An eV-scale sterile neutrino search using eight years of atmospheric muon neutrino data from the IceCube Neutrino Observatory
M. G. Aartsen, R. Abbasi, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, M. Ahrens, C. Alispach, N. M. Amin, K. Andeen, T. Anderson, I. Ansseau, G. Anton, C. Argüelles, J. Auffenberg, S. Axani, H. Bagherpour, X. Bai, A. Balagopal V., A. Barbano, S. W. Barwick, B. Bastian, V. Basu, V. Baum, S. Baur, R. Bay, J. J. Beatty, K.-H. Becker, J. Becker Tjus, S. BenZvi, D. Berley, E. Bernardini, D. Z. Besson, G. Binder, D. Bindig, E. Blaufuss, S. Blot, C. Bohm, S. Böser, O. Botner, J. Böttcher, E. Bourbeau, J. Bourbeau, F. Bradascio, J. Braun, S. Bron, J. Brostean-Kaiser, A. Burgman, J. Buscher, R. S. Busse, T. Carver, C. Chen, E. Cheung, D. Chirkin, S. Choi, B. A. Clark, K. Clark, L. Classen, A. Coleman, G. H. Collin, J. M. Conrad, P. Coppin, P. Correa, D. F. Cowen, R. Cross, P. Dave, C. De Clercq, J. J. DeLaunay, H. Dembinski, K. Deoskar, S. De Ridder, A. Desai, P. Desiati, K. D. de Vries, G. de Wasseige, M. de With, T. DeYoung, S. Dharani, A. Diaz, J. C. Díaz-Vélez, H. Dujmovic, M. Dunkman, M. A. DuVernois, E. Dvorak, T. Ehrhardt, P. Eller, R. Engel, P. A. Evenson, S. Fahey, A. R. Fazely, A. Fedynitch, J. Felde, A. T. Fienberg, K. Filimonov, C. Finley, D. Fox, A. Franckowiak, E. Friedman, A. Fritz, T. K. Gaisser, et al. (277 additional authors not shown)
AAn eV-scale sterile neutrino search using eight years of atmospheric muon neutrinodata from the IceCube Neutrino Observatory
M. G. Aartsen, R. Abbasi, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, M. Ahrens, C.Alispach, N. M. Amin, K. Andeen, T. Anderson, I. Ansseau, G. Anton, C. Arg¨uelles, J. Auffenberg, S.Axani, H. Bagherpour, X. Bai, A. Balagopal V., A. Barbano, S. W. Barwick, B. Bastian, V. Basu, V.Baum, S. Baur, R. Bay, J. J. Beatty,
19, 20
K.-H. Becker, J. Becker Tjus, S. BenZvi, D. Berley, E.Bernardini, ∗ D. Z. Besson, † G. Binder,
8, 9
D. Bindig, E. Blaufuss, S. Blot, C. Bohm, S. B¨oser, O.Botner, J. B¨ottcher, E. Bourbeau, J. Bourbeau, F. Bradascio, J. Braun, S. Bron, J. Brostean-Kaiser, A. Burgman, J. Buscher, R. S. Busse, T. Carver, C. Chen, E. Cheung, D. Chirkin, S. Choi, B. A.Clark, K. Clark, L. Classen, A. Coleman, G. H. Collin, J. M. Conrad, P. Coppin, P. Correa, D. F.Cowen,
52, 53
R. Cross, P. Dave, C. De Clercq, J. J. DeLaunay, H. Dembinski, K. Deoskar, S. De Ridder, A. Desai, P. Desiati, K. D. de Vries, G. de Wasseige, M. de With, T. DeYoung, S. Dharani, A. Diaz, J. C. D´ıaz-V´elez, H. Dujmovic, M. Dunkman, M. A. DuVernois, E. Dvorak, T. Ehrhardt, P. Eller, R.Engel, P. A. Evenson, S. Fahey, A. R. Fazely, A. Fedynitch, J. Felde, A. T. Fienberg, K. Filimonov, C.Finley, D. Fox, A. Franckowiak, E. Friedman, A. Fritz, T. K. Gaisser, J. Gallagher, E. Ganster, S.Garrappa, L. Gerhardt, T. Glauch, T. Gl¨usenkamp, A. Goldschmidt, J. G. Gonzalez, D. Grant, T.Gr´egoire, Z. Griffith, S. Griswold, M. G¨under, M. G¨und¨uz, C. Haack, A. Hallgren, R. Halliday, L.Halve, F. Halzen, K. Hanson, J. Hardin, A. Haungs, S. Hauser, D. Hebecker, D. Heereman, P. Heix, K. Helbing, R. Hellauer, F. Henningsen, S. Hickford, J. Hignight, G. C. Hill, K. D. Hoffman, R.Hoffmann, T. Hoinka, B. Hokanson-Fasig, K. Hoshina, ‡ F. Huang, M. Huber, T. Huber,
30, 56
