Neutrino telescopes and high-energy cosmic neutrinos
NNeutrino telescopes and high-energy cosmic neutrinos
Andrea Palladino ,Maurizio Spurio , ,and Francesco Vissani , , Deutsches Elektronen-Synchrotron (DESY), Platanenallee 6, D-15738 Zeuthen, Germany NFN-Sezione di Bologna, Viale Berti-Pichat 6/2, 40127 Bologna, Italy Dipartimento di Fisica e Astronomia, dell’Universit`a, Viale Berti Pichat 6/2, 40127 Bologna, Italy INFN, Laboratori Nazionali del Gran Sasso, 67100 L’Aquila, Italy Gran Sasso Science Institute, 67100 L’Aquila, Italy
Abstract
In this review paper, we present the main aspects of high-energy cosmic neutrino astro-physics. We begin by describing the generic expectations for cosmic neutrinos, including theeffects of propagation from their sources to the detectors. Then we introduce the operatingprinciples of current neutrino telescopes, and examine the main features (topologies) of theobservable events. After a discussion of the main background processes, due to the concomi-tant presence of secondary particles produced in the terrestrial atmosphere by cosmic rays, wesummarize the current status of the observations with astrophysical relevance that have beengreatly contributed by IceCube detector. Then, we examine various interpretations of thesefindings, trying to assess the best candidate sources of cosmic neutrinos. We conclude with abrief perspective on how the field could evolve within a few years.
The search for high-energy neutrinos from the cosmos is closely linked to cosmic rays and particlephysics. In fact, cosmic ray collisions produce particles from whose decays the neutrinos are born,mainly charged pions and muons. So, the roots of high-energy neutrino astronomy are linked to thenames of Hess, Pacini, Pauli, Fermi, Yukawa, Anderson, Neddermeyer, Powell, Lattes, Occhialiniand other famous physicists of the early 20th century.History begins with a handful of theoretical works. In the middle of the Cold War, two inde-pendent papers [1, 2] proposed to the scientific communities of the opponent countries the (same)idea, namely, of building high-energy neutrino telescopes. This is why the birth of this field ofresearch is often attributed to these two works, but earlier explorations had been conducted in aDiploma thesis presented in 1958 at Moscow State University by Zheleznikh, by the time a studentof Markov: see [2] and [3]. In this thesis it is written “It is worth searching for high energy neu-trinos from Outer Space, especially, if the high energy γ -rays beyond the atmosphere were found”[3]: in other words, a very close connection between neutrinos and high-energy gamma rays wasexpected from the very beginning, because of the associated and inevitable production of chargedand neutral pions. Incidentally, the study of gamma-ray radiation began in the same years by1 a r X i v : . [ a s t r o - ph . H E ] S e p he paper of Morrison [4] (who mentions “the still unexploited neutrino channel”, even if only inconnection to stellar processes) and it is one of the most interesting branches of astronomy today.We cite the inspired words from Reference [1]: “one may predict that these fields of high-energyquantum and neutrino astronomy will be opened up in the near future” which are particularlyinteresting, as nowadays there is occasionally still some resistance in accepting the consistence of“neutrino astronomy”.The first experimental searches for high energy neutrinos were conducted soon later by twoexperiments (KGF in India and CWI in South Africa, which were attended by scientists from allover the world, including the host countries, USA and USSR, UK, China and Japan) who releasedtheir final results in the beginning of the 1970s [5, 6, 7] and revealed for the first time atmosphericneutrinos but did not find evidence of other components in their dataset. Shortly afterwardsthe idea emerged of building a much larger detector, about a kilometer in size, as the way toproceed in the search for high-energy neutrinos from the cosmos. This led to the proposal of oneexperiment named DUMAND, carried out by scientists from USA and USSR; however, the well-known geopolitical circumstances prevented its realization. The first detector that succeeded in thisgoal has been IceCube, which built upon the experience of AMANDA, 1996–2005. In 2013, IceCubeshowed the first evidence of a new component of cosmic neutrinos [8], whose nature, however, isnot yet identified.For further historical discussion, see Reference [9, 10, 11]. The plan of this review paper is as follows: we begin by expounding the general expectations oncosmic neutrinos; next, we describe the principles of neutrino telescopes; we outline the possiblesignals and the background processes; then, we summarize the main observational results thathave astrophysical significance; finally, we consider a few specific astrophysical models, as possibleinterpretations of these findings. In fact, even though numerous theoretical proposals preceded thediscovery, it does not seem fair to say that the theory provided a solid guide to the discovery.However, before proceeding in the discussion, it seems useful to conclude this brief introductionby highlighting a last momentous point, namely the discovery of the phenomenon of neutrino oscil-lations, anticipated in the decade 1957–1967 by Pontecorvo’s theories [12] and fully accomplishedthanks to a long series of experiments, including the Neutrino Detector Experiment in the Kamiokamine (Super-KamiokaNDE) in Japan and the Sudbury Neutrino Observatory (SNO) in Canadarecognized by the Nobel prize in Physics in 2015 [13]. As this aspect has direct implications on thefield of cosmic neutrinos of very high energies, and it seems to be one of the most reliable points inthe theoretical interpretation, we will discuss in detail here.
