# Interpreting IceCube 6-year HESE data as an evidence for hundred TeV decaying Dark Matter

###### Abstract

The assumption of a single astrophysical power-law flux to explain the IceCube 6-year HESE extraterrestrial events yields a large spectral index that is in tension with gamma-ray observations and the 6-year up-going muon neutrinos data. Adopting a spectral index belonging to the range , which is compatible with the one deduced by the analysis performed on the 6-year up-going muon neutrinos data and with - astrophysical sources, the latest IceCube data show an up to excess in the number of events in the energy range 40–200 TeV. We interpret such an excess as a decaying Dark Matter signal and we perform a likelihood-ratio statistical test to compare the two-component scenario with respect to the single-component one.

In the last few years IceCube (IC) Neutrino Telescope has been collecting neutrino events in the TeV - PeV range Aartsen:2013jdh (); Aartsen:2014gkd (); Aartsen:2014muf (); Kopper:2015vzf (); Aartsen:2016xlq (); Aartsen:2013eka () that are providing striking evidences for extraterrestrial neutrinos even though their origin still remains unknown. According to the IC veto implementation, the IC data are mainly divided in two samples: “Medium Energy Starting Events” (MESE) with an energy threshold of 1 TeV and “High Energy Starting Events” (HESE) for neutrino energies larger than 20 TeV. In both data sets, the neutrino interaction vertex is located inside the detector. The analysis of such events has triggered an interesting discussion in the scientific community about their possible astrophysical origin, as well as an intriguing connection with Dark Matter (DM). In particular, IC events have been related to the decay or annihilation of very heavy DM particles Anisimov:2008gg (); Feldstein:2013kka (); Esmaili:2013gha (); Bai:2013nga (); Ema:2013nda (); Esmaili:2014rma (); Bhattacharya:2014vwa (); Higaki:2014dwa (); Rott:2014kfa (); Ema:2014ufa (); Murase:2015gea (); Dudas:2014bca (); Fong:2014bsa (); Aisati:2015vma (); Ko:2015nma (); Dev:2016qbd (); Fiorentin:2016avj (); DiBari:2016guw (); Zavala:2014dla (); Anchordoqui:2015lqa (); Dev:2016uxj (); Chianese:2016smc (); Borah:2017xgm (); Boucenna:2015tra (); Chianese:2016opp (); Chianese:2016kpu (); Hiroshima:2017hmy (); Bhattacharya:2017jaw (); ElAisati:2017ppn (); Bhattacharya:2014yha (); Bhattacharya:2016tma (). A pure astrophysical explanation of neutrino events has been also extensively discussed in the literature where different sources have been proposed. In particular, among such sources one can quote the stellar remnants in star-forming galaxies Loeb:2006tw (); Murase:2013rfa (), extragalactic Supernovae and Hypernovae remnants Chakraborty:2015sta (), active galactic nuclei Stecker:1991vm (); Kalashev:2013vba (); Kalashev:2014vya (), and gamma-ray bursts Waxman:1997ti ().

At the ICRC 2017 Conference the IceCube Collaboration has released the 6-year HESE data proceedingIC (), which consist of a sample of 82 events (track + shower). The analysis performed on the neutrinos with a deposited energy above 60 TeV provides a best-fit power-law with spectral index^{1}^{1}1Note that a hard power-law behavior is predicted by the Waxman-Bahcall bound Waxman:1998yy () according to the standard Fermi acceleration mechanism at shock fronts Fermi:1949ee (). equal to . Note that such a best-fit spectral index is larger than the one obtained by the 4-year HESE data () Kopper:2015vzf (). This is due to the fact that, during the last two years, IC experiment has not observed neutrinos with deposited energy larger than about 200 TeV.