K.Hultqvist, M. H¨unnefeld, R. Hussain, S. In, N. Iovine, A. Ishihara, M. Jansson, G. S. Japaridze, M.Jeong, B. J. P. Jones, F. Jonske, R. Joppe, D. Kang, W. Kang, A. Kappes, D. Kappesser, T. Karg, M. Karl, A. Karle, U. Katz, M. Kauer, M. Kellermann, J. L. Kelley, A. Kheirandish, J. Kim, T.Kintscher, J. Kiryluk, T. Kittler, S. R. Klein,
8, 9
R. Koirala, H. Kolanoski, L. K¨opke, C. Kopper, S.Kopper, D. J. Koskinen, P. Koundal, M. Kowalski,
10, 56
K. Krings, G. Kr¨uckl, N. Kulacz, N. Kurahashi, A. Kyriacou, J. L. Lanfranchi, M. J. Larson, F. Lauber, J. P. Lazar, K. Leonard, A. Leszczy´nska, Y.Li, Q. R. Liu, E. Lohfink, C. J. Lozano Mariscal, L. Lu, F. Lucarelli, A. Ludwig, J. L¨unemann, W.Luszczak, Y. Lyu,
8, 9
W. Y. Ma, J. Madsen, G. Maggi, K. B. M. Mahn, Y. Makino, P. Mallik, S.Mancina, I. C. Mari¸s, R. Maruyama, K. Mase, R. Maunu, F. McNally, K. Meagher, M. Medici, A.Medina, M. Meier, S. Meighen-Berger, J. Merz, T. Meures, J. Micallef, D. Mockler, G. Moment´e, T.Montaruli, R. W. Moore, R. Morse, M. Moulai, P. Muth, R. Nagai, U. Naumann, G. Neer, L. V.Nguyen, H. Niederhausen, M. U. Nisa, S. C. Nowicki, D. R. Nygren, A. Obertacke Pollmann, M.Oehler, A. Olivas, A. O’Murchadha, E. O’Sullivan, T. Palczewski,
8, 9
H. Pandya, D. V. Pankova, N.Park, G. K. Parker, E. N. Paudel, P. Peiffer, C. P´erez de los Heros, S. Philippen, D. Pieloth, S. Pieper, E. Pinat, A. Pizzuto, M. Plum, Y. Popovych, A. Porcelli, M. Prado Rodriguez, P. B. Price, G. T.Przybylski, C. Raab, A. Raissi, M. Rameez, L. Rauch, K. Rawlins, I. C. Rea, A. Rehman, R.Reimann, B. Relethford, M. Renschler, G. Renzi, E. Resconi, W. Rhode, M. Richman, B. Riedel, S.Robertson, M. Rongen, C. Rott, T. Ruhe, D. Ryckbosch, D. Rysewyk Cantu, I. Safa, S. E. SanchezHerrera, A. Sandrock, J. Sandroos, M. Santander, S. Sarkar, S. Sarkar, K. Satalecka, M. Scharf, M.Schaufel, H. Schieler, P. Schlunder, T. Schmidt, A. Schneider, J. Schneider, F. G. Schr¨oder,
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L.Schumacher, S. Sclafani, D. Seckel, S. Seunarine, S. Shefali, M. Silva, B. Smithers, R. Snihur, J.Soedingrekso, D. Soldin, M. Song, G. M. Spiczak, C. Spiering, J. Stachurska, M. Stamatikos, T.Stanev, R. Stein, J. Stettner, A. Steuer, T. Stezelberger, R. G. Stokstad, A. St¨oßl, N. L. Strotjohann, T. St¨urwald, T. Stuttard, G. W. Sullivan, I. Taboada, F. Tenholt, S. Ter-Antonyan, A. Terliuk, S.Tilav, K. Tollefson, L. Tomankova, C. T¨onnis, S. Toscano, D. Tosi, A. Trettin, M. Tselengidou, C. F.Tung, A. Turcati, R. Turcotte, C. F. Turley, B. Ty, E. Unger, M. A. Unland Elorrieta, M. Usner, J.Vandenbroucke, W. Van Driessche, D. van Eijk, N. van Eijndhoven, D. Vannerom, J. van Santen, S.Verpoest, M. Vraeghe, C. Walck, A. Wallace, M. Wallraff, T. B. Watson, C. Weaver, A. Weindl, M. J. Weiss, J. Weldert, C. Wendt, J. Werthebach, B. J. Whelan, N. Whitehorn, K. Wiebe, C. H. Wiebusch, D. R. Williams, L. Wills, M. Wolf, T. R. Wood, K. Woschnagg, G. Wrede, J. a r X i v : . [ h e p - e x ] J un Wulff, X. W. Xu, Y. Xu, J. P. Yanez, G. Yodh, S. Yoshida, T. Yuan, Z. Zhang, and M. Z¨ocklein(IceCube Collaboration) III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany Department of Physics, University of Adelaide, Adelaide, 5005, Australia Dept. of Physics and Astronomy, University of Alaska Anchorage,3211 Providence Dr., Anchorage, AK 99508, USA Dept. of Physics, University of Texas at Arlington, 502 Yates St.,Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA School of Physics and Center for Relativistic Astrophysics,Georgia Institute of Technology, Atlanta, GA 