Search

Active galactic nuclei (AGN) are prime candidate sources of the high-energy, astrophysical neutrinos detected by IceCube. This is demonstrated by the real-time multimessenger detection of the blazar TXS 0506+056 and the recent evidence of neutrino emission from NGC 1068 from a separate time-averaged study. However, the production mechanism of the astrophysical neutrinos in AGN is not well established, which can be resolved via correlation studies with photon observations. For neutrinos produced due to photohadronic interactions in AGN, in addition to a correlation of neutrinos with high-energy photons, there would also be a correlation of neutrinos with photons emitted at radio wavelengths. In this work, we perform an in-depth stacking study of the correlation between 15 GHz radio observations of AGN reported in the MOJAVE XV catalog, and 10 yr of neutrino data from IceCube. We also use a time-dependent approach, which improves the statistical power of the stacking analysis. No significant correlation was found for both analyses, and upper limits are reported. When compared to the IceCube diffuse flux, at 100 TeV and for a spectral index of 2.5, the upper limits derived are ∼3% and ∼9% for the time-averaged and time-dependent cases, respectively.

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,717 new measurements from 869 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 120 reviews are updated, including many that are heavily revised. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app. The 2024 edition of the Review of Particle Physics should be cited as: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

A measurement of the diffuse astrophysical neutrino spectrum is presented using IceCube data collected from 2011-2022 (10.3 years). We developed novel detection techniques to search for events with a contained vertex and exiting track induced by muon neutrinos undergoing a charged-current interaction. Searching for these starting track events allows us to not only more effectively reject atmospheric muons but also atmospheric neutrino backgrounds in the southern sky, opening a new window to the sub-100 TeV astrophysical neutrino sky. The event selection is constructed using a dynamic starting track veto and machine learning algorithms. We use this data to measure the astrophysical diffuse flux as a single power law flux (SPL) with a best-fit spectral index of γ=2.58-0.09+0.10 and per-flavor normalization of φper-flavorAstro=1.68-0.22+0.19×10-18×GeV-1 cm-2 s-1 sr-1 (at 100 TeV). The sensitive energy range for this dataset is 3-550 TeV under the SPL assumption. This data was also used to measure the flux under a broken power law, however we did not find any evidence of a low energy cutoff.

Neutrino oscillations at the highest energies and longest baselines can be used to study the structure of spacetime and test the fundamental principles of quantum mechanics. If the metric of spacetime has a quantum mechanical description, its fluctuations at the Planck scale are expected to introduce non-unitary effects that are inconsistent with the standard unitary time evolution of quantum mechanics. Neutrinos interacting with such fluctuations would lose their quantum coherence, deviating from the expected oscillatory flavour composition at long distances and high energies. Here we use atmospheric neutrinos detected by the IceCube South Pole Neutrino Observatory in the energy range of 0.5–10.0 TeV to search for coherence loss in neutrino propagation. We find no evidence of anomalous neutrino decoherence and determine limits on neutrino–quantum gravity interactions. The constraint on the effective decoherence strength parameter within an energy-independent decoherence model improves on previous limits by a factor of 30. For decoherence effects scaling as E2, our limits are advanced by more than six orders of magnitude beyond past measurements compared with the state of the art.

The IceCube Neutrino Observatory relies on an array of photomultiplier tubes to detect Cherenkov light produced by charged particles in the South Pole ice. IceCube data analyses depend on an in-depth characterization of the glacial ice, and on novel approaches in event reconstruction that utilize fast approximations of photoelectron yields. Here, a more accurate model is derived for event reconstruction that better captures our current knowledge of ice optical properties. When evaluated on a Monte Carlo simulation set, the median angular resolution for in-ice particle showers improves by over a factor of three compared to a reconstruction based on a simplified model of the ice. The most substantial improvement is obtained when including effects of birefringence due to the polycrystalline structure of the ice. When evaluated on data classified as particle showers in the high-energy starting events sample, a significantly improved description of the events is observed.

Neutrino flares in the sky are searched for in data collected by IceCube between 2011 and 2021 May. This data set contains cascade-like events originating from charged-current electron neutrino and tau neutrino interactions and all-flavor neutral-current interactions. IceCube’s previous all-sky searches for neutrino flares used data sets consisting of track-like events originating from charged-current muon neutrino interactions. The cascade data set is statistically independent of the track data sets, and while inferior in angular resolution, the low-background nature makes it competitive and complementary to previous searches. No statistically significant flare of neutrino emission was observed in an all-sky scan. Upper limits are calculated on neutrino flares of varying duration from 1 hr to 100 days. Furthermore, constraints on the contribution of these flares to the diffuse astrophysical neutrino flux are presented, showing that multiple unresolved transient sources may contribute to the diffuse astrophysical neutrino flux.

We present the results of a search for 10-1000 GeV neutrinos from 2268 gamma-ray bursts (GRBs) over 8 yr of IceCube-DeepCore data. This work probes burst physics below the photosphere where electromagnetic radiation cannot escape. Neutrinos of tens of giga electronvolts are predicted in sub-photospheric collision of free-streaming neutrons with bulk-jet protons. In a first analysis, we searched for the most significant neutrino-GRB coincidence using six overlapping time windows centered on the prompt phase of each GRB. In a second analysis, we conducted a search for a group of GRBs, each individually too weak to be detectable, but potentially significant when combined. No evidence of neutrino emission is found for either analysis. The most significant neutrino coincidence is for Fermi-GBM GRB bn 140807500, with a p-value of 0.097 corrected for all trials. The binomial test used to search for a group of GRBs had a p-value of 0.65 after all trial corrections. The binomial test found a group consisting only of GRB bn 140807500 and no additional GRBs. The neutrino limits of this work complement those obtained by IceCube at tera electronvolt to peta electronvolt energies. We compare our findings for the large set of GRBs as well as GRB 221009A to the sub-photospheric neutron-proton collision model and find that GRB 221009A provides the most constraining limit on baryon loading. For a jet Lorentz factor of 300 (800), the baryon loading on GRB 221009A is lower than 3.85 (2.13) at a 90% confidence level.

IceCube alert events are neutrinos with a moderate-to-high probability of having astrophysical origin. In this study, we analyze 11 yr of IceCube data and investigate 122 alert events and a selection of high-energy tracks detected between 2009 and the end of 2021. This high-energy event selection (alert events + high-energy tracks) has an average probability of ≥0.5 of being of astrophysical origin. We search for additional continuous and transient neutrino emission within the high-energy events’ error regions. We find no evidence for significant continuous neutrino emission from any of the alert event directions. The only locally significant neutrino emission is the transient emission associated with the blazar TXS 0506+056, with a local significance of 3σ, which confirms previous IceCube studies. When correcting for 122 test positions, the global p-value is 0.156 and compatible with the background hypothesis. We constrain the total continuous flux emitted from all 122 test positions at 100 TeV to be below 1.2 × 10−15 (TeV cm2 s)−1 at 90% confidence assuming an E −2 spectrum. This corresponds to 4.5% of IceCube’s astrophysical diffuse flux. Overall, we find no indication that alert events in general are linked to lower-energetic continuous or transient neutrino emission.

Name that Neutrino is a citizen science project where volunteers aid in classification of events for the IceCube Neutrino Observatory, an immense particle detector at the geographic South Pole. From March 2023 to September 2023, volunteers did classifications of videos produced from simulated data of both neutrino signal and background interactions. Name that Neutrino obtained more than 128,000 classifications by over 1800 registered volunteers that were compared to results obtained by a deep neural network machine-learning algorithm. Possible improvements for both Name that Neutrino and the deep neural network are discussed.

The LIGO/Virgo collaboration published the catalogs GWTC-1, GWTC-2.1, and GWTC-3 containing candidate gravitational-wave (GW) events detected during its runs O1, O2, and O3. These GW events can be possible sites of neutrino emission. In this paper, we present a search for neutrino counterparts of 90 GW candidates using IceCube DeepCore, the low-energy infill array of the IceCube Neutrino Observatory. The search is conducted using an unbinned maximum likelihood method, within a time window of 1000 s, and uses the spatial and timing information from the GW events. The neutrinos used for the search have energies ranging from a few GeV to several tens of TeV. We do not find any significant emission of neutrinos, and place upper limits on the flux and the isotropic-equivalent energy emitted in low-energy neutrinos. We also conduct a binomial test to search for source populations potentially contributing to neutrino emission. We report a nondetection of a significant neutrino-source population with this test.

Dark matter particles in the Galactic Center and halo can annihilate or decay into a pair of neutrinos producing a monochromatic flux of neutrinos. The spectral feature of this signal is unique and it is not expected from any astrophysical production mechanism. Its observation would constitute a dark matter smoking gun signal. We performed the first dedicated search with a neutrino telescope for such signal, by looking at both the angular and energy information of the neutrino events. To this end, a total of five years of IceCube's DeepCore data has been used to test dark matter masses ranging from 10 GeV to 40 TeV. No significant neutrino excess was found and upper limits on the annihilation cross section, as well as lower limits on the dark matter lifetime, were set. The limits reached are of the order of 10-24 cm3/s for an annihilation and up to 1027 s for decaying dark matter. Using the same data sample we also derive limits for dark matter annihilation or decay into a pair of Standard Model charged particles.

We present a catalog of likely astrophysical neutrino track-like events from the IceCube Neutrino Observatory. IceCube began reporting likely astrophysical neutrinos in 2016, and this system was updated in 2019. The catalog presented here includes events that were reported in real time since 2019, as well as events identified in archival data samples starting from 2011. We report 275 neutrino events from two selection channels as the first entries in the catalog, the IceCube Event Catalog of Alert Tracks, which will see ongoing extensions with additional alerts. The Gold and Bronze alert channels respectively provide neutrino candidates with a 50% and 30% probability of being astrophysical, on average assuming an astrophysical neutrino power-law energy spectral index of 2.19. For each neutrino alert, we provide the reconstructed energy, direction, false-alarm rate, probability of being astrophysical in origin, and likelihood contours describing the spatial uncertainty in the alert's reconstructed location. We also investigate a directional correlation of these neutrino events with gamma-ray and X-ray catalogs, including 4FGL, 3HWC, TeVCat, and Swift-BAT.

The IceCube Neutrino Observatory sends realtime neutrino alerts with a high probability of being astrophysical in origin. We present a new method to correlate these events and possible candidate sources using 2089 blazars from the Fermi-LAT 4LAC-DR2 catalog and with 3413 active galactic nuclei (AGNs) from the Radio Fundamental Catalog. No statistically significant neutrino emission was found in any of the catalog searches. The result suggests that a small fraction,

The understanding of novae, the thermonuclear eruptions on the surfaces of white dwarf stars in binaries, has recently undergone a major paradigm shift. Though the bolometric luminosity of novae was long thought to arise directly from photons supplied by the thermonuclear runaway, recent gigaelectronvolt (GeV) gamma-ray observations have supported the notion that a significant portion of the luminosity could come from radiative shocks. More recently, observations of novae have lent evidence that these shocks are acceleration sites for hadrons for at least some types of novae. In this scenario, a flux of neutrinos may accompany the observed gamma rays. As the gamma rays from most novae have only been observed up to a few GeV, novae have previously not been considered as targets for neutrino telescopes, which are most sensitive at and above teraelectronvolt (TeV) energies. Here, we present the first search for neutrinos from novae with energies between a few GeV and 10 TeV using IceCube-DeepCore, a densely instrumented region of the IceCube Neutrino Observatory with a reduced energy threshold. We search both for a correlation between gamma-ray and neutrino emission as well as between optical and neutrino emission from novae. We find no evidence for neutrino emission from the novae considered in this analysis and set upper limits for all gamma-ray detected novae.