It is widely believed that certain cosmic sources produce high-energy neutrinos. The simplest reasonis just the knowledge of atmospheric neutrinos, that originate from cosmic ray interactions with2arth’s atmosphere. Many variants of the known mechanism, which could lead to a potentiallyobservable population of cosmic neutrinos, can be imagined. However, the reference picture for theproduction of high energy neutrinos is simply that, the same sites where cosmic rays are accelerated- or the environment that surround them—if endowed with sufficient target to convert a fraction ofthe energy into secondary particles, are potentially observable sources of high energy neutrinos.Therefore, neutrino astronomy could be ultimately a major avenue to discover the sources ofcosmic rays, which are still a matter of theoretical speculation and to date not yet sufficientlyknown. For this reason, we begin by collecting the main important facts on cosmic rays.It is useful to recall some important observational facts concerning cosmic rays. The observa-tion of high-energy part of cosmic ray spectrum at Earth allows us to distinguish several pieces,continuously connected but different among them. The flux is characterized by four main energyintervals: (1) the part below the knee at about E knee ∼ ankle, which is at about E ankle ∼ suppression region, which corresponds to the end of the observed spectrum. In allthese regions, except the last one the distribution can be roughly described as power laws, namelyby energy distributions of the form: Φ CR ∼ E − α CR , (1)which are the characteristic features of the occurrence of (highly) non-thermal processes. Theparameter α is called the slope. The observed slopes in the different energy intervals are notdirectly related to the slope at production; effects of propagation and/or of escape are plausiblyalso energy dependent. Indeed, the mechanisms of cosmic ray accelerations—for example, the Fermimechanism—are expected to produce in several cases a distribution with slope α ∼ pp and pγ Mechanisms of Neutrino Production
We assume that (most of) the observable cosmic neutrinos derive from astrophysical mechanism,that is, from cosmic ray collisions. Consider the case of very high energy protons (or nucleons)colliding over a nucleus N at rest, described approximately as an assembly of nucleons. Thiscollision will lead to the production of many π + , π − , π , roughly in similar amount that we canresume symbolically by: p + N → X + many × ( π + + π − + π ) . (2)The experimental observation shows that the highest energy pion (called the leading pion) carrieson average 1/5 of the initial kinetic energy of the proton—see for example, Reference [28, 29]. Itsdecay will eventually lead to high-energy neutrinos and gamma rays: π → γ + γ and π ± → µ ± + ( − ) ν µ , followed e.g., by µ + → e + + ν e + ¯ ν µ . (3)The kinematic of these decays is such that, in the decay of the neutral π , each gamma rayscarries 1/2 of the initial energy, and likewise, in the decay chain of the charged leptons, anyone of3he four light (anti)leptons carries away 1/4 of the initial energy (this corresponds to the result ofthe accurate calculation [30]; see also Appendix A). Thus, we have the very simple and useful ruleof thumb: E ν ∼ E γ ∼ E π ∼ E p . (4)Interestingly, this remains unchanged also for a completely different case, when the target isreplaced by (high-energy) gamma rays. In fact, consider the process: p + γ → ∆ + → n + π + or alternatively → p + π . (5)By simple kinematic considerations, one obtains that, on average, the mesons carry away 1/5of the initial kinetic energy; therefore, the same rule of thumb (4) applies. For instance: E ν = 100 TeV −
10 PeV corresponds to E p ∼ − , PeVwhich is the region above (or just around) the knee of the cosmic rays spectrum. Note that noelectron antineutrinos are formed in the decay chain of Equation (5). These appear after oscillations(see Section 3.1) even if a relative shortage of ¯ ν e persists.The two major mechanisms for high-energy neutrino production, discussed just above, are usu-ally referred to as pp -mechanism (Equation (2)) and pγ -mechanism (Equation (5)). They can applyto various situations in the cosmos. The interconnection between cosmic rays (CRs), γ -rays andneutrinos is sketched in Figure 1.Let us examine now some differences between the pp - and the pγ -mechanism. The main onesconcern the spectrum,( i ) The pγ -mechanism is a process with a defined threshold. For example, suppose having aphoton target between the UV and X bands, say with energies of ε ∼ . E p > m ε γ = (cid:18)
100 eV ε γ (cid:19) × , (6)which, according to (4), corresponds to neutrinos with minimal energy of ∼