30332, USA Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA Dept. of Physics, University of California, Berkeley, CA 94720, USA Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Institut f¨ur Physik, Humboldt-Universit¨at zu Berlin, D-12489 Berlin, Germany Fakult¨at f¨ur Physik & Astronomie, Ruhr-Universit¨at Bochum, D-44780 Bochum, Germany Universit´e Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Dept. of Physics and Institute for Global Prominent Research, Chiba University, Chiba 263-8522, Japan Department of Physics, Loyola University Chicago, Chicago, IL 60660, USA Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Dept. of Physics, University of Maryland, College Park, MD 20742, USA Dept. of Astronomy, Ohio State University, Columbus, OH 43210, USA Dept. of Physics and Center for Cosmology and Astro-Particle Physics,Ohio State University, Columbus, OH 43210, USA Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1 Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg, D-91058 Erlangen, Germany Physik-department, Technische Universit¨at M¨unchen, D-85748 Garching, Germany D´epartement de physique nucl´eaire et corpusculaire,Universit´e de Gen`eve, CH-1211 Gen`eve, Switzerland Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium Dept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA Karlsruhe Institute of Technology, Institut f¨ur Kernphysik, D-76021 Karlsruhe, Germany Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA SNOLAB, 1039 Regional Road 24, Creighton Mine 9, Lively, ON, Canada P3Y 1N2 Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095, USA Department of Physics, Mercer University, Macon, GA 31207-0001, USA Dept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,University of Wisconsin, Madison, WI 53706, USA Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany Department of Physics, Marquette University, Milwaukee, WI, 53201, USA Institut f¨ur Kernphysik, Westf¨alische Wilhelms-Universit¨at M¨unster, D-48149 M¨unster, Germany Bartol Research Institute and Dept. of Physics and Astronomy,University of Delaware, Newark, DE 19716, USA Dept. of Physics, Yale University, New Haven, CT 06520, USA Dept. of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK Dept. of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA Physics Department, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA Dept. of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA Oskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden Dept. of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA Dept. of Physics, Sungkyunkwan University, Suwon 16419, Korea Institute of Basic Science, Sungkyunkwan University, Suwon 16419, Korea Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA Dept. of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany DESY, D-15738 Zeuthen, Germany Institute for Cosmic Ray Research, the University of Tokyo,5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8582, Japan (Dated: June 16, 2020)The results of a 3+1 sterile neutrino search using eight years of data from the IceCube NeutrinoObservatory are presented. A total of 305,735 muon neutrino events are analyzed in reconstructedenergy-zenith space to test for signatures of a matter-enhanced oscillation that would occur givena sterile neutrino state with a mass-squared differences between 0.01 eV and 100 eV . The best-fitpoint is found to be at sin (2 θ ) = 0 .