According to multi-messenger analyses^{2}^{2}2In this case, it means to compare the predictions of the associated gamma-ray spectrum with the available measurements., one would expect a spectral index in case of hadronic (–) astrophysical sources Loeb:2006tw (); Murase:2013rfa (); Bechtol:2015uqb (); Chakraborty:2016mvc (). On the other hand, photo-hadronic (–) sources, that would produce a softer power-law neutrino flux, are strongly constrained by searches of spatial and temporal correlations with gamma-ray observations Aartsen:2016lir (); Aartsen:2017wea (). In this framework, if one takes a conservative approach, the ambiguity (– vs –) that concerns the nature of dominant neutrino sources does not allow to fix a reliable bound on the spectral index.

Nevertheless, the analysis restricted to the 6-year up-going muon neutrinos data requires a spectral index as best-fit Aartsen:2016xlq (). Therefore, assuming isotropy (extragalactic sources) and an equal neutrino flavor ratio at the Earth, one would reasonably expect such a hard power-law for the whole diffuse TeV-PeV neutrino flux.

Hence, for the above arguments, large values for the spectral index like , and even more , seem to suggest that an additional component dominating at energies TeV is required. The additional second component, superimposed to a single unbroken power-law flux, can be given, for instance, by an extra power-law proceedingIC (); Chen:2014gxa (); Palladino:2016zoe (); Vincent:2016nut (); Palladino:2016xsy (); Anchordoqui:2016ewn () (hidden cosmic-ray accelerators are viable astrophysical candidates for the second component Kimura:2014jba (); Murase:2015xka (); Senno:2015tsn ()) or by decay/annihilating DM particles Chianese:2016opp (); Chianese:2016kpu ().

In Figure 1 we show the residual in number of neutrino events with respect to the sum of the conventional atmospheric background and a power-law with spectral index 2.0 (upper panel) and 2.2 (lower panel). The power-law normalization has been obtained by a maximum likelihood procedure in both cases. We highlight the presence of an excess at low energy, in the energy bins between 40 and 200 TeV. In case of spectral index 2.0, the maximum local statistical significance of such an excess is (6-year HESE), hence slightly larger than the one of obtained in the previous analysis concerning 4-year HESE Chianese:2016opp (). The maximum local statistical significance decreases to in case of a power-law with spectral index 2.2. We note that in case of 2-year MESE data sample Aartsen:2014muf () the discrepancy is () for (), as shown in Ref. Chianese:2016kpu (). Hence, independent of the spectral index adopted, the statistical evidence for an excess slightly improves once the 6-year HESE data are used instead of 4-year HESE or 2-year MESE.

In this Letter, we focus on the interpretation of the low-energy excess in terms of two components, an Astrophysical (Astro) power-law and a decaying Dark Matter (DM) signal.^{3}^{3}3Note that the annihilation scenario is almost excluded by unitarity constraint Chianese:2016kpu () and by search for a signal in the Milky Way Albert:2016emp (). Therefore, in addition to the conventional atmospheric background Honda:2006qj (), the whole extraterrestrial differential neutrino flux is given by

(1) |

The quantity is the normalization of the astrophysical neutrino flux, whereas the quantity is the normalization of the DM neutrino flux, i.e. the inverse lifetime in case of decaying DM with mass . For the sake of brevity we omit all the details of the above definitions. An extensive discussion of such a parametrization can be found in Ref. Chianese:2016kpu (). Note that the prompt atmospheric background (neutrinos produced by the decays of charmed mesons) Enberg:2008te () is here considered negligible, in agreement with the IceCube results contained in Ref. Aartsen:2016xlq (); Aartsen:2014muf (); Aartsen:2013eka ().