200 TeV (see alsoReference [16]). In this production mechanism, the resulting neutrino (and very high-energy γ -ray) spectra will reflect the energy distribution of the target photons.( ii ) The pp -mechanism is featured by a very important property of the hadronic interactions,namely the hypothesis of limiting fragmentation [31], to which we refer in the following as scaling . A detailed description of scaling variables, their definition, and the application oncosmic ray physics can be found in Reference [25]. According to the scaling, the secondaryparticle spectra corresponds quite strictly to the primary distribution. Consequently, if thecosmic rays are power-law distributed, also the neutrinos and the very high-energy γ -rays willbe power law distributed, with (almost) the same slope. One commonly says that, in this case, the neutrino and gamma-ray spectra reflect the primary (cosmic ray) spectra . In particular,if some variant of Fermi acceleration mechanism applies, we would haveΦ ν ∝ E − αν with α ∼ . (7)4igure 1: Astrophysical sources can accelerate CRs (protons, electrons and nuclei). A fraction of theseparticles diffuses outside the acceleration region, propagates in the galactic space (or intergalactic, if thesource is external to the Galaxy) and can reach the Earth. Electrically charged cosmic rays do not travelin a straight line due to magnetic field deflections. Another fraction of accelerated protons (or nuclei) caninstead interact with matter ( pp -mechanism) or radiation fields ( pγ -mechanism) surrounding the source.In this case, the decay of a neutral secondary particle (mainly π ) produces a γγ -pair, while the decayof charged particles (mainly π ± ) produces (anti)neutrinos. The interaction of electrons with matter orradiation produces only γ -rays. Thus, the detection of neutrinos from the direction of a source is a uniqueway to find out what are the accelerators of protons and nuclei. Other differences between the pp -mechanism and pγ -mechanism concern the proportions of theneutrinos and gamma-rays. Because a fraction of cosmic rays are nuclei, the pp -collision fromindividual nucleons in the nuclei will still produce neutrinos, where pγ -collisions will mostly lead tophoto-disintegration which attenuates their energy [32]. The latter process reduces the productionof secondary neutrinos. Finally, in the pγ -mechanism, a relatively larger amount of neutral pionsis produced than for the pp -mechanism, yielding more γ -rays than ν ’s. The pp - and pγ - production of secondary particles described in Section 2.2 is usually referred asthe hadronic mechanism for γ -rays and ν production. However, a direct connection between high-energy neutrinos and γ -rays requires that certain assumptions be fulfilled. Differences arises from5he fact that • γ -rays can be produced also in the leptonic mechanisms in which only electrons are usuallyinvolved; • γ -rays can be absorbed if the target is thick; • when the γ -rays propagate for long distances, they are subject to absorption over backgroundphotons due to pair production γ + γ bkgr → e + + e − . (8)Concerning the last point, for instance, the opacity due to a thermal population with tempera-ture T bkgr and distributed over a region with size L is [33]: τ pair = 1 . × L
10 kpc × f (cid:18) E (cid:63) E γ (cid:19) with E (cid:63) = m e /T bkgr f ( x ) ≈ − . x ln (cid:16) − e − . x . (cid:17) . (9)Consider for example, the ubiquitous CMB photons such that E (cid:63) = 1 . E γ = 100 TeV, we expect a survival fraction ofexp( − τ pair ) = 28%; but also for a Galactic distance L = 8 . E γ = 1 PeV hasexp( − τ pair ) = 39%. Therefore, the attenuation effect is very important for propagation over extra-galactic distances, but it is not negligible for the highest energy galactic cosmic rays. When thecontribution of background infrared photons (due to reprocessed star light) is included, the Uni-verse is expected to become opaque already at the TeV energy scale. Thus, at the highest energies,the connection between extragalactic gamma rays and neutrinos is indirect. Detailed numericalcodes for the description of more complex situation where absorption occur are publicly available,see for example, those of nuFATE and nuSQuIDS codes in Reference [34].On the contrary, there are various cases when the connection is much more direct. For instance,consider the case of young supernova remnants (SNRs), namely, the mass of gas expelled by asupernova. This is considered as a plausible candidate for the acceleration of (galactic) cosmicrays. Moreover, the regions where core collapse supernovae explode are also sites of intense stellarformation activity, and therefore, it often happens that SNRs are surrounded by large amountsof target material, see References [35, 36] and compare with Reference [37] that focusses only onparticle physics aspects instead. This is the case of the SNR denoted as RX J1713.7-3946, thatis just 1 kpc from the Earth and it is considered as a promising source of high energy neutrinos,whose neutrino flux can be predicted thanks to the observed gamma rays: see Reference [38] for afirst discussion, Reference [39] for an accurate evaluation.In general, considering this type of galactic source, we expect [40] a discernible signal in theneutrino telescopes of a 1 km -scale only if the γ -ray flux is larger than: I γ ( >