10 and ∆ m = 4 . , which is consistent with the no sterileneutrino hypothesis with a p-value of 8.0%. INTRODUCTION
The three-flavor massive neutrino oscillation formalismhas been well-established experimentally [1–4]. The stan-dard paradigm has also been challenged, by several ex-periments exhibiting anomalous ν e (¯ ν e ) appearance in ν µ (¯ ν µ ) beams [5, 6]. These anomalies can be interpreted asevidence for subleading oscillations of ν µ → ν e or ¯ ν µ → ¯ ν e caused by additional neutrinos with large mass-squareddifferences in the range of ∆ m ∼ . −
10 eV [7].On the other hand, measurements of the Z -boson de-cay width to invisible final states demonstrate that onlythree light neutrinos participate in weak interactions [8],so any additional neutrino flavor states must be non-weakly-interacting, or “sterile.” The simplest such modelis referred to as a “3+1” model, where in addition to thethree known mass states, a fourth heavier one is added.The relationship between the flavor and mass statesis described by a unitary matrix, U P NMS , which in thethree-neutrino model can be parameterized in terms ofthree mixing angles and one oscillation-accessible CP -violating phase. Adding a sterile state expands the mix-ing matrix to four dimensions, in which the added de-grees of freedom can be parameterized by introducingthree new rotations with angles θ , θ , and θ , and twonew oscillation-accessible CP -violating phases, δ and δ . The oscillation phenomenology of the 3+1 modeladds both shorter baseline vacuumlike oscillations, andalso novel oscillation effects in the presence of matter [9–13]. For eV-scale sterile neutrino states, for example,a matter-enhanced resonance [14–19] would result in thenear complete disappearance of TeV-scale muon antineu-trinos passing through the Earth’s core, as shown inFig. 1. By measuring and characterizing the flux of at-mospheric neutrinos in the GeV to PeV energy range, theIceCube Neutrino Observatory is uniquely positioned tosearch for such matter-enhanced oscillations, a smoking-gun signature of eV-scale sterile neutrinos.Testing the 3+1 model as an explanation of short-baseline anomalies and constraining its free parametersrequires measurements in multiple oscillation channels,including ν µ → ν µ [21–29], ν e → ν e [30–38], and ν µ → ν e [5, 6, 39–41]. Fits to global data [20, 42, 43] find astrong preference for models with sterile neutrinos over the standard three-neutrino paradigm. However, even atthe most preferred values of ∆ m ∼ , the mixing an-gles required to viably explain anomalies in the ν µ → ν e and ¯ ν µ → ¯ ν e channels are in strong tension with mea-surements of ν µ and ¯ ν µ disappearance. Evidence for os-cillation effects beyond the three-neutrino paradigm in ¯ ν µ disappearance are yet to be observed [43]. One of thesenonobservations was made by IceCube, using a sample of20,145 atmospheric ν µ and ¯ ν µ events collected over oneyear of detector livetime [26].This paper updates IceCube’s high-energy sterile neu-trino search using an eight-year dataset and improvedevent selection. The sample includes 305,735 well-reconstructed charged-current ν µ and ¯ ν µ events col-lected from May 13 th th E µ reco ) spanning E µ reco ∈ E t r u e ν [ G e V ] ν µ D i s a pp e a r a n ce [ % ] − . − . − . − .
25 0 . θ truez ) FIG. 1.
Muon-antineutrino oscillogram.
Atmospheric ¯ ν µ disappearance probability vs. true energy and cosine zenith atthe globally preferred sterile neutrino hypothesis of Ref. [20](∆ m = 1 . , sin (2 θ ) = 0 .
07, sin (2 θ ) = 0 . m >
0. Vertical white lines indicatetransitions between inner to outer core (cos( θ true ν ) = − . θ true z ) = − . C o un t s Best-fit 3+1 hypothesisNull HypothesisData E proxyµ [GeV]0.951.001.05 R a t i o t o N u ll FIG. 2.
Reconstructed muon energy.
Data points areshown as black markers with error bars that represent thestatistical error. The solid blue and red lines show the best-fitsterile neutrino hypothesis and the null (no sterile neutrino)hypothesis, respectively, with nuisance parameters set to theirbest-fit values in each case. [500 GeV , θ reco z spanning the up-going region from − . ICECUBE UP-GOING TRACK SAMPLE
The IceCube Neutrino Observatory is a cubic-kilometer neutrino detector buried in the Antarcticglacier [45]. It is comprised of photomultiplier tubesenclosed in glass pressure housings called “Digital Op-tical Modules” (DOMs) [46]. These are arranged in ver-tical strings on a hexagonal lattice. The main array con-sists of 78 strings spaced 125 m apart, each supporting60 downward-facing DOMs with a 17 m vertical spac-ing. A denser array called DeepCore [47] instrumentsthe clearest part of the ice within the main array. Theeight strings of DeepCore are arranged with lateral spac-ing between 42 m and 72 m and vertical DOM separationof 7 m. This analysis uses the complete set of IceCube DOMs in both the main array and DeepCore.The majority of IceCube events are produced by high-energy muons and neutrinos from cosmic-ray air showers.Down-going (cos θ true z >
0) atmospheric muons (and an-timuons) can penetrate the 1450 m vertical overburden ofthe detector, triggering at a rate of ∼ ν µ interaction will produce a forward secondary muon,with an energy typically between 50% and 80% of thatof the parent ν µ [49]. The muon travels through the iceemitting Cherenkov radiation. While photons travel tensto hundreds of meters before being absorbed by the im-purities in the ice [50–52], muons with TeV energies areable to penetrate multiple kilometers of ice before fallingbelow the Cherenkov threshold [53, 54]. This producesan extended tracklike signature. These events originateeither inside of the detector or from a target volume ex-tending meters to kilometers outside the array, dependingon energy [53, 55].Events used in this analysis first pass a filter that se-lects muon-like events for satellite transmission to theNorth, and are then subject to further data-reductiontechniques to reject low-energy and poorly reconstructedtracks. Only data periods with 86 active IceCube stringsand greater than 5,000 active DOMs in the detectorare considered. A high-level event selection is applied,leveraging morphology, measures of track reconstructionquality, and the expected transmission of signal eventsthrough the zenith-dependent overburden, explained indetail in Ref. [44] and based on Ref. [56]. The recon-structed energy and direction of each event is calculatedaccording to the time and geometry of light detectedthroughout the array [57, 58]. The angular resolution σ cos θ z varies between 0.005 and 0.015 and energy resolu-tion of σ log E µ ∼ .
