 GeV2 to extrapolate to |t| → 0, the total cross section, σtot(pp → X), is measured via the optical theorem to be: σtot(pp → X) = 95.35 ± 0.38 (stat.) ± 1.25 (exp.) ± 0.37 (extr.) mb, where the first error is statistical, the second accounts for all experimental systematic uncertainties and the\ud last is related to uncertainties in the extrapolation to |t| → 0. In addition, the slope of the elastic cross section at small |t| is determined to be B = 19.73 ± 0.14 (stat.) ± 0.26 (syst.) GeV−2

    Searching for VHE gamma-ray emission associated with IceCube neutrino alerts using FACT, H.E.S.S., MAGIC, and VERITAS

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    The realtime follow-up of neutrino events is a promising approach to search for astrophysical neutrino sources. It has so far provided compelling evidence for a neutrino point source: the flaring gamma-ray blazar TXS 0506+056 observed in coincidence with the high-energy neutrino IceCube-170922A detected by IceCube. The detection of very-high-energy gamma rays (VHE, E>100GeV E > 100 G e V ) from this source helped establish the coincidence and constrained the modeling of the blazar emission at the time of the IceCube event. The four major imaging atmospheric Cherenkov telescope arrays (IACTs) - FACT, H.E.S.S., MAGIC, and VERITAS - operate an active follow-up program of target-of-opportunity observations of neutrino alerts sent by IceCube. This program has two main components. One are the observations of known gamma-ray sources around which a cluster of candidate neutrino events has been identified by IceCube (Gamma-ray Follow-Up, GFU). Second one is the follow-up of single high-energy neutrino candidate events of potential astrophysical origin such as IceCube-170922A. GFU has been recently upgraded by IceCube in collaboration with the IACT groups. We present here recent results from the IACT follow-up programs of IceCube neutrino alerts and a description of the upgraded IceCube GFU system

    Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A

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