As shown in Eq. (1) the whole extraterrestrial neutrino flux depends on four free parameters, namely , , and . Hence, a statistical analysis to study the relevance of the additional DM component should consider the whole set of parameters. In this letter we follow the same approach of Ref. Chianese:2016kpu () that is strongly based on the prior previously discussed. Clearly, relaxing such a constraint the evidence for an additional component becomes almost statistically irrelevant. In particular, one would obtain the best-fit that is however in tension with the 6-year up-going muon neutrinos data. In the following analysis we consider two fixed values that corresponding to the extreme cases give an idea of the dependence of the results on the spectral index. To further simplify the analysis, the remaining free parameter for the astrophysical component, namely , can be fixed at its best-fit value. This ansatz corresponds to a conservative approach where one leaves to the additional DM component the smallest room possible.

Concerning the DM component, we only consider two different decay channels of DM particles (hereafter denoted as ), which can be seen as benchmarks. In particular, we focus on the hadronic decay channel , and on the leptonic one . Since the neutrino spectra produced in channels with hadronic or leptonic final-states have very different shape, considering these two decay channels practically covers all the possible phenomenological scenarios. The neutrino energy spectra provided by DM decays at the production are obtained by using the tables of Ref. Cirelli:2010xx (). Moreover, we consider the Navarro-Frenk-White (NFW) distribution Navarro:1995iw () for the DM halo density profile of the Milky Way and the CDM parameters according to the Planck analysis Ade:2015xua (). In the present analysis, in order to account for the neutrino oscillations we adopt the same approach used in Ref. Chianese:2016kpu ().

In order to quantify how the fit is statistically improved by adding a DM neutrino component of a given mass on top of an astrophysical power-law, we remake the analysis given in Ref. Chianese:2016kpu () with the latest 6-year HESE data proceedingIC (). In particular, we perform a likelihood-ratio statistical analysis on the neutrino energy spectrum, where the Test Statistics () is defined as

(2) |

Following the above discussion, the Test Statistics is evaluated by fixing the particular DM model (final-states and ), the spectral index and to its best-fit value, and by scanning over the only remaining free parameter, namely the normalization of the DM flux. According to Wilks Wilks:1938dza () and Chernoff Chernoff () theorems, the TS follows the distribution . Therefore, we evaluate the preference of the data for a two-component flux with respect to the single astrophysical power-law, in number of standard deviations . The likelihood function adopted in Eq. (2) is a binned multi-Poisson likelihood Baker:1983tu (), whose expression is equal to

(3) |

where the quantity is the observed number of neutrinos in the energy bin , whereas is the expected number of events given by the sum of events related to the flux of Eq. (1) and the background ones (conventional atmospheric neutrinos and penetrating muons). The number of extraterrestrial neutrinos is obtained by integrating the flux of Eq. (1) with the IceCube effective area Aartsen:2013jdh () and considering an exposure time of 2078 days (for more details see Ref. Chianese:2016kpu ()).

The main results of the present analysis are presented in Figures 2 and 3. The plots display the number of standard deviations in the – plane for the decay channels considered, namely and . In particular, the darker the color, the larger the significance in of the DM neutrino component. The upper and lower panels of both Figures refer to an astrophysical power-law with spectral index 2.0 and 2.2, respectively. In the plots, the best-fit values (maximum significance) is represented by white stars (the capital letter “H” refers to 6-year HESE analysis) and they are compared to the previous results of Ref. Chianese:2016kpu () represented here with black dots (the capital letter “M” refers to 2-year MESE analysis). The white solid (dashed) contours enclose the regions in the – plane where the statistical significance is larger than (). As can be seen from the plots, the maximum value of depends on the spectral index only, while it is almost independent of the decay channel considered. In particular, the statistical significance at the best-fit is and in case of spectral index 2.0 and 2.2, respectively.

Moreover, the present constraints on decaying DM models from IceCube observations are presented by the red lines. In particular, the solid red lines bound from above the regions that are excluded by the 6-year HESE data, while the dashed ones correspond to the same limit deduced by the 2-year MESE data. It is worth noting that the 6-year HESE data bound the possible DM models in a region with TeV. This feature depends on two effects. On one side the different energy thresholds for HESE data set (20 TeV) and MESE sample (1 TeV) provide different sensitivity of data and hence of TS for light . On the other side as can be seen from Figure 1, the second energy bin from left, corresponding to almost 25–40 TeV, shows a defect in the number of events and thus it disfavors any additional second component contributing to this energy. This pushes the possible DM models to higher masses.

Furthermore, the almost horizontal black lines, instead, correspond to the gamma-ray constraints on DM models deduced by the Fermi-LAT measurements of the isotropic diffuse gamma-ray background (IGRB) spectrum Ackermann:2014usa (). Such limits have been obtained by considering the total electromagnetic energy density of the IGRB integrated in the energy range from GeV to the maximum energy corresponding to . We report the constraints for DM contribution equal to 1%, 10% and 100% of , respectively. In particular, the solid black lines () bound from below the allowed region in the – plane. However, since it is quite reasonable to assume that the majority of the IGRB spectrum is accounted for by standard astrophysical sources, we consider the limit as a realistic constraint for the DM contribution to the gamma-ray flux. Therefore, only the regions above the short dashed black lines correspond to viable choices of parameters for DM models compatible with both neutrino and gamma-ray observations. Such multi-messenger constraints are affected by an uncertainty of about 20%, as discussed in Ref. Chianese:2016kpu () (see also Ref.s Esmaili:2014rma (); Murase:2012xs (); Esmaili:2015xpa (); Cohen:2016uyg () for different analyses about gamma-rays constraints on DM models).

We note that hadronic channel requires smaller values for the lifetime and larger DM masses with respect to the channel with leptons in the final-states in order to account for the IceCube data. This implies that the DM models with quarks as final-states are more in tension with Fermi-LAT data with respect to the models involving leptons, confirming the previous results discussed in Ref. Chianese:2016kpu (). In particular, in case of a DM decaying into top quarks the best-fit values are TeV and sec, while for the leptonic case we have TeV and sec. In Figure 4 we report the predictions of the two-component neutrino flux for the latter case.

In summary, in this Letter we have focused on the latest IceCube 6-year HESE data that improve the statistics with two more years of data-taking. The IceCube analysis performed on this data sample, with the assumption of a single astrophysical power-law flux, yields a best-fit spectral index . This large value for the spectral index (even larger with respect to of IceCube 4-year HESE) is in tension with the theoretical expectation of a hard power-law behavior for the neutrino flux (- astrophysical sources) and with the analysis performed on the 6-year up-going muon neutrinos data. Hence, it suggests the presence of a second component at low energy ( TeV) added to a hard power-law flux. Here, following the same approach of Ref. Chianese:2016kpu (), we have scrutinized the interpretation of such an additional component to diffuse neutrino flux in terms of a decaying DM signal.

The 6-year HESE data show an excess between 40 and 200 TeV, with a maximum local significance of , improving the previous estimate of corresponding to 2-year MESE Chianese:2016kpu (). The likelihood-ratio statistical test shows that the statistical improvement of the fit with the two-component flux reaches () at the best-fit for the case of (), confirming the previous results on 2-year MESE data Chianese:2016kpu (). However, differently from 2-year MESE, the best-fit for 6-year HESE seem to prefer larger values for even though this could be partially explained in terms of a lower sensitivity of such data set to low energy events.

Acknowledgments. We thank E. Cameron for the useful comments. We acknowledge support by the Istituto Nazionale di Fisica Nucleare I.S. TASP and the PRIN 2012 “Theoretical Astroparticle Physics” of the Italian Ministero dell’Istruzione, Università e Ricerca.

## References

- (1) M. G. Aartsen et al. [IceCube Collaboration], Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector, Science 342 (2013) 1242856 [arXiv:1311.5238].
- (2) M. G. Aartsen et al. [IceCube Collaboration], Search for a diffuse flux of astrophysical muon neutrinos with the IceCube 59-string configuration, Phys. Rev. D 89 (2014) no.6, 062007 [arXiv:1311.7048].
- (3) M. G. Aartsen et al. [IceCube Collaboration], Observation of High-Energy Astrophysical Neutrinos in Three Years of IceCube Data, Phys. Rev. Lett. 113 (2014) 101101 [arXiv:1405.5303].
- (4) M. G. Aartsen et al. [IceCube Collaboration], Atmospheric and astrophysical neutrinos above 1 TeV interacting in IceCube, Phys. Rev. D 91 (2015) no.2, 022001 [arXiv:1410.1749].
- (5) C. Kopper et al. [IceCube Collaboration], Observation of Astrophysical Neutrinos in Four Years of IceCube Data, PoS ICRC 2015 (2016) 1081.
- (6) M. G. Aartsen et al. [IceCube Collaboration], Observation and Characterization of a Cosmic Muon Neutrino Flux from the Northern Hemisphere using six years of IceCube data, [arXiv:1607.08006].
- (7) A. Anisimov and P. Di Bari, Cold Dark Matter from heavy Right-Handed neutrino mixing, Phys. Rev. D 80 (2009) 073017 [arXiv:0812.5085].
- (8) B. Feldstein, A. Kusenko, S. Matsumoto and T. T. Yanagida, Neutrinos at IceCube from Heavy Decaying Dark Matter, Phys. Rev. D 88 (2013) no.1, 015004 [arXiv:1303.7320].
- (9) A. Esmaili and P. D. Serpico, Are IceCube neutrinos unveiling PeV-scale decaying dark matter?, JCAP 1311 (2013) 054 [arXiv:1308.1105].
- (10) Y. Bai, R. Lu and J. Salvado, Geometric Compatibility of IceCube TeV-PeV Neutrino Excess and its Galactic Dark Matter Origin, JHEP 1601 (2016) 161 [arXiv:1311.5864].
- (11) Y. Ema, R. Jinno and T. Moroi, Cosmic-Ray Neutrinos from the Decay of Long-Lived Particle and the Recent IceCube Result, Phys. Lett. B 733 (2014) 120 [arXiv:1312.3501].
- (12) A. Bhattacharya, M. H. Reno and I. Sarcevic, Reconciling neutrino flux from heavy dark matter decay and recent events at IceCube, JHEP 1406 (2014) 110 [arXiv:1403.1862].
- (13) J. Zavala, Galactic PeV neutrinos from dark matter annihilation, Phys. Rev. D 89 (2014) no.12, 123516 [arXiv:1404.2932].
- (14) T. Higaki, R. Kitano and R. Sato, Neutrinoful Universe, JHEP 1407 (2014) 044 [arXiv:1405.0013].
- (15) A. Bhattacharya, R. Gandhi and A. Gupta, The Direct Detection of Boosted Dark Matter at High Energies and PeV events at IceCube, JCAP 1503 (2015) no.03, 027 [arXiv:1407.3280].
- (16) Y. Ema, R. Jinno and T. Moroi, Cosmological Implications of High-Energy Neutrino Emission from the Decay of Long-Lived Particle, JHEP 1410 (2014) 150 [arXiv:1408.1745].
- (17) C. Rott, K. Kohri and S. C. Park, Superheavy dark matter and IceCube neutrino signals: Bounds on decaying dark matter, Phys. Rev. D 92 (2015) no.2, 023529 [arXiv:1408.4575].
- (18) A. Esmaili, S. K. Kang and P. D. Serpico, IceCube events and decaying dark matter: hints and constraints, JCAP 1412 (2014) no.12, 054 [arXiv:1410.5979].
- (19) C. S. Fong, H. Minakata, B. Panes and R. Zukanovich Funchal, Possible Interpretations of IceCube High-Energy Neutrino Events, JHEP 1502 (2015) 189 [arXiv:1411.5318].
- (20) E. Dudas, Y. Mambrini and K. A. Olive, Monochromatic neutrinos generated by dark matter and the seesaw mechanism, Phys. Rev. D 91 (2015) 075001 [arXiv:1412.3459].
- (21) K. Murase, R. Laha, S. Ando and M. Ahlers, Testing the Dark Matter Scenario for PeV Neutrinos Observed in IceCube, Phys. Rev. Lett. 115 (2015) no.7, 071301 [arXiv:1503.04663].
- (22) C. El Aisati, M. Gustafsson and T. Hambye, New Search for Monochromatic Neutrinos from Dark Matter Decay, Phys. Rev. D 92 (2015) no.12, 123515 [arXiv:1506.02657].
- (23) L. A. Anchordoqui, V. Barger, H. Goldberg, X. Huang, D. Marfatia, L. H. M. da Silva and T. J. Weiler, IceCube neutrinos, decaying dark matter, and the Hubble constant, Phys. Rev. D 92 (2015) no.6, 061301 Erratum: [Phys. Rev. D 94 (2016) no.6, 069901] [arXiv:1506.08788].
- (24) S. M. Boucenna, M. Chianese, G. Mangano, G. Miele, S. Morisi, O. Pisanti and E. Vitagliano, Decaying Leptophilic Dark Matter at IceCube, JCAP 1512, no. 12, 055 (2015) [arXiv:1507.01000].
- (25) P. Ko and Y. Tang, IceCube Events from Heavy DM decays through the Right-handed Neutrino Portal, Phys. Lett. B 751 (2015) 81 [arXiv:1508.02500].
- (26) M. Chianese, G. Miele, S. Morisi and E. Vitagliano, Low energy IceCube data and a possible Dark Matter related excess, Phys. Lett. B 757, 251 (2016) [arXiv:1601.02934].
- (27) P. S. B. Dev, D. K. Ghosh and W. Rodejohann, R-parity Violating Supersymmetry at IceCube, Phys. Lett. B 762 (2016) 116 [arXiv:1605.09743].
- (28) M. Re Fiorentin, V. Niro and N. Fornengo, A consistent model for leptogenesis, dark matter and the IceCube signal, [arXiv:1606.04445].
- (29) P. S. B. Dev, D. Kazanas, R. N. Mohapatra, V. L. Teplitz and Y. Zhang, Heavy right-handed neutrino dark matter and PeV neutrinos at IceCube, JCAP 1608 (2016) no.08, 034 [arXiv:1606.04517].
- (30) P. Di Bari, P. O. Ludl and S. Palomares-Ruiz, Unifying leptogenesis, dark matter and high-energy neutrinos with right-handed neutrino mixing via Higgs portal, [arXiv:1606.06238].
- (31) M. Chianese and A. Merle, A Consistent Theory of Decaying Dark Matter Connecting IceCube to the Sesame Street, JCAP 1704 (2017) no.04, 017 [arXiv:1607.05283].
- (32) M. Chianese, G. Miele and S. Morisi, Dark Matter interpretation of low energy IceCube MESE excess, JCAP 1701 (2017) no.01, 007 [arXiv:1610.04612].
- (33) A. Bhattacharya, R. Gandhi, A. Gupta and S. Mukhopadhyay, Boosted Dark Matter and its implications for the features in IceCube HESE data, JCAP 1705 (2017) no.05, 002 [arXiv:1612.02834].
- (34) D. Borah, A. Dasgupta, U. K. Dey, S. Patra and G. Tomar, Multi-component Fermionic Dark Matter and IceCube PeV scale Neutrinos in Left-Right Model with Gauge Unification, [arXiv:1704.04138].
- (35) N. Hiroshima, R. Kitano, K. Kohri and K. Murase, High-energy Neutrinos from Multi-body Decaying Dark Matter, [arXiv:1705.04419].
- (36) A. Bhattacharya, A. Esmaili, S. Palomares-Ruiz and I. Sarcevic, Probing decaying heavy dark matter with the 4-year IceCube HESE data, JCAP 1707 (2017) no.07, 027 [arXiv:1706.05746].
- (37) C. El Aisati, C. Garcia-Cely, T. Hambye and L. Vanderheyden, Prospects for discovering a neutrino line induced by dark matter annihilation, [arXiv:1706.06600].
- (38) A. Loeb and E. Waxman, The Cumulative background of high energy neutrinos from starburst galaxies, JCAP 0605 (2006) 003 [astro-ph/0601695].
- (39) K. Murase, M. Ahlers and B. C. Lacki, Testing the Hadronuclear Origin of PeV Neutrinos Observed with IceCube, Phys. Rev. D 88 (2013) no.12, 121301 [arXiv:1306.3417].
- (40) S. Chakraborty and I. Izaguirre, Diffuse neutrinos from extragalactic supernova remnants: Dominating the 100 TeV IceCube flux, Phys. Lett. B 745 (2015) 35 [arXiv:1501.02615].
- (41) F. W. Stecker, C. Done, M. H. Salamon and P. Sommers, High-energy neutrinos from active galactic nuclei, Phys. Rev. Lett. 66 (1991) 2697 Erratum: [Phys. Rev. Lett. 69 (1992) 2738].
- (42) O. E. Kalashev, A. Kusenko and W. Essey, PeV neutrinos from intergalactic interactions of cosmic rays emitted by active galactic nuclei, Phys. Rev. Lett. 111 (2013) no.4, 041103 [arXiv:1303.0300].
- (43) O. Kalashev, D. Semikoz and I. Tkachev, Neutrinos in IceCube from active galactic nuclei, J. Exp. Theor. Phys. 120 (2015) no.3, 541 [arXiv:1410.8124].
- (44) E. Waxman and J. N. Bahcall, High-energy neutrinos from cosmological gamma-ray burst fireballs, Phys. Rev. Lett. 78 (1997) 2292 [astro-ph/9701231].
- (45) C. Kopper, Observation of Astrophysical Neutrinos in Six Years of IceCube Data, contributed talk at ICRC 2017 Conference.
- (46) E. Waxman and J. N. Bahcall, High-energy neutrinos from astrophysical sources: An Upper bound, Phys. Rev. D 59 (1999) 023002 [hep-ph/9807282].
- (47) E. Fermi, On the Origin of the Cosmic Radiation, Phys. Rev. 75 (1949) 1169.
- (48) K. Bechtol, M. Ahlers, M. Di Mauro, M. Ajello and J. Vandenbroucke, Evidence against star-forming galaxies as the dominant source of IceCube neutrinos, [arXiv:1511.00688].
- (49) S. Chakraborty and I. Izaguirre, Star-forming galaxies as the origin of IceCube neutrinos: Reconciliation with Fermi-LAT gamma rays, [arXiv:1607.03361].
- (50) M. G. Aartsen et al. [IceCube Collaboration], The contribution of Fermi-2LAC blazars to the diffuse TeV-PeV neutrino flux, Astrophys. J. 835 (2017) no.1, 45 [arXiv:1611.03874].
- (51) M. G. Aartsen et al. [IceCube Collaboration], Extending the search for muon neutrinos coincident with gamma-ray bursts in IceCube data, Astrophys. J. 843 (2017) no.2, 112 [arXiv:1702.06868].
- (52) C. Y. Chen, P. S. Bhupal Dev and A. Soni, Two-component flux explanation for the high energy neutrino events at IceCube, Phys. Rev. D 92 (2015) no.7, 073001 [arXiv:1411.5658].
- (53) A. Palladino and F. Vissani, Extragalactic plus Galactic model for IceCube neutrino events, Astrophys. J. 826 (2016) no.2, 185 [arXiv:1601.06678].
- (54) A. C. Vincent, S. Palomares-Ruiz and O. Mena, Analysis of the 4-year IceCube high-energy starting events, Phys. Rev. D 94 (2016) no.2, 023009 [arXiv:1605.01556].
- (55) A. Palladino, M. Spurio and F. Vissani, On the IceCube spectral anomaly, JCAP 1612 (2016) no.12, 045 [arXiv:1610.07015].
- (56) L. A. Anchordoqui, M. M. Block, L. Durand, P. Ha, J. F. Soriano and T. J. Weiler, Evidence for a break in the spectrum of astrophysical neutrinos, Phys. Rev. D 95 (2017) no.8, 083009 [arXiv:1611.07905].
- (57) S. S. Kimura, K. Murase and K. Toma, Neutrino and Cosmic-Ray Emission and Cumulative Background from Radiatively Inefficient Accretion Flows in Low-Luminosity Active Galactic Nuclei, Astrophys. J. 806 (2015) 159 [arXiv:1411.3588].
- (58) K. Murase, D. Guetta and M. Ahlers, Hidden Cosmic-Ray Accelerators as an Origin of TeV-PeV Cosmic Neutrinos, Phys. Rev. Lett. 116 (2016) no.7, 071101 [arXiv:1509.00805].
- (59) N. Senno, K. Murase and P. Meszaros, Choked Jets and Low-Luminosity Gamma-Ray Bursts as Hidden Neutrino Sources, Phys. Rev. D 93 (2016) no.8, 083003 [arXiv:1512.08513].
- (60) A. Albert et al., Results from the search for dark matter in the Milky Way with 9 years of data of the ANTARES neutrino telescope, Phys. Lett. B 769 (2017) 249 [arXiv:1612.04595].
- (61) M. Honda, T. Kajita, K. Kasahara, S. Midorikawa and T. Sanuki, Calculation of atmospheric neutrino flux using the interaction model calibrated with atmospheric muon data, Phys. Rev. D 75 (2007) 043006 [astro-ph/0611418].
- (62) R. Enberg, M. H. Reno and I. Sarcevic, Prompt neutrino fluxes from atmospheric charm, Phys. Rev. D 78 (2008) 043005 [arXiv:0806.0418].
- (63) M. Cirelli et al., PPPC 4 DM ID: A Poor Particle Physicist Cookbook for Dark Matter Indirect Detection, JCAP 1103, 051 (2011) Erratum: [JCAP 1210, E01 (2012)] [arXiv:1012.4515].
- (64) J. F. Navarro, C. S. Frenk and S. D. M. White, The Structure of cold dark matter halos, [astro-ph/9508025].
- (65) P. A. R. Ade et al. [Planck Collaboration], Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589].
- (66) S. S. Wilks, The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses, Annals Math. Statist. 9 (1938) no.1, 60.
- (67) H. Chernoff, Annals Math. Statist. 25 (1938), 573.
- (68) S. Baker and R. D. Cousins, Clarification of the Use of Chi Square and Likelihood Functions in Fits to Histograms, Nucl. Instrum. Meth. 221, 437 (1984).
- (69) M. Ackermann et al. [Fermi-LAT Collaboration], The spectrum of isotropic diffuse gamma-ray emission between 100 MeV and 820 GeV, Astrophys. J. 799 (2015) 86 [arXiv:1410.3696].
- (70) K. Murase and J. F. Beacom, Constraining Very Heavy Dark Matter Using Diffuse Backgrounds of Neutrinos and Cascaded Gamma Rays, JCAP 1210 (2012) 043 [arXiv:1206.2595].
- (71) A. Esmaili and P. D. Serpico, Gamma-ray bounds from EAS detectors and heavy decaying dark matter constraints, JCAP 1510 (2015) no.10, 014 [arXiv:1505.06486].
- (72) T. Cohen, K. Murase, N. L. Rodd, B. R. Safdi and Y. Soreq, Gamma-ray Constraints on Decaying Dark Matter and Implications for IceCube, [arXiv:1612.05638].