5, as in the previous version of thisanalysis [26]. The energy distribution of selected eventsis shown in Fig. 2.Cosmic-ray muon background contamination is as-sessed using
CORSIKA [59], with primary cosmic-ray ener-gies ranging from 600 GeV to 10 GeV. Approximately10% of the dataset of neutrino events are predicted tocontain a coincident cosmic-ray muon within the readoutframe. The ν µ and cosmic-ray muon tracks are sepa-rated into sub-events using an event splitter, and eachsub-event is treated independently in the event selection.After splitting and event selection, the sample is pre-dicted to be > .
9% pure in ν µ / ¯ ν µ induced events [44]. STERILE NEUTRINO ANALYSIS
In this analysis, we consider a sterile neutrino modelparameterized by one mass-squared difference, ∆ m ,and one mixing angle, sin ( θ ). For each hypothesispoint on a grid of ∆ m from 10 − eV to 10 eV andsin (2 θ ) from 10 − to 1, the neutrino flux incident onthe detector is calculated using the four-flavor formalism.The neutrino flux includes contributions from both at-mospheric and astrophysical neutrinos. The conventionalatmospheric ν µ and ¯ ν µ flux is produced by the decay ofpions and kaons and is calculated using the MCEq cas-cade equation solver [60, 61]. The hadronic interactionsare modeled with Sibyll2.3c [62]. The primary cosmic-ray spectrum is a three-population model [63, 64], inwhich each population contains five groups of nuclei. Thezenith-dependent seasonal atmospheric density profile,through which the cascade develops, is determined us-ing data from the Atmospheric Infrared Sounder (AIRS)satellite [65]. The prompt ν µ component from the decayof charmed mesons is implemented as in Ref. [66]. Theastrophysical neutrino flux is assumed to have equal partsof each neutrino flavor and to be symmetric in neutrinosand antineutrinos [67–69]; be isotropically distributed;and have a single power-law energy spectrum consistentwith previous IceCube measurements [70]. These fluxesare subject to a suite of systematic uncertainties, sum-marized in the following section.For each sterile neutrino hypothesis, the atmo-spheric and astrophysical neutrino fluxes are propagatedthrough the Earth using the nuSQuIDS neutrino evolu-tion code [71, 72]. This accounts for both coherent andnon-coherent interactions [73]; namely charged-current,neutral-current, and Glashow resonance interactions [74],as well as tau-neutrino regeneration [75]. We use theCSMS [76] neutrino-nucleon cross section to describeboth interactions during neutrino propagation and nearthe detector. This requires as an input the Earth densityprofile, which we parameterize via the spherically sym-metric PREM model [77]. Using the above, we obtaina prediction for the up-going ν µ flux at the detector foreach physics parameter point. These fluxes are used toweight detector Monte Carlo (MC) event sets, with effec-tive livetime ≥ × the sample size.We account for systematic uncertainties by means ofnuisance parameters, which reweight the MC by apply-ing continuous parameterizations of the effects discussedin the following section. We then compare the data toexpectation using a modified version of the Poisson like-lihood to account for MC statistical uncertainty [78]. Forour frequentist analysis, the likelihood is profiled over theeighteen nuisance parameters to construct a test statistic.Frequentist contours are constructed using Wilks’ theo-rem [79], validated at an array of parameter points usingMC ensembles and the Feldman-Cousins [80] procedure. A Bayesian hypothesis test is also performed, by meansof comparing the model evidences [81] with respect to theno sterile neutrino hypothesis. The model evidences, as afunction of sterile neutrino parameters, are computed byintegrating the likelihood over the nuisance parametersusing MultiNest [82]. These two statistical approachesare complementary: the Bayesian approach conveys thelikelihood of the model given observed data and priorknowledge, whereas the frequentist approach yields in-tervals that are likely to contain the true model parame-ters for repeated experiments, enabling direct comparisonwith previous publications.
SYSTEMATIC UNCERTAINTIES
Dominant sources of uncertainty derive from the shapeand normalization of astrophysical and atmospheric neu-trino fluxes; the bulk properties of the South Pole ice;the local response of the IceCube DOMs; and neutrinointeraction cross sections. Other uncertainties, such asthe Earth density profile, neutrino interactions in therock/ice transition region, prompt neutrino flux, and ν µ /¯ ν µ astrophysical ratio were investigated but estab-lished as negligible relative to statistical uncertainty. Atmospheric Neutrino Flux:
In the relevant en-ergy range the spectrum of cosmic-ray primaries followsapproximately an E − . energy (E) dependence. To ac-count for the uncertainty in the cosmic-ray spectral in-dex, we apply a spectral shift ∆ γ with an uncertaintyof 0.03 pivoting at 2.2 TeV [83–86]. The meson produc-tion uncertainty in the interaction between the primarycosmic ray and air and in subsequent hadronic interac-tions is described through the Barr et al . scheme [87].In this scheme, the uncertainty in the differential crosssection for meson production is quantified in regions ofprimary proton energy E p and meson fractional momenta x lab . The charged-kaon production yield carries the lead-ing uncertainty. We parameterize its production overthree kinematic regions: x lab < . E p >
30 GeV; x lab ≥ . < E p <
500 GeV; and x lab > . E p ≥
500 GeV. We include two collider-constrainednuisance parameters for each region, one for particles andone for antiparticles, which rescale the production crosssection. The highest-energy uncertainties are obtainedthrough extrapolation, and both the scale and energydependence have ascribed uncertainties. Kaon energylosses by interaction with oxygen and nitrogen nuclei areaccounted for via the total kaon-nucleus cross-sectionaluncertainty [88]. The charged-pion production and in-teraction uncertainties were studied and found negligi-ble. The atmospheric density profile is inferred fromthe zenith-dependent vertical temperature profile mea-sured by the AIRS satellite. To incorporate its uncer-tainty, showers are recomputed through randomly per-turbed density models within the statistical and system-atic uncertainties reported in the AIRS measurements.Finally, the total conventional atmospheric ν µ flux car-ries an additional 40% normalization uncertainty follow-ing Ref. [61]. Astrophysical Neutrino Flux:
The central astro-physical model is a single power law with an equal nor-malization for all neutrino and antineutrino flavors at100 TeV of 0.787 × − GeV − sr − s − cm − and a spec-tral index of 2.5. The Gaussian priors on the normal-ization and spectral index are correlated and selectedto accommodate all IceCube astrophysical neutrino fluxmeasurements to date [70, 89–93], with allowed spectralindices of γ astro ∼ . − . γ astro . Bulk Ice Model:
The uncertainty associated withthe measured scattering and absorption of the undis-turbed glacial ice is implemented as described in Ref. [94].This treatment expresses the depth dependence of the iceoptical properties using a Fourier decomposition. Thecovariance of the Fourier mode coefficients are deter-mined using LED flasher calibration data [52]. Onlythe six lowest modes contribute a sizeable shape differ-ence in the reconstructed event distributions. The ef-fect of these modes is parameterized using two empiricalenergy-dependent basis functions. The two associatedamplitudes are incorporated as nuisance parameters witha correlated bivariate Gaussian prior.
DOM Response and Local Ice Effects:
The ice inthe immediate vicinity of the DOMs has optical proper-ties distinct from the bulk ice between strings [95], causedby bubble formation during the refreezing process aftertheir deployment. This introduces uncertainties via twoeffects. First, the global photon detection efficiency isimpacted. This is modeled by an efficiency correctionwith an effectively flat prior, ultimately constrained witha tight posterior through its effect on the overall energyscale. Second, the bubble column influences the angulardependence of photon detection. This is encoded in twoparameters tuned to detailed optical simulations of bub-ble scattering near the DOM [96], with only one havinga substantial impact.
