A

Conditional normalizing flows for IceCube event reconstruction

International Cosmic Ray Conference, pp. 1003

Abstract

The IceCube Neutrino Observatory is a cubic-kilometer high-energy neutrino detector deployed in the Antarctic ice. Two major event classes are charged-current electron and muon neutrino interactions. In this contribution, we discuss the inference of direction and energy for these classes using conditional normalizing flows. They allow to derive a posterior distribution for each individual event based on the raw data that can include systematic uncertainties, which makes them very promising for next-generation reconstructions. For each normalizing flow we use the differential entropy and the KL-divergence to its maximum entropy approximation to interpret the results. The normalizing flows correctly incorporate complex optical properties of the Antarctic ice and their relation to the embedded detector. For showers, the differential entropy increases in regions of high photon absorption and decreases in clear ice. For muons, the differential entropy strongly correlates with the contained track length. Coverage is maintained, even for low photon counts and highly asymmetrical contour shapes. For high-photon counts, the distributions get narrower and become more symmetrical, as expected from the asymptotic theorem of Bernstein-von-Mises. For shower directional reconstruction, we find the region between 1 TeV and 100 TeV to potentially benefit the most from normalizing flows because of azimuth-zenith asymmetries which have been neglected in previous analyses by assuming symmetrical contours. Events in this energy range play a vital role in the recent discovery of the galactic plane diffuse neutrino emission.

Authors 99

  1. Uppsala University · RWTH Aachen University

    Affiliation as printed

    III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany

    Uppsala University , Uppsala , Sweden

    III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany

    Uppsala University, Uppsala, Sweden

  2. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  3. University of Canterbury

    Affiliation as printed

    Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

  4. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  5. Université Libre de Bruxelles

    Affiliation as printed

    Université Libre de Bruxelles , Science Faculty CP230 , B-1050 Brussels , Belgium

    Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium

  6. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  7. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  8. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  9. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  10. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  11. Harvard University

    Affiliation as printed

    Department of Physics and Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA

  12. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  13. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  14. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  15. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  16. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  17. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  18. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  19. University of California, Berkeley

    Affiliation as printed

    Dept. of Physics , University of California , Berkeley , CA 94720 , USA

    Dept. of Physics, University of California, Berkeley, CA 94720, USA

  20. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  21. Ruhr University Bochum

    Affiliation as printed

    Fakultät für Physik & Astronomie , Ruhr-Universität Bochum , D-44780 Bochum , Germany

    Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

  22. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  23. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  24. Uppsala University · RWTH Aachen University

    Affiliation as printed

    III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany

    Uppsala University , Uppsala , Sweden

    III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany

    Uppsala University, Uppsala, Sweden

  25. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  26. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  27. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  28. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  29. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  30. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  31. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  32. Harvard University

    Affiliation as printed

    Department of Physics and Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA

  33. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  34. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  35. Uppsala University · RWTH Aachen University

    Affiliation as printed

    III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany

    Uppsala University , Uppsala , Sweden

    III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany

    Uppsala University, Uppsala, Sweden

  36. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  37. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  38. Georgia Institute of Technology

    Affiliation as printed

    School of Physics and Center for Relativistic Astrophysics , Georgia Institute of Technology , Atlanta , GA 30332 , USA

    School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA

  39. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  40. The University of Adelaide

    Affiliation as printed

    Department of Physics , University of Adelaide , Adelaide , 5005 , Australia

    Department of Physics, University of Adelaide, Adelaide, 5005, Australia

  41. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  42. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  43. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  44. Harvard University

    Affiliation as printed

    Department of Physics and Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA

  45. The University of Adelaide

    Affiliation as printed

    Department of Physics , University of Adelaide , Adelaide , 5005 , Australia

    Department of Physics, University of Adelaide, Adelaide, 5005, Australia

  46. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  47. Université Libre de Bruxelles

    Affiliation as printed

    Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium

  48. Georgia Institute of Technology

    Affiliation as printed

    School of Physics and Center for Relativistic Astrophysics , Georgia Institute of Technology , Atlanta , GA 30332 , USA

    School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA

  49. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  50. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  51. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  52. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  53. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  54. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  55. Massachusetts Institute of Technology

    Affiliation as printed

    Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

  56. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  57. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  58. Vrije Universiteit Brussel

    Affiliation as printed

    Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium

  59. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  60. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  61. Georgia Institute of Technology · Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    School of Physics and Center for Relativistic Astrophysics , Georgia Institute of Technology , Atlanta , GA 30332 , USA

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  62. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  63. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  64. Uppsala University · Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University · RWTH Aachen University

    Affiliation as printed

    III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany

    Uppsala University , Uppsala , Sweden

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  65. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  66. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  67. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  68. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  69. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  70. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  71. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  72. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  73. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  74. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  75. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  76. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  77. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  78. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  79. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  80. Uppsala University · Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University · RWTH Aachen University

    Affiliation as printed

    III. Physikalisches Institut , RWTH Aachen University , D-52056 Aachen , Germany

    Uppsala University , Uppsala , Sweden

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  81. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  82. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  83. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  84. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  85. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  86. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  87. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  88. Chiba University

    Affiliation as printed

    Dept. of Physics and The International Center for Hadron Astrophysics, Chiba University, Chiba 263-8522, Japan

  89. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    Dept. of Physics , Southern University , Baton Rouge , LA 70813 , USA

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  90. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  91. Humboldt-Universität zu Berlin

    Affiliation as printed

    Institut für Physik , Humboldt-Universität zu Berlin , D-12489 Berlin , Germany

    Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany

  92. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  93. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  94. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  95. Southern University and Agricultural and Mechanical College · University of Alaska Anchorage · Lawrence Berkeley National Laboratory · The University of Texas at Arlington · Clark Atlanta University

    Affiliation as printed

    CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

    Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA

    Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

    Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

    Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

  96. Ruhr University Bochum

    Affiliation as printed

    Fakultät für Physik & Astronomie , Ruhr-Universität Bochum , D-44780 Bochum , Germany

    Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

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