10 TeV) = (1 − × − cm − s − . (10)A detailed discussion of the signal of the neutrinos, derived following these principles from the γ -ray observations of certain specific galactic sources, can be found in Reference [41], see Figure 2 fromthis reference. There, it is shown that for the KM3NeT detector (see Section 4.2.3) an observationwith 3 σ significance is possible in about six years of operation for sources as RX J1713.7-3946 andVela Jr. 6igure 2: Prediction of the ν µ fluxes for different galactic sources used in the sensitivity studies of theKM3NeT collaboration [41]. The relevance of neutrinos oscillations to the interpretation of cosmic neutrinos was remarked quitesoon, see for example [42, 43, 44]. For instance, in Reference [43] we read “if neutrino oscillationsoccur and cause the transition ¯ ν e (cid:29) ¯ ν µ , then the flux of ¯ ν e increases. This effect is particularlyimportant for pγ neutrinos” while in Reference [44] we read “if there exist more than two neutrinotypes with mixing of all neutrinos, cosmic neutrino oscillations may result in the appearance of newtype neutrinos, the field of which may be present in the weak interaction hamiltonian together withheavy charged lepton fields.” Actually, these observations still delimit the frontier of research inthe field of cosmic neutrinos, for the reasons we recall here below and will elaborate in Sections 5.3and 5.4.The vacuum oscillation phases that have been probed in terrestrial experiments can be param-eterized as: ϕ = ∆ m L E ν = 3 × ∆ m . × − eV TeV E ν . L pc (11)This means that vacuum oscillations have to affect neutrino propagating over cosmic distances.When we discuss astrophysical neutrinos, in the energy range between hundreds of TeV and multi-PeV, produced by extragalactic sources (i.e., at least at distances of Mpc), the oscillation phasebecomes order of 10 or more. In this case the only observable and meaningful physical quantity7s the phase averaged oscillation. The minimal setup to analyze the effect on cosmic neutrinos isjust the average value of the vacuum probabilities when the oscillating phases are set to zero: P (cid:96) → (cid:96) (cid:48) = (cid:88) i =1 | U (cid:96)i | | U (cid:96) (cid:48) i | . (12)This limit, when the oscillation probabilities reduce to constant values, is known as Gribov-Pontecorvo regime [42]. Using the most recent best fit values of the mixing angles [45]: { θ , θ , θ , θ CP } = { . ◦ , . ◦ , . ◦ , ◦ } (13)the resulting approximate values of the oscillation probabilities in Equation (12) correspond to:matrix( P (cid:96) → (cid:96) (cid:48) ) = .
548 0 .
185 0 . .
185 0 .
436 0 . .
267 0 .
379 0 . with (cid:96), (cid:96) (cid:48) = e , µ, τ (14)Given a flavor fraction of different neutrinos at the source, f (cid:96) , such that 0 ≤ f (cid:96) ≤ f e + f µ + f τ = 1, one calculates the final flavor fraction at Earth as: f (cid:96) = (cid:88) (cid:96) =e ,µ,τ P (cid:96) → (cid:96) (cid:48) f (cid:96) (cid:48) . (15)(For a thorough investigation of the relevant parameters and an assessment of the uncertainties,see References [46, 47].)The major consequence of Equation (15) for cosmic neutrinos on Earth is that the spectra ofthe three neutrino flavors are approximately the same, if they have exactly the same power lawdistribution. This is particularly true in the case of muon and tau neutrinos, due to the parametersof oscillations, which display an approximate mu-tau exchange symmetry.Assuming in fact that neutrinos originate from pp or pγ production (Section 2.2). In astro-physical environments, the pion decay chain is complete (i.e., also the muon decays). Accordingto Equation (3), one has exactly a ( ν µ + ¯ ν µ ) pair for each ν e or ¯ ν e , leading to flavor fractions atthe source f e = 1 / f µ = 2 / f τ < − . In all large apparata used to study cosmic neu-trinos, there is no experimental method able to distinguish reactions induced by a neutrino or ananti-neutrino; thus, no separation between particles and anti-particles can be made.The flavor fractions can thus be written using a single parameter, f = f e , as: { f e , f µ , f τ } = { f, − f, } . (16)With oscillation parameters given in Equation (14), we obtain: { f e , f µ , f τ } = { .