Neutrino Cross Section:
The neutrino-nucleoncross section enters the analysis in two ways, influencing:1) absorption during the neutrino propagation throughthe Earth [49, 97] and 2) the rates and inelasticitiesof interactions near the detector [49, 76, 98]. The lat-ter source of uncertainty was previously investigated inRefs. [99, 100] and found to be negligible. The formeris found to be non-negligible and is taken into accountby separately parameterizing the change in neutrino ab-sorption when the ν µ and ¯ ν µ cross sections are scaled.The priors on these parameters are fixed at the largestuncertainties in our energy range from Ref. [76], whichare 3% for ν µ and 7% for ¯ ν µ . RESULTS − . − . − . − . − . . θ recoz )10 E p r o x y µ [ G e V ] . - . - . - . - . - . - . - . - . - . - . - . - . . - . - . - . - . - . - . - . - . - . - . - . - . . . - . - . - . - . - . - . - . - . - . - . - . . . . - . - . - . - . - . - . - . - . - . - . . . . . - . - . - . - . - . - . - . - . - . . . . . - . - . - . - . - . - . - . - . - . . . . . . - . - . - . - . - . - . - . - . . . . . . - . - . - . - . - . - . - . - . . . . . . - . - . - . - . - . - . - . - . . . . . . - . - . - . - . - . - . - . - . . . . . . - . - . - . - . - . - . - . - . . . . . . . - . - . - . - . - . - . - . . . . . . . - . - . - . - . - . - . - . . . . . . . - . - . - . - . - . - . . . . . . . . . - . - . - . - . - . . . . . . . . . - . - . - . . . . . . . . . . - . - . - . - . . . . . . . . - . - . - . - . - . . . . . . . - . - . - . - . - . . . . . . . - . - . - . - . - . - . . . . . . . . − − − − − ( B F | F i t - N u ll | B F S y s ) / N u ll | B F S y s [ % ] − . − . − . − . − . . θ recoz )10 E p r o x y µ [ G e V ] . - . - . - . - . . . - . - . - . - . - . - . . - . - . - . . . - . - . . - . . . - . . . . . . . - . - . - . - . - . - . . - . - . - . - . - . - . - . - . - . - . . - . . . - . . . - . . . . . - . . - . . . - . - . . . . - . - . . . - . - . . . . - . . . - . . . . . - . - . - . - . . - . . . . - . . - . . . . - . . . - . - . - . . - . - . . . . - . - . - . . . . - . - . . - . - . . . . . - . - . . - . - . . . - . - . - . - . . . . . - . - . . . . - . . . - . . - . . . - . - . - . - . - . - . - . . . - . . - . - . . . - . . - . - . - . - . . - . - . . . . . . . - . - . - . - . . - . . - . . - . - . . . - . . - . - . - . - . - . . . . . - . . . - . - . . - . - . - . - . . - . - . . . . - . - . - . . . . - . . . . - . - . - . - . - . - . . . - . - . . - . - . . - . . . . . . . . − − − − − ( D a t a - N u ll | B F S y s ) / N u ll | B F S y s [ % ] FIG. 3.
Best-fit signal shapes compared to data.
Top:The signal shape at the best-fit point compared to the nullhypothesis with the same nuisance parameters. Bottom: datacompared to the null hypothesis with the nuisance parametersheld at the same values.
The frequentist analysis best-fit point is ∆ m =4 . and sin (2 θ ) = 0 .
10. At this point, the largestnuisance parameter pull was observed in the cosmic-rayspectral index, which shifted the cosmic-ray spectrumby 0.068 (2.3 σ ); the other nuisance parameter best-fitvalues are within one sigma of their respective centralvalues and can be found in the accompanying Ref. [44].Fig. 3 shows the signal shape at the best-fit point, giventhe best-fit nuisance parameters, as well as the pull be-tween data and no sterile neutrino hypothesis, evalu-ated at those same nuisance parameters. Fig. 4 showsthe 90% and 99% C.L. contours calculated according toWilks’ theorem with two degrees of freedom. Sensitivityenvelopes, illustrating symmetrically counted ensemblesof 68% and 95% non-closed contours derived from 2,000pseudoexperiments, are shown overlaid for the 99% con-tour. The IceCube 90% C.L. preferred region is con-sistent with constraints from previous ν µ disappearance (2 θ )0.010.1110100 ∆m [ e V ]
99% CL:
This work 90% CLThis work 99% CL68% (trials)95% (trials)CDHSIceCubeDeepCoreMINOS/MINOS+Super-KamiokandeMiniBooNE-SciBooNECDHSIceCubeDeepCoreMINOS/MINOS+Super-KamiokandeMiniBooNE-SciBooNE
FIG. 4.
Frequentist analysis result.
The 90% and 99%C.L. contours, assuming Wilks’ theorem, shown as dashedand solid bold blue lines respectively. The green / yellow bandshows the region where 68% / 95% of the pseudoexperiment99% C.L. observations lie; the dashed white line correspondsto the median. Other muon-neutrino disappearance measure-ments at 99% C.L. are shown in black [22–27, 101]; where re-sults were not available at 99% C.L., methods of Ref. [20] wereapplied using public data releases. Finally, the star marks theanalysis best-fit point location. experiments, and the 99% contour is stronger than otherexclusion limits at values of ∆ m up to 1 eV .Fig. 5 shows the corresponding Bayesian result, wherethe point-wise Bayes factor is calculated relative to theno sterile neutrino hypothesis. The best-model locationis at ∆ m ∼ . and sin (2 θ ) ∼ . (2 θ )0.010.1110100 ∆m [ e V ] LogLog (BF)(BF) == LogLog (BF)(BF) == LogLog (BF)(BF) == − . − . − . − . − . . . . . . . L og ( B a y e s F a c t o r) FIG. 5.
Bayesian analysis result.
The logarithm of theBayes Factor [102] relative to the null hypothesis (color scale).Red indicates hypotheses preferred over the null hypothesis,while the blue indicates the null is preferred. Solid lines de-lineate likelihood ratios of 1 in 10 for a priori equally likelyhypotheses. The best-model location is shown at the whitestar with a log (Bayes Factor) minimum of − . duce closed contours at 90% C.L. in 10% of trials.In summary, we have studied 305,735 up-going atmo-spheric and astrophysical muon-neutrinos to search forevidence of eV-sterile neutrino signatures. The best-fitpoint is consistent with the no sterile neutrino hypothe-sis at a p-value of 8%. Because of its unique statisticalstrength this result is expected to have a substantial im-pact on the global sterile neutrino landscape. ACKNOWLEDGEMENTS
The IceCube collaboration acknowledges the signif-icant contributions to this manuscript from the Mas-sachusetts Institute of Technology and University ofTexas at Arlington groups.We acknowledge the support from the following agen-cies: USA – U.S. National Science Foundation-Officeof Polar Programs, U.S. National Science Foundation-Physics Division, Wisconsin Alumni Research Founda-tion, Center for High Throughput Computing (CHTC)at the University of Wisconsin-Madison, Open ScienceGrid (OSG), Extreme Science and Engineering Discov-ery Environment (XSEDE), U.S. Department of Energy-National Energy Research Scientific Computing Cen-ter, Particle astrophysics research computing center atthe University of Maryland, Institute for Cyber-EnabledResearch at Michigan State University, and Astropar-ticle physics computational facility at Marquette Uni-versity; Belgium – Funds for Scientific Research (FRS-FNRS and FWO), FWO Odysseus and Big Science pro-grammes, and Belgian Federal Science Policy Office (Bel-spo); Germany – Bundesministerium f¨ur Bildung undForschung (BMBF), Deutsche Forschungsgemeinschaft(DFG), Helmholtz Alliance for Astroparticle Physics(HAP), Initiative and Networking Fund of the HelmholtzAssociation, Deutsches Elektronen Synchrotron (DESY),and High Performance Computing cluster of the RWTHAachen; Sweden – Swedish Research Council, SwedishPolar Research Secretariat, Swedish National Infrastruc-ture for Computing (SNIC), and Knut and Alice Wallen-berg Foundation; Australia – Australian Research Coun-cil; Canada – Natural Sciences and Engineering ResearchCouncil of Canada, Calcul Qu´ebec, Compute Ontario,Canada Foundation for Innovation, WestGrid, and Com-pute Canada; Denmark – Villum Fonden, Danish Na-tional Research Foundation (DNRF), Carlsberg Foun-dation; New Zealand – Marsden Fund; Japan – JapanSociety for Promotion of Science (JSPS) and Institutefor Global Prominent Research (IGPR) of Chiba Uni-versity; Korea – National Research Foundation of Korea(NRF); Switzerland – Swiss National Science Foundation(SNSF); United Kingdom – Department of Physics, Uni-versity of Oxford. ∗ also at Universit`a di Padova, I-35131 Padova, Italy † also at National Research Nuclear University, MoscowEngineering Physics Institute (MEPhI), Moscow115409, Russia ‡ Earthquake Research Institute, University of Tokyo,Bunkyo, Tokyo 113-0032, Japan[1] M. Tanabashi et al. (Particle Data Group), Review ofParticle Physics, Phys. Rev.
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