Beginning in 2016, the IceCube Neutrino Observatory has sent out alerts in real time containing the information of high-energy (E ≳ 100 TeV) neutrino candidate events with moderate to high (≳30%) probability of astrophysical origin. In this work, we use a recent catalog of such alert events, which, in addition to events announced in real time, includes events that were identified retroactively and covers the time period of 2011-2020. We also search for additional, lower-energy neutrinos from the arrival directions of these IceCube alerts. We show how performing such an analysis can constrain the contribution of rare populations of cosmic neutrino sources to the diffuse astrophysical neutrino flux. After searching for neutrino emission coincident with these alert events on various timescales, we find no significant evidence of either minute-scale or day-scale transient neutrino emission or of steady neutrino emission in the direction of these alert events. This study also shows how numerous a population of neutrino sources has to be to account for the complete astrophysical neutrino flux. Assuming that sources have the same luminosity, an E −2.5 neutrino spectrum, and number densities that follow star formation rates, the population of sources has to be more numerous than 7 × 10−9 Mpc−3. This number changes to 3 × 10−7 Mpc−3 if number densities instead have no cosmic evolution.

Core-collapse supernovae are a promising potential high-energy neutrino source class. We test for correlation between seven years of IceCube neutrino data and a catalog containing more than 1000 core-collapse supernovae of types IIn and IIP and a sample of stripped-envelope supernovae. We search both for neutrino emission from individual supernovae as well as for combined emission from the whole supernova sample, through a stacking analysis. No significant spatial or temporal correlation of neutrinos with the cataloged supernovae was found. All scenarios were tested against the background expectation and together yield an overall p-value of 93%; therefore, they show consistency with the background only. The derived upper limits on the total energy emitted in neutrinos are 1.7 × 1048 erg for stripped-envelope supernovae, 2.8 × 1048 erg for type IIP, and 1.3 × 1049 erg for type IIn SNe, the latter disfavoring models with optimistic assumptions for neutrino production in interacting supernovae. We conclude that stripped-envelope supernovae and supernovae of type IIn do not contribute more than 14.6% and 33.9%, respectively, to the diffuse neutrino flux in the energy range of about [ 103-105] GeV, assuming that the neutrino energy spectrum follows a power-law with an index of −2.5. Under the same assumption, we can only constrain the contribution of type IIP SNe to no more than 59.9%. Thus, core-collapse supernovae of types IIn and stripped-envelope supernovae can both be ruled out as the dominant source of the diffuse neutrino flux under the given assumptions.

The D-Egg, an acronym for "Dual optical sensors in an Ellipsoid Glass for Gen2,"is one of the optical modules designed for future extensions of the IceCube experiment at the South Pole. The D-Egg has an elongated-sphere shape to maximize the photon-sensitive effective area while maintaining a narrow diameter to reduce the cost and the time needed for drilling of the deployment holes in the glacial ice for the optical modules at depths up to 2700 m. The D-Egg design is utilized for the IceCube Upgrade, the next stage of the IceCube project also known as IceCube-Gen2 Phase 1, where nearly half of the optical sensors to be deployed are D-Eggs. With two 8-inch high-quantum efficiency photomultiplier tubes (PMTs) per module, D-Eggs offer an increased effective area while retaining the successful design of the IceCube digital optical module (DOM). The convolution of the wavelength-dependent effective area and the Cherenkov emission spectrum provides an effective photodetection sensitivity that is 2.8 times larger than that of IceCube DOMs. The signal of each of the two PMTs is digitized using ultra-low-power 14-bit analog-to-digital converters with a sampling frequency of 240 MSPS, enabling a flexible event triggering, as well as seamless and lossless event recording of single-photon signals to multi-photons exceeding 200 photoelectrons within 10 ns. Mass production of D-Eggs has been completed, with 277 out of the 310 D-Eggs produced to be used in the IceCube Upgrade. In this paper, we report the design of the D-Eggs, as well as the sensitivity and the single to multi-photon detection performance of mass-produced D-Eggs measured in a laboratory using the built-in data acquisition system in each D-Egg optical sensor module.

Gamma-ray bursts (GRBs) have long been considered a possible source of high-energy neutrinos. While no correlations have yet been detected between high-energy neutrinos and GRBs, the recent observation of GRB 221009A—the brightest GRB observed by Fermi-GBM to date and the first one to be observed above an energy of 10 TeV—provides a unique opportunity to test for hadronic emission. In this paper, we leverage the wide energy range of the IceCube Neutrino Observatory to search for neutrinos from GRB 221009A. We find no significant deviation from background expectation across event samples ranging from MeV to PeV energies, placing stringent upper limits on the neutrino emission from this source.

Galactic PeV cosmic-ray accelerators (PeVatrons) are Galactic sources theorized to accelerate cosmic rays up to PeV in energy. The accelerated cosmic rays are expected to interact hadronically with nearby ambient gas or the interstellar medium, resulting in γ-rays and neutrinos. Recently, the Large High Altitude Air Shower Observatory (LHAASO) identified 12 γ-ray sources with emissions above 100 TeV, making them candidates for PeVatrons. While at these high energies the Klein-Nishina effect exponentially suppresses leptonic emission from Galactic sources, evidence for neutrino emission would unequivocally confirm hadronic acceleration. Here, we present the results of a search for neutrinos from these γ-ray sources and stacking searches testing for excess neutrino emission from all 12 sources as well as their subcatalogs of supernova remnants and pulsar wind nebulae with 11 yr of track events from the IceCube Neutrino Observatory. No significant emissions were found. Based on the resulting limits, we place constraints on the fraction of γ-ray flux originating from the hadronic processes in the Crab Nebula and LHAASO J2226+6057.

In the hopes of observing the highest-energy neutrinos (E>1 EeV) populating the Universe, both past (RICE, AURA, ANITA) and current (RNO-G, ARIANNA, ARA and TAROGE-M) polar-sited experiments exploit the impulsive radio emission produced by neutrino interactions. In such experiments, rare single event candidates must be unambiguously identified above backgrounds. Background rejection strategies to date primarily target thermal noise fluctuations and also impulsive radio-frequency signals of anthropogenic origin. In this paper, we consider the possibility that ‘fake’ neutrino signals may also be generated naturally via the ‘triboelectric effect.’ This broadly describes any process in which force applied at a boundary layer results in displacement of surface charge, leading to the production of an electrostatic potential difference ΔV. Wind blowing over granular surfaces such as snow can induce such a potential difference, with subsequent coronal discharge. Discharges over timescales as short as nanoseconds can then lead to radio-frequency emissions at characteristic MHz–GHz frequencies. Using data from various past (RICE, AURA, SATRA, ANITA) and current (RNO-G, ARIANNA and ARA) neutrino experiments, we find evidence for such backgrounds, which are generally characterized by: (a) a threshold wind velocity which likely depends on the experimental trigger criteria and layout; for the experiments considered herein, this value is typically O(10 m/s), (b) frequency spectra generally shifted to the low-end of the frequency regime to which current radio experiments are typically sensitive (100–200 MHz), (c) for the strongest background signals, an apparent preference for discharges from above-surface structures, although the presence of more isotropic, lower amplitude triboelectric discharges cannot be excluded.