185 + 0 . f, . − . f, . − . f } (17)that verify the properties mentioned just above. In particular, for f = 1 / / {− . , +0 . , +0 . } , namely, they are very close to each other after oscillations.8au neutrinos, in this context of discussion, have a central role as they are not produced incharged mesons decay, either in atmospheric or astrophysical environments. The conventional com-ponent of atmospheric neutrinos from pion and kaon decays, as described in Section 6.1, is mostly composed by ν µ + ¯ ν µ ; at few 10-100 TeV one expects the onset of a new component due to charmedmeson decays, that should instead be almost equally composed by electron and muon neutrinos(more discussion below). Because at energy scales larger than 1 TeV atmospheric neutrinos arenot significantly subject to oscillations in a path of length of the Earth diameter, we do not expectthe presence of any atmospheric ν τ . Instead it is for sure that cosmic neutrinos are subject toneutrino oscillations, and therefore tau neutrinos have to be present. The interpretation of tauneutrino events should be regarded with high confidence as due to high-energy neutrinos that havetraveled upon cosmic distances. See Reference [48] for a quantitative and updated discussion ofthe expectations.Note that, generally, neutrino and antineutrino events are not distinguishable and thereforeare added together - the Glashow resonance events due to ¯ ν e ’s, discussed in Section 5.4, are anexception to this rule. The distance traveled by a neutrino in the Earth volume, before reaching the detector, is: (cid:96) ( θ N ; d ) = ( R ⊕ − d ) cos θ N + (cid:112) ( R ⊕ ) − ( R ⊕ − d ) · (sin θ N ) , (18)where θ N is the nadir angle, R ⊕ = 6371 km the average Earth radius. The quantity d representsthe depth of the detector (of the order of a few km at most). The formula is derived from basictrigonometric considerations.The Earth is not fully transparent to the highest energy neutrinos, due to the increase of theabsorption cross section of the matter, σ abs , with the increase of the neutrino energy E ν . Themain contribution is due to the charged current (CC) interaction with nucleons σ abs (cid:39) σ CC thatcan be modeled as deep inelastic scattering. The neutral current interaction produces a neutrinowith a reduced energy, and this does not significantly affect the absorption cross section. Detailedcalculations (performed also through Monte Carlo methods) can account for the deformation ofthe arrival energy spectrum due to neutral current interactions and due to the ν τ regenerationeffect [49]. The propagation of the ¯ ν e flavor at 6.3 PeV is also affected by the resonant formationof the W boson in ¯ ν e + e − collisions, described in Section 5.4.The absorption coefficient of the neutrinos, according to the usual formula e − τ , depends on the opacity factor τ , defined as: τ ≡ σ abs ( E ν ) × z ( θ N ) . (19)Here, the column density z ( θ N ), which corresponds to the number of nucleons per cm that arecrossed from a certain nadir angle, can be estimated by the formula z ( θ N ) = 2 N A (cid:90) R ⊕ cos θ N ρ (cid:16)(cid:112) x + ( R ⊕ sin θ N ) (cid:17) dx, (20)where N A is the Avogadro number, x is the coordinate along the neutrino path inside the Earth.Here, we neglected d (and h ) in the formula (18) for (cid:96) ( θ N ; h, d ), which is sufficient for our purposes.9 ° R 〚 km 〛 ρ g cm3
100 TeV1 PeV10 PeV0 20 40 60 80 θ N [ degree ] × - × - × - × - × - σ cm2 Figure 3:
Left panel: Earth’s density in g/cm according to the PREM model [50]; note the discontinuitybetween the mantle (brown area) and the core (red area) at a distance from the center of R core = 3840km. The limiting angle θ N , core = arcsin( R core /R ⊕ ) = 33 . ◦ is emphasized. Right panel; three values ofthe neutrino (continuous lines) and antineutrino (dotted lines) cross sections, as compared with the criticalvalue of the cross section σ (cid:63) ( θ N ) related to e-folding absorption, as defined in the text. The terrestrial density as a function of the distance from the center ρ ( R ), estimated using thePREM model [50] with an accuracy adequate to the current need, is shown in the left panel ofFigure 3. One can define the inverse of the column density as the critical value of the cross section σ (cid:63) ( θ N ) = 1 /z ( θ N ) . (21)In fact, when the absorption cross section satisfies the condition σ abs ( E ν ) = σ (cid:63) ( θ N ), the opacity is τ = 1 and the absorption coefficients is 1 /e ∼ .
37. The right panel of Figure 3 compares σ (cid:63) ( θ N ),depicted in blue and shown as a function of the nadir angle, with the cross section given for threevalues of the energy, indicated in the black lines. The angles at which the absorption coefficientsof the neutrinos is 1 /e are, 32 ◦ for E ν = 100 TeV, 59 ◦ for E ν = 1 PeV, 81 ◦ for E ν = 10 PeV.Therefore, at very-high energies, we receive neutrinos arriving only from a limited patch of the sky,close to the local horizon. Note that the rotation of the Earth changes the region of the sky seen inthe course of the day, except for the case of a detector located at the poles (such as IceCube) whenthis does not change. The basic structure of a high-energy neutrino telescope is a matrix of light detectors inside atransparent medium. This medium, such as ice or water at great depths: • offers a large volume of target nucleons for neutrino interactions; • provides shielding against secondary particles produced by cosmic rays;10 allows the propagation of Cherenkov photons emitted by relativistic charged particles pro-duced by the neutrino interaction.The primary aim of these telescopes is the search for point sources and the characterization ofthe neutrino flux produced by diffuse/unresolved sources. While the idea in the former case is tostand out the atmospheric background in a specific direction of the sky, in the latter case the ideais to rely fully on the study of the spectrum, in the hope that a cosmic component, harder than theone due to atmospheric neutrinos, can eventually become visible. This is illustrated in Figure 4 forthe case of muon neutrinos.Finally, a neutrino candidate can be characterized in time and direction of arrival, and it can becorrelated with some temporal/spatial coincidence with an external triggers (such as that resultingfrom a γ -ray burst observation, from a gravitational wave event, or from other transients observedby space- or ground-based observations.) This last case is usually referred to as the multimessengerstrategy . See Reference [51, 52] for recent reviews. The golden channel for point-like neutrinosource searches is represented by ν µ ’s, where a (sub) degree pointing can be attained in the energyof interest.Neutrinos are also characterized by their flavor , and each flavor and interaction mechanisminduces different event topologies, as discussed in Section 5. The expected occurrence of neu-trino oscillations give us a powerful manner to test the interpretation of the collected data (seeSection 3.1). The activities for the construction of a neutrino telescope started in the early 1970s with a jointRussian-American tentative. Successively, the efforts of the two communities turned toward anexperiment in a Russian lake with an iced surface and in the ice of South Pole. At the beginningof 1990’s, European groups began the exploration of the Mediterranean Sea as a possible site foran underwater neutrino telescope. A detailed description of the experimental activities toward therealization of neutrino telescopes can be found in Reference [10].
The IceCube experiment at the South Pole is, at present, the only running km -scale neutrinoobservatory. The instrumented detector volume is a cubic kilometer of highly transparent Antarcticice instrumented with an array of 5160 Digital Optical Modules (DOMs). The IceCube array [53] iscomposed of 86 strings instrumented each with 60 Digital Optical Modules (DOMs). Among them,78 strings are arranged on a hexagonal grid with a spacing of 125 m, with a vertical separation of17 m between each DOM. The eight remaining strings are deployed more compactly at the centreof the array, forming the DeepCore sub-detector [54]. A horizontal distance of 72 m separates theDeepCore strings with a vertical spacing of 7 m between each PMT.The DOMs are spherical, pressure-resistant glass housings each containing a 25 cm diameterphotomultiplier tube (PMT) plus electronics for waveform digitization, and vertically spaced 17 mfrom each other along each string. High quantum efficiency PMTs are used in a denser sub-arraylocated in the center of the detector. This sub-array, called DeepCore, enhances the sensitivity to11 -
100 TeV atmosphericneutrinos cosmicneutrinos
MuonenergyFlux
Figure 4:
Schematic representation of how a new “hard” muon neutrino component of cosmic origincan stand out over the atmospheric neutrino at the highest energies, becoming observable. The energyregions where the uncertainties are larger are represented with dashed lines. For atmospheric neutrinos theuncertainty is due to the precise shape of the cosmic ray knee and the amount of prompt neutrinos; forcosmic neutrinos it is due to the production mechanism—moreover at low energies it is difficult to isolatethem, while at high energies events are rare. low energy neutrinos. Data acquisition with the complete configuration started in May 2011 [55].
In the sea, to minimize the noises induced by external agents, a telescope must be located farenough from continental shelf breaks and river estuaries. At the same time, the detector should beclose to scientific and logistic infrastructures on shore. With such requirements, the MediterraneanSea offers optimal conditions on a worldwide scale.The ANTARES detector [56] was completed in 2008, after several years of site exploration anddetector R&D. The detector is located at a depth of 2475 m in the Mediterranean Sea, 40 km fromthe French town of Toulon. It comprises a three-dimensional array of 885 optical modules (OMs)looking 45 ◦ downward and distributed along 12 vertical detection lines. An OM consists of a 10 (cid:48)(cid:48) PMT housed in a pressure-resistant glass sphere together with its electronics [57]. The total lengthof each line is 450 m; these are kept taut by a buoy located at the top of the line. The instrumentedvolume corresponds to about 1/40 of that of IceCube, but due to the water properties, and thedenser configuration of OMs, its sensitivity is relatively larger at energies below 100 TeV. In additionthe Galactic center is below the horizon ∼
70 % of the time.12 .2.3 KM3NeT
KM3NeT is a research infrastructure that will house the next generation neutrino telescope in theMediterranean Sea [58]. KM3NeT will consists of two different structures.The KM3NeT/ARCA telescope is in construction about 100 km off-shore Portopalo di CapoPassero (Sicily), at a depth of 3500 m. The DOM spacing along the DU is 36 m with an averagedistance among DUs of 90 m. ARCA will consists of two building blocks of 115 vertical detectionunits (DUs) anchored at a depth of about 3500 m. The telescope will have an instrumented volumeslightly larger than that of IceCube. The main scientific objectives are the study of astrophysicalpotential neutrino sources, with particular attention for galactic ones [41]. The golden channel isthe detection of long track muon produced in charged current ν µ interactions. For this kind ofevents an angular resolution better than 0.1 ◦ and an energy resolution of 30% in log(Energy) arereached for neutrino energies greater than 10 TeV [58, 59].The KM3NeT/ORCA detector is located on the French site off-shore Toulon and at a depth of2450 m. The main scientific objectives are the determination of the neutrino mass hierarchy andthe searches for dark matter. The two KM3NeT facilities will also house instrumentation for Earthand Sea sciences for long-term and on-line monitoring of the deep-sea environment. The DOMspacing along the DU is 9 m and the average distance among the DUs is 23 m. It will consists ofone building block, with an instrumented mass of 8 Mton.Both KM3NeT structures will use the same DUs equipped with 18 optical modules, with eachoptical module comprising 31 small PMTs. The technical implementation and solutions of ARCAand ORCA are almost identical, apart from the different spacing between DOMs. Finally, many years of experience with smaller neutrino telescope installations in Lake Baikal inSiberia, have led to the Baikal- Gigaton Volume Detector (GVD) project, aiming at a detectorinstrumenting a cubic-kilometer of water [60]. Baikal-GVD is formed by a three-dimensional latticeof optical modules, which consist of PMTs housed in transparent pressure spheres. They arearranged at vertical load-carrying cables to form strings. The telescope has a modular structure andconsists of functionally independent clusters. Each cluster is a sub-array that comprises 8 strings.Each cluster is connected to the shore station by an individual electro-optical cable. The first clusterwith reduced size was deployed and operated in 2015. In April 2016, this array has been upgradedto the baseline configuration of a GVD-cluster, which comprises 288 optical modules attachedalong 8 strings at depths from 750 m to 1275 m. In 2017–2019, four additional GVD-clusters werecommissioned, increasing the total number of optical modules up to 1440 OMs. As part of phase1 of the Baikal-GVD construction, an array of nine clusters will be deployed until 2021. GVD willprimarily target neutrinos in the multi-TeV range. First results have recently been reported [61].
In neutrino telescopes, one can distinguish between two main event classes—events with a long track due to a through-going muon (induced by ν µ charged current (CC) interactions), and events13ith a shower , without the presence of a muon. The special case of ν µ CC interactions inside thedetector will contain a shower originating in the interaction vertex and an accompanying track aswell.A high-energy electron resulting from a CC ν e interaction radiates a photon via bremsstrahlungafter a few tens of cm of water/ice (the radiation length in water is ∼
36 cm): this process leadsto the development of an electromagnetic cascade (the shower ). Showers are induced as well byneutral current interactions and by ν τ CC interactions occurring inside the instrumented volume ofthe detector. Tau neutrino interactions can produce also a particular event topology, with eventscalled in this review double core .Neutrino and anti-neutrino reactions are not distinguishable; thus, no separation between parti-cles and anti-particles can be made. A shower of particles is produced in proximity of the interactionvertex in all neutrino interactions. However, for CC ν µ , often only the muon track is detected, as thepath length of a muon in water exceeds that of a shower by more than 3 orders of magnitude forenergies above 2 TeV. Therefore, such an event might very well be detected even if the interac-tion has taken place several km outside the instrumented volume, in the Earth’s crust or in thesurrounding transparent medium, provided that the muon traverses the detector. More in detail,the muon range R can be described in the continuous-energy-loss approximation as: dRdE µ = − α + βE µ with α ≈ × − TeV cm g ,β ≈ × − cm g . (22)The α coefficients describes the well-known fact that low energy muons (minimum ionizingparticles , mip) loose about 2 MeV/cm in water, while the second coefficients β describes that theenergy loss processes become ‘catastrophic’ at high energies. This implies the travel distance inwater or ice ( ρ (cid:39) − ): d ( E µ , E thr. ) ≈ D × log (cid:18) E µ /ε E thr. /ε (cid:19) with D = 1 ρ · β ≈ ε = αβ ≈ . (23)The properties of showers (total visible energy, a rough estimate of the neutrino direction) areobtained if the interaction occurs inside (or very close to) the instrumented volume. Figure 5 showsa sketch of neutrino interactions giving the two different types of events. Passing-events are due to tracks induced by ν µ and ¯ ν µ CC interactions around the detector andpassing through the detector. The same signal is called (depending on the experiment) also through-going muons, up-going muons, passing muons, tracks, and so forth emphasizing a feature or anotherone. (As recalled above, there is also the possibility of track events that start inside the detector.)The angular precision for passing-events depends on the muon energy and detection medium.Deep ice is more transparent than seawater. Thus, the same instrumented volume of ice correspondsto a larger effective volume than in seawater. On the other hand, the effective scattering length for14igure 5:
Neutrino interactions give two different types of events: ν µ charged current (CC) interactionthat produces a muon (left) and ν e CC interaction that produces an electron inducing an electromagneticcascade (shower). Neutral current (NC) interactions also produce showers. In this sketch, provided by theKM3NeT Collaboration, each point represents an optical module (OM), spaced about 100 m from eachother. In gray are the OMs not interested by optical photons (mainly from the Cherenkov effect) producedby the event. The colors show the temporal sequence of the hit OMs—the red color indicates the beginningof the event. ice is smaller than water. This is a cause of a larger degradation of the angular resolution of detectedneutrino-induced muons in ice with respect to water. Passing-events are better reconstructed inseawater than in ice. Refer to Reference [18] for a detailed discussion of differences between waterand ice properties. The typical angular resolution of tracks in ice, δθ passing ∼ . − ◦ , while it isforeseen to reach 0 . ◦ in the KMeNeT detector.Passing-events are mostly selected from the direction of the Sky below the detector, in orderto keep under control the background of atmospheric muons. Therefore, the neutrinos that haveto cross a large fraction of the Earth, above few 100 of TeV, are subject to absorption (Section3.2); the optimal region of observation is therefore a crown of azimuthal directions, just below thehorizon of the detector. 15 .2 Contained Events The first operating km -class telescope, IceCube, has demonstrated that also events partially orfully contained in the detector can be used to observe high-energy cosmic neutrinos.The method rely on the request that the interaction point, and possibly the whole event, islocated into the instrumented volume. In this manner, the background can be suppressed, and thisis even more effective for electron type events, that are less abundant among atmospheric neutrinos.The ratio of the through-going events with respect contained ones is roughly given by N throug. N contained ∼ area × D volume (24)where a detector with typical dimension L has an area ∼ L for muon detection and a volume L for contained event detection. The scale distance D is defined in Equation (23). The ratio isjust ∼ D/L and this is not small as long as the detector has physical dimension L ∼ D namely,kilometer size, just what has been attained by IceCube.This method allows the telescope to observe also events coming from above the detector, differ-ently from the previous method. However, the risk of background contamination from atmosphericmuons does exist, especially at the lowest energies. For zenith angles θ < ◦ and E ν >
100 TeV theatmospheric muon self-veto (Section 6.2) can help to suppress the atmospheric neutrino background.
The presence of ν τ would be an unequivocal signature of a cosmic neutrino. The direct productionin cosmic ray collision is very suppressed. High-energy atmospheric neutrinos do not have enoughtime to undergo flavor transformation. Thus, