Abstract: For several decades, the origin of ultra-high-energy cosmic rays (UHECRs) has been an unsolved question of high-energy astrophysics. One approach for solving this puzzle is to correlate UHECRs with high-energy neutrinos, since neutrinos are a direct probe of hadronic interactions of cosmic rays and are not deflected by magnetic fields. In this paper, we present three different approaches for correlating the arrival directions of neutrinos with the arrival directions of UHECRs. The neutrino data are provided by the IceCube Neutrino Observatory and ANTARES, while the UHECR data with energies above similar to 50 EeV are provided by the Pierre Auger Observatory and the Telescope Array. All experiments provide increased statistics and improved reconstructions with respect to our previous results reported in 2015. The first analysis uses a high-statistics neutrino sample optimized for point-source searches to search for excesses of neutrino clustering in the vicinity of UHECR directions. The second analysis searches for an excess of UHECRs in the direction of the highest-energy neutrinos. The third analysis searches for an excess of pairs of UHECRs and highest-energy neutrinos on different angular scales. None of the analyses have found a significant excess, and previously reported overfluctuations are reduced in significance. Based on these results, we further constrain the neutrino flux spatially correlated with UHECRs.

Abstract: We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings A(v)(Q(2)) for complex or real squared momenta Q(2). These couplings are holomorphic analogs of the powers a(Q(2))(v) of the underlying perturbative QCD (pQCD) coupling a(Q(2)) equivalent to alpha(s)(Q(2))/pi, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2 delta anQCD), and Massive Perturbation Theory (MPT). The index v can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetic, 2015), but are now written in Fortran. Program summary Program title: AanQCDext Catalogue identifier: AEYKv10 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYICv1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12105 No. of bytes in distributed program, including test data, etc.: 98822 Distribution format: tar.gz Programming language: Fortran. Computer: Any work-station or PC where Fortran 95/200312008 (gfortran) is running. Operating system: Operating system Linux (Ubuntu and Scientific Linux), Windows (in all cases using gfortran). Classification: 11.1, 11.5. Nature of problem: Calculation of values of the running analytic couplings A(v)(Q(2); N-f) for general complex squared momenta Q(2) equivalent to -q(2), in three analytic QCD models, where A(v)(Q(2); N-f) is the analytic (holomorphic) analog of the power (alpha(s)(Q(2); N-f)/pi)(v). Here, A(v)(Q(2); N-f) is a holomorphic function in the Q(2) complex plane, with the exception of the negative semiaxis (-infinity, -M-thr(2)], reflecting the analyticity properties of the spacelike renormalization invariant quantities D(Q(2)) in QCD. In contrast, the perturbative QCD power (alpha(s)(Q(2); N-f)/pi)(v) has singularities even outside the negative semiaxis (Landau ghosts). The three considered models are: Analytic Perturbation theory (APT); Two-delta analytic QCD (2 delta anQCD); Massive Perturbation Theory (MPT). We refer to Ref. [1] for more details and literature. Solution method: The Fortran programs for FAPT and 2 delta anQCD models contain routines and functions needed to perform two-dimensional numerical integrations involving the spectral function, in order to evaluate A(v)(Q(2)) couplings. In MPT model, one-dimensional numerical integration involving A(1)(Q(2)) is sufficient to evaluate any A(v)(Q(2)) coupling. Restrictions: For unphysical choices of the input parameters the results are meaningless. When Q(2) is close to the cut region of the couplings (Q(2) real negative), the calculations can take more time and can have less precision. Running time: For evaluation of a set of about 10 related couplings, the times vary in the range t similar to 10(1)-10(2) s. MPT requires less time, t similar to 1-10(1) s. References: [1] C. Ayala and G. Cvetic, anQCD: a Mathematica package for calculations in general analytic QCD models, Comput. Phys. Commun. 190 (2015) 182.