Using data from the IceCube Neutrino Observatory, we searched for high-energy neutrino emission from the gravitational-wave events detected by the advanced LIGO and Virgo detectors during their third observing run. We did a low-latency follow-up on the public candidate events released during the detectors' third observing run and an archival search on the 80 confident events reported in the GWTC-2.1 and GWTC-3 catalogs. An extended search was also conducted for neutrino emission on longer timescales from neutron star containing mergers. Follow-up searches on the candidate optical counterpart of GW190521 were also conducted. We used two methods; an unbinned maximum likelihood analysis and a Bayesian analysis using astrophysical priors, both of which were previously used to search for high-energy neutrino emission from gravitational-wave events. No significant neutrino emission was observed by any analysis, and upper limits were placed on the time-integrated neutrino flux as well as the total isotropic equivalent energy emitted in high-energy neutrinos.

Atmospheric muon neutrinos are produced by meson decays in cosmic-ray-induced air showers. The flux depends on meteorological quantities such as the air temperature, which affects the density of air. Competition between decay and re-interaction of those mesons in the first particle production generations gives rise to a higher neutrino flux when the air density in the stratosphere is lower, corresponding to a higher temperature. A measurement of a temperature dependence of the atmospheric νμ flux provides a novel method for constraining hadronic interaction models of air showers. It is particularly sensitive to the production of kaons. Studying this temperature dependence for the first time requires a large sample of high-energy neutrinos as well as a detailed understanding of atmospheric properties. We report the significant (>10σ) observation of a correlation between the rate of more than 260,000 neutrinos, detected by IceCube between 2012 and 2018, and atmospheric temperatures of the stratosphere, measured by the Atmospheric Infrared Sounder (AIRS) instrument aboard NASA’s AQUA satellite. For the observed 10 % seasonal change of effective atmospheric temperature we measure a 3.5(3) % change in the muon neutrino flux. This observed correlation deviates by about 2-3 standard deviations from the expected correlation of 4.3 % as obtained from theoretical predictions under the assumption of various hadronic interaction models.

IceCube, a cubic-kilometer array of optical sensors built to detect atmospheric and astrophysical neutrinos between 1 GeV and 1 PeV, is deployed 1.45 km to 2.45 km below the surface of the ice sheet at the South Pole. The classification and reconstruction of events from the in-ice detectors play a central role in the analysis of data from IceCube. Reconstructing and classifying events is a challenge due to the irregular detector geometry, inhomogeneous scattering and absorption of light in the ice and, below 100 GeV, the relatively low number of signal photons produced per event. To address this challenge, it is possible to represent IceCube events as point cloud graphs and use a Graph Neural Network (GNN) as the classification and reconstruction method. The GNN is capable of distinguishing neutrino events from cosmic-ray backgrounds, classifying different neutrino event types, and reconstructing the deposited energy, direction and interaction vertex. Based on simulation, we provide a comparison in the 1 GeV-100 GeV energy range to the current state-of-the-art maximum likelihood techniques used in current IceCube analyses, including the effects of known systematic uncertainties. For neutrino event classification, the GNN increases the signal efficiency by 18% at a fixed background rate, compared to current IceCube methods. Alternatively, the GNN offers a reduction of the background (i.e. false positive) rate by over a factor 8 (to below half a percent) at a fixed signal efficiency. For the reconstruction of energy, direction, and interaction vertex, the resolution improves by an average of 13%-20% compared to current maximum likelihood techniques in the energy range of 1 GeV-30 GeV. The GNN, when run on a GPU, is capable of processing IceCube events at a rate nearly double of the median IceCube trigger rate of 2.7 kHz, which opens the possibility of using low energy neutrinos in online searches for transient events.

Along their long propagation from production to detection, neutrinos undergo flavour conversions that convert their types or flavours1,2. High-energy astrophysical neutrinos propagate unperturbed over a billion light years in vacuum3 and are sensitive to small effects caused by new physics. Effects of quantum gravity4 are expected to appear at the Planck energy scale. Such a high-energy universe would have existed only immediately after the Big Bang and is inaccessible by human technologies. On the other hand, quantum gravity effects may exist in our low-energy vacuum5–8, but are suppressed by inverse powers of the Planck energy. Measuring the coupling of particles to such small effects is difficult via kinematic observables, but could be observable through flavour conversions. Here we report a search with the IceCube Neutrino Observatory, using astrophysical neutrino flavours9,10 to search for new space–time structure. We did not find any evidence of anomalous flavour conversion in the IceCube astrophysical neutrino flavour data. We apply the most stringent limits of any known technologies, down to 10−42 GeV−2 with Bayes factor greater than 10 on the dimension-six operators that parameterize the space–time defects. We thus unambiguously reach the parameter space of quantum-gravity-motivated physics.

Gamma-ray bursts (GRBs) are considered as promising sources of ultra-high-energy cosmic rays (UHECRs) due to their large power output. Observing a neutrino flux from GRBs would offer evidence that GRBs are hadronic accelerators of UHECRs. Previous IceCube analyses, which primarily focused on neutrinos arriving in temporal coincidence with the prompt gamma-rays, found no significant neutrino excess. The four analyses presented in this paper extend the region of interest to 14 days before and after the prompt phase, including generic extended time windows and targeted precursor searches. GRBs were selected between 2011 May and 2018 October to align with the data set of candidate muon-neutrino events observed by IceCube. No evidence of correlation between neutrino events and GRBs was found in these analyses. Limits are set to constrain the contribution of the cosmic GRB population to the diffuse astrophysical neutrino flux observed by IceCube. Prompt neutrino emission from GRBs is limited to 21% of the observed diffuse neutrino flux, and emission on timescales up to 104 s is constrained to 24% of the total diffuse flux.

We present a search for an unstable sterile neutrino by looking for a resonant signal in eight years of atmospheric ν_{μ} data collected from 2011 to 2019 at the IceCube Neutrino Observatory. Both the (stable) three-neutrino and the 3+1 sterile neutrino models are disfavored relative to the unstable sterile neutrino model, though with p values of 2.8% and 0.81%, respectively, we do not observe evidence for 3+1 neutrinos with neutrino decay. The best-fit parameters for the sterile neutrino with decay model from this study are Δm_{41}^{2}=6.7_{-2.5}^{+3.9}  eV^{2}, sin^{2}2θ_{24}=0.33_{-0.17}^{+0.20}, and g^{2}=2.5π±1.5π, where g is the decay-mediating coupling. The preferred regions of the 3+1+decay model from short-baseline oscillation searches are excluded at 90% C.L.

The majority of astrophysical neutrinos have undetermined origins. The IceCube Neutrino Observatory has observed astrophysical neutrinos but has not yet identified their sources. Blazars are promising source candidates, but previous searches for neutrino emission from populations of blazars detected in ≳ GeV gamma rays have not observed any significant neutrino excess. Recent findings in multimessenger astronomy indicate that high-energy photons, coproduced with high-energy neutrinos, are likely to be absorbed and reemitted at lower energies. Thus, lower-energy photons may be better indicators of TeV-PeV neutrino production. This paper presents the first time-integrated stacking search for astrophysical neutrino emission from MeV-detected blazars in the first Fermi Large Area Telescope low energy (1FLE) catalog using ten years of IceCube muon-neutrino data. The results of this analysis are found to be consistent with a background-only hypothesis. Assuming an E-2 neutrino spectrum and proportionality between the blazars MeV gamma-ray fluxes and TeV-PeV neutrino flux, the upper limit on the 1FLE blazar energy-scaled neutrino flux is determined to be 1.64 × 10-12 TeV cm-2 s-1 at 90% confidence level. This upper limit is approximately 1% of IceCube's diffuse muon-neutrino flux measurement.

Galaxy clusters have the potential to accelerate cosmic rays (CRs) to ultrahigh energies via accretion shocks or embedded CR acceleration sites. The CRs with energies below the Hillas condition will be confined within the cluster and eventually interact with the intracluster medium gas to produce secondary neutrinos and gamma rays. Using 9.5 yr of muon neutrino track events from the IceCube Neutrino Observatory, we report the results of a stacking analysis of 1094 galaxy clusters with masses ≳1014 Me and redshifts between 0.01 and ∼1 detected by the Planck mission via the Sunyaev–Zel’dovich effect. We find no evidence for significant neutrino emission and report upper limits on the cumulative unresolved neutrino flux from massive galaxy clusters after accounting for the completeness of the catalog up to a redshift of 2, assuming three different weighting scenarios for the stacking and three different power-law spectra. Weighting the sources according to mass and distance, we set upper limits at a 90% confidence level that constrain the flux of neutrinos from massive galaxy clusters (≳1014 Me) to be no more than 4.6% of the diffuse IceCube observations at 100 TeV, assuming an unbroken E−2.5 power-law spectrum.

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.

We present a measurement of the density of GeV muons in near-vertical air showers using three years of data recorded by the IceTop array at the South Pole. Depending on the shower size, the muon densities have been measured at lateral distances between 200 and 1000 m. From these lateral distributions, we derive the muon densities as functions of energy at reference distances of 600 and 800 m for primary energies between 2.5 and 40 PeV and between 9 and 120 PeV, respectively. The muon densities are determined using, as a baseline, the hadronic interaction model Sibyll 2.1 together with various composition models. The measurements are consistent with the predicted muon densities within these baseline interaction and composition models. The measured muon densities have also been compared to simulations using the post-LHC models EPOS-LHC and QGSJet-II.04. The result of this comparison is that the post-LHC models together with any given composition model yield higher muon densities than observed. This is in contrast to the observations above 1 EeV where all model simulations yield for any mass composition lower muon densities than the measured ones. The post-LHC models in general feature higher muon densities so that the agreement with experimental data at the highest energies is improved but the muon densities are not correct in the energy range between 2.5 and about 100 PeV.

We report a search for nonstandard neutrino interactions (NSI) using eight years of TeV-scale atmospheric muon neutrino data from the IceCube Neutrino Observatory. By reconstructing incident energies and zenith angles for atmospheric neutrino events, this analysis presents unified confidence intervals for the NSI parameter ε_{μτ}. The best-fit value is consistent with no NSI at a p value of 25.2%. With a 90% confidence interval of -0.0041≤ε_{μτ}≤0.0031 along the real axis and similar strength in the complex plane, this result is the strongest constraint on any NSI parameter from any oscillation channel to date.

We present the first comprehensive search for high-energy neutrino emission from high- A nd low-mass X-ray binaries conducted by IceCube. Galactic X-ray binaries are long-standing candidates for the source of Galactic hadronic cosmic rays and neutrinos. The compact object in these systems can be the site of cosmic-ray acceleration, and neutrinos can be produced by interactions of cosmic rays with radiation or gas, in the jet of a microquasar, in the stellar wind, or in the atmosphere of the companion star. We study X-ray binaries using 7.5 yr of IceCube data with three separate analyses. In the first, we search for periodic neutrino emission from 55 binaries in the Northern Sky with known orbital periods. In the second, the X-ray light curves of 102 binaries across the entire sky are used as templates to search for time-dependent neutrino emission. Finally, we search for time-integrated emission of neutrinos for a list of 4 notable binaries identified as microquasars. In the absence of a significant excess, we place upper limits on the neutrino flux for each hypothesis and compare our results with theoretical predictions for several binaries. In addition, we evaluate the sensitivity of the next generation neutrino telescope at the South Pole, IceCube-Gen2, and demonstrate its power to identify potential neutrino emission from these binary sources in the Galaxy.

The Sun provides an excellent target for studying spin-dependent dark matter-proton scattering due to its high matter density and abundant hydrogen content. Dark matter particles from the Galactic halo can elastically interact with Solar nuclei, resulting in their capture and thermalization in the Sun. The captured dark matter can annihilate into Standard Model particles including an observable flux of neutrinos. We present the results of a search for low-energy (

We present a measurement of the high-energy astrophysical muon-neutrino flux with the IceCube Neutrino Observatory. The measurement uses a high-purity selection of 650k neutrino-induced muon tracks from the northern celestial hemisphere, corresponding to 9.5 yr of experimental data. With respect to previous publications, the measurement is improved by the increased size of the event sample and the extended model testing beyond simple power-law hypotheses. An updated treatment of systematic uncertainties and atmospheric background fluxes has been implemented based on recent models. The best-fit single power-law parameterization for the astrophysical energy spectrum results in a normalization of φ@100TeVνμ+ν¯μ=1.44-0.26+0.25×10-18GeV-1cm-2s-1sr-1 and a spectral index γSPL=2.37-0.09+0.09, constrained in the energy range from 15 TeV to 5 PeV. The model tests include a single power law with a spectral cutoff at high energies, a log-parabola model, several source-class-specific flux predictions from the literature, and a model-independent spectral unfolding. The data are consistent with a single power-law hypothesis, however, spectra with softening above one PeV are statistically more favorable at a two-sigma level.

High-energy tau neutrinos are rarely produced in atmospheric cosmic-ray showers or at cosmic particle accelerators, but are expected to emerge during neutrino propagation over cosmic distances due to flavor mixing. When high energy tau neutrinos interact inside the IceCube detector, two spatially separated energy depositions may be resolved, the first from the charged current interaction and the second from the tau lepton decay. We report a novel analysis of 7.5 years of IceCube data that identifies two candidate tau neutrinos among the 60 “High-Energy Starting Events” (HESE) collected during that period. The HESE sample offers high purity, all-sky sensitivity, and distinct observational signatures for each neutrino flavor, enabling a new measurement of the flavor composition. The measured astrophysical neutrino flavor composition is consistent with expectations, and an astrophysical tau neutrino flux is indicated at 2.8σ significance.

Since the discovery of a flux of high-energy astrophysical neutrinos, searches for their origins have focused primarily at TeV-PeV energies. Compared to sub-TeV searches, high-energy searches benefit from an increase in the neutrino cross section, improved angular resolution on the neutrino direction, and a reduced background from atmospheric neutrinos and muons. However, the focus on high energy does not preclude the existence of sub-TeV neutrino emission where IceCube retains sensitivity. Here we present the first all-flavor search from IceCube for transient emission of low-energy neutrinos, focusing on the energy region of 5.6-100 GeV using three years of data obtained with the IceCube-DeepCore detector. We find no evidence of transient neutrino emission in the data, thus leading to a constraint on the volumetric rate of astrophysical transient sources in the range of ∼ 705-2301 Gpc-3 yr-1 for sources following a subphotospheric energy spectrum with a mean energy of 100 GeV and a bolometric energy of 1052 erg.

A recent time-integrated analysis of a catalog of 110 candidate neutrino sources revealed a cumulative neutrino excess in the data collected by IceCube between 2008 April 6 and 2018 July 10. This excess, inconsistent with the background hypothesis in the Northern Hemisphere at the 3.3σ level, is associated with four sources: NGC 1068, TXS 0506+056, PKS 1424+240, and GB6 J1542+6129. This Letter presents two time-dependent neutrino emission searches on the same data sample and catalog: a point-source search that looks for the most significant time-dependent source of the catalog by combining space, energy, and time information of the events, and a population test based on binomial statistics that looks for a cumulative time-dependent neutrino excess from a subset of sources. Compared to previous time-dependent searches, these analyses enable a feature to possibly find multiple flares from a single direction with an unbinned maximum-likelihood method. M87 is found to be the most significant time-dependent source of this catalog at the level of 1.7σ post-trial, and TXS 0506+056 is the only source for which two flares are reconstructed. The binomial test reports a cumulative time-dependent neutrino excess in the Northern Hemisphere at the level of 3.0σ associated with four sources: M87, TXS 0506+056, GB6 J1542+6129, and NGC 1068.

We report constraints on nonstandard neutrino interactions (NSI) from the observation of atmospheric neutrinos with IceCube, limiting all individual coupling strengths from a single dataset. Furthermore, IceCube is the first experiment to constrain flavor-violating and nonuniversal couplings simultaneously. Hypothetical NSI are generically expected to arise due to the exchange of a new heavy mediator particle. Neutrinos propagating in matter scatter off fermions in the forward direction with negligible momentum transfer. Hence the study of the matter effect on neutrinos propagating in the Earth is sensitive to NSI independently of the energy scale of new physics. We present constraints on NSI obtained with an all-flavor event sample of atmospheric neutrinos based on three years of IceCube DeepCore data. The analysis uses neutrinos arriving from all directions, with reconstructed energies between 5.6 GeV and 100 GeV. We report constraints on the individual NSI coupling strengths considered singly, allowing for complex phases in the case of flavor-violating couplings. This demonstrates that IceCube is sensitive to the full NSI flavor structure at a level competitive with limits from the global analysis of all other experiments. In addition, we investigate a generalized matter potential, whose overall scale and flavor structure are also constrained.

We present a high-energy neutrino event generator, called LeptonInjector, alongside an event weighter, called LeptonWeighter. Both are designed for large-volume Cherenkov neutrino telescopes such as IceCube. The neutrino event generator allows for quick and flexible simulation of neutrino events within and around the detector volume, and implements the leading Standard Model neutrino interaction processes relevant for neutrino observatories: neutrino-nucleon deep-inelastic scattering and neutrino-electron annihilation. In this paper, we discuss the event generation algorithm, the weighting algorithm, and the main functions of the publicly available code, with examples. Program summary: Program Titles: LeptonInjector and LeptonWeighter CPC Library link to program files: https://doi.org/10.17632/662gkpjfd9.1 Developer's repository links: https://github.com/icecube/LeptonInjector and https://github.com/icecube/LeptonWeighter Licensing provisions: GNU Lesser General Public License, version 3. Programming Language: C++11 External Routines: • Boost • HDF5 • nuflux (https://github.com/icecube/nuflux) • nuSQuIDS (https://github.com/arguelles/nuSQuIDS) • Photospline (https://github.com/icecube/photospline) • SuiteSparse (https://github.com/DrTimothyAldenDavis/SuiteSparse) Nature of problem: LeptonInjector: Generate neutrino interaction events of all possible topologies and energies throughout and around a detector volume. LeptonWeighter: Reweight Monte Carlo events, generated by a set of LeptonInjector Generators, to any desired physical neutrino flux or cross section. Solution method: LeptonInjector: Projected ranges of generated leptons and the extent of the detector, in terms of column depth, are used to inject events in and around the detector volume. Event kinematics follow distributions provided in cross section files. LeptonWeighter: Event generation probabilities are calculated for each Generator, which are then combined into a generation weight and used to calculate an overall event weight.

The flux of high-energy neutrinos passing through the Earth is attenuated due to their interactions with matter. The interaction rate is determined by the neutrino interaction cross section and affects the flux arriving at the IceCube Neutrino Observatory, a cubic-kilometer neutrino detector embedded in the Antarctic ice sheet. We present a measurement of the neutrino cross section between 60 TeV and 10 PeV using the high-energy starting event (HESE) sample from IceCube with 7.5 years of data. The result is binned in neutrino energy and obtained using both Bayesian and frequentist statistics. We find it compatible with predictions from the Standard Model. While the cross section is expected to be flavor independent above 1 TeV, additional constraints on the measurement are included through updated experimental particle identification (PID) classifiers, proxies for the three neutrino flavors. This is the first such measurement to use a ternary PID observable and the first to account for neutrinos from tau decay.

The IceCube Neutrino Observatory has established the existence of a high-energy all-sky neutrino flux of astrophysical origin. This discovery was made using events interacting within a fiducial region of the detector surrounded by an active veto and with reconstructed energy above 60 TeV, commonly known as the high-energy starting event sample (HESE). We revisit the analysis of the HESE sample with an additional 4.5 years of data, newer glacial ice models, and improved systematics treatment. This paper describes the sample in detail, reports on the latest astrophysical neutrino flux measurements, and presents a source search for astrophysical neutrinos. We give the compatibility of these observations with specific isotropic flux models proposed in the literature as well as generic power-law-like scenarios. Assuming νe:νμ:ντ=1:1:1, and an equal flux of neutrinos and antineutrinos, we find that the astrophysical neutrino spectrum is compatible with an unbroken power law, with a preferred spectral index of 2.87-0.19+0.20 for the 68% confidence interval.

The observation of electromagnetic radiation from radio to γ-ray wavelengths has provided a wealth of information about the Universe. However, at PeV (1015 eV) energies and above, most of the Universe is impenetrable to photons. New messengers, namely cosmic neutrinos, are needed to explore the most extreme environments of the Universe where black holes, neutron stars, and stellar explosions transform gravitational energy into non-thermal cosmic rays. These energetic particles havemillions of times higher energies than those produced in the most powerful particle accelerators on Earth. As neutrinos can escape from regions otherwise opaque to radiation, they allow an unique view deep into exploding stars and the vicinity of the event horizons of black holes. The discovery of cosmic neutrinos with IceCube has opened this new window on the Universe. IceCube has been successful in finding first evidence for cosmic particle acceleration in the jet of an active galactic nucleus. Yet, ultimately, its sensitivity is too limited to detect even the brightest neutrino sources with high significance, or to detect populations of less luminous sources. In thiswhite paper, we present an overview of a next-generation instrument, IceCube-Gen2, which will sharpen our understanding of the processes and environments that govern the Universe at the highest energies. IceCube-Gen2 is designed to: (a) Resolve the high-energy neutrino sky from TeV to EeV energies (b) Investigate cosmic particle acceleration through multi-messenger observations (c) Reveal the sources and propagation of the highest energy particles in the Universe (d) Probe fundamental physics with high-energy neutrinos IceCube-Gen2 will enhance the existing IceCube detector at the South Pole. It will increase the annual rate of observed cosmic neutrinos by a factor of ten compared to IceCube, and will be able to detect sources five times fainter than its predecessor. Furthermore, through the addition of a radio array, IceCube- Gen2 will extend the energy range by several orders of magnitude compared to IceCube. Construction will take 8 years and cost about $350M. The goal is to have IceCube-Gen2 fully operational by 2033. IceCube-Gen2 will play an essential role in shaping the new era of multimessenger astronomy, fundamentally advancing our knowledge of the highenergy Universe. This challenging mission can be fully addressed only through the combination of the information from the neutrino, electromagnetic, and gravitational wave emission of high-energy sources, in concert with the new survey instruments across the electromagnetic spectrum and gravitational wave detectors which will be available in the coming years.

Solar flares convert magnetic energy into thermal and nonthermal plasma energy, the latter implying particle acceleration of charged particles such as protons. Protons are injected out of the coronal acceleration region and can interact with dense plasma in the lower solar atmosphere, producing mesons that subsequently decay into gamma rays and neutrinos at O(MeV-GeV) energies. We present the results of the first search for GeV neutrinos emitted during solar flares carried out with the IceCube Neutrino Observatory. While the experiment was originally designed to detect neutrinos with energies between 10 GeV and a few PeV, a new approach allowing for a O(GeV) energy threshold will be presented. The resulting limits allow us to constrain some of the theoretical estimates of the expected neutrino flux.

High-energy neutrinos are unique messengers of the high-energy universe, tracing the processes of cosmic ray acceleration. This paper presents analyses focusing on time-dependent neutrino point-source searches. A scan of the whole sky, making no prior assumption about source candidates, is performed, looking for a space and time clustering of high-energy neutrinos in data collected by the IceCube Neutrino Observatory between 2012 and 2017. No statistically significant evidence for a time-dependent neutrino signal is found with this search during this period, as all results are consistent with the background expectation. Within this study period, the blazar 3C 279, showed strong variability, inducing a very prominent gamma-ray flare observed in 2015 June. This event motivated a dedicated study of the blazar, which consists of searching for a time-dependent neutrino signal correlated with the gamma-ray emission. No evidence for a time-dependent signal is found. Hence, an upper limit on the neutrino fluence is derived, allowing us to constrain a hadronic emission model.

In multi-messenger astronomy, rapid investigation of interesting transients is imperative. As an observatory with a 4π steradian field of view, and ∼99% uptime, the IceCube Neutrino Observatory is a unique facility to follow up transients, as well as to provide valuable insights for other observatories and inform their observational decisions. Since 2016, IceCube has been using low-latency data to rapidly respond to interesting astrophysical events reported by the multi-messenger observational community. Here, we describe the pipeline used to perform these followup analyses, and provide a summary of the 58 analyses performed as of July 2020. We find no significant signal in the first 58 analyses performed. The pipeline has helped inform various electromagnetic observation strategies, and has constrained neutrino emission from potential hadronic cosmic accelerators.

The Glashow resonance describes the resonant formation of a W- boson during the interaction of a high-energy electron antineutrino with an electron1, peaking at an antineutrino energy of 6.3 petaelectronvolts (PeV) in the rest frame of the electron. Whereas this energy scale is out of reach for currently operating and future planned particle accelerators, natural astrophysical phenomena are expected to produce antineutrinos with energies beyond the PeV scale. Here we report the detection by the IceCube neutrino observatory of a cascade of high-energy particles (a particle shower) consistent with being created at the Glashow resonance. A shower with an energy of 6.05 ± 0.72 PeV (determined from Cherenkov radiation in the Antarctic Ice Sheet) was measured. Features consistent with the production of secondary muons in the particle shower indicate the hadronic decay of a resonant W- boson, confirm that the source is astrophysical and provide improved directional localization. The evidence of the Glashow resonance suggests the presence of electron antineutrinos in the astrophysical flux, while also providing further validation of the standard model of particle physics. Its unique signature indicates a method of distinguishing neutrinos from antineutrinos, thus providing a way to identify astronomical accelerators that produce neutrinos via hadronuclear or photohadronic interactions, with or without strong magnetic fields. As such, knowledge of both the flavour (that is, electron, muon or tau neutrinos) and charge (neutrino or antineutrino) will facilitate the advancement of neutrino astronomy.

Observations of the time-dependent cosmic-ray Sun shadow have been proven as a valuable diagnostic for the assessment of solar magnetic field models. In this paper, seven years of IceCube data are compared to solar activity and solar magnetic field models. A quantitative comparison of solar magnetic field models with IceCube data on the event rate level is performed for the first time. Additionally, a first energy-dependent analysis is presented and compared to recent predictions. We use seven years of IceCube data for the moon and the Sun and compare them to simulations on data rate level. The simulations are performed for the geometrical shadow hypothesis for the moon and the Sun and for a cosmic-ray propagation model governed by the solar magnetic field for the case of the Sun. We find that a linearly decreasing relationship between Sun shadow strength and solar activity is preferred over a constant relationship at the 6.4σ level. We test two commonly used models of the coronal magnetic field, both combined with a Parker spiral, by modeling cosmic-ray propagation in the solar magnetic field. Both models predict a weakening of the shadow in times of high solar activity as it is also visible in the data. We find tensions with the data on the order of 3σ for both models, assuming only statistical uncertainties. The magnetic field model CSSS fits the data slightly better than the PFSS model. This is generally consistent with what is found previously by the Tibet AS-γ Experiment; a deviation of the data from the two models is, however, not significant at this point. Regarding the energy dependence of the Sun shadow, we find indications that the shadowing effect increases with energy during times of high solar activity, in agreement with theoretical predictions.

Cosmic-ray interactions with the solar atmosphere are expected to produce particle showers which in turn produce neutrinos from weak decays of mesons. These solar atmospheric neutrinos (SAνs) have never been observed experimentally. A detection would be an important step in understanding cosmic-ray propagation in the inner solar system and the dynamics of solar magnetic fields. SAνs also represent an irreducible background to solar dark matter searches and a detection would allow precise characterization of this background. Here, we present the first experimental search based on seven years of data collected from May 2010 to May 2017 in the austral winter with the IceCube Neutrino Observatory. An unbinned likelihood analysis is performed for events reconstructed within 5 degrees of the center of the Sun. No evidence for a SAν flux is observed. After inclusion of systematic uncertainties, we set a 90% upper limit of 1.02+0.20-0.18·10-13 GeV-1cm-2s-1 at 1 TeV.

The current and upcoming generation of Very Large Volume Neutrino Telescopes – collecting unprecedented quantities of neutrino events – can be used to explore subtle effects in oscillation physics, such as (but not restricted to) the neutrino mass ordering. The sensitivity of an experiment to these effects can be estimated from Monte Carlo simulations. With the high number of events that will be collected, there is a trade-off between the computational expense of running such simulations and the inherent statistical uncertainty in the determined values. In such a scenario, it becomes impractical to produce and use adequately-sized sets of simulated events with traditional methods, such as Monte Carlo weighting. In this work we present a staged approach to the generation of expected distributions of observables in order to overcome these challenges. By combining multiple integration and smoothing techniques which address limited statistics from simulation it arrives at reliable analysis results using modest computational resources.

The results of a 3+1 sterile neutrino search using eight years of data from the IceCube Neutrino Observatory are presented. A total of 305 735 muon neutrino events are analyzed in reconstructed energy-zenith space to test for signatures of a matter-enhanced oscillation that would occur given a sterile neutrino state with a mass-squared differences between 0.01 and 100  eV^{2}. The best-fit point is found to be at sin^{2}(2θ_{24})=0.10 and Δm_{41}^{2}=4.5  eV^{2}, which is consistent with the no sterile neutrino hypothesis with a p value of 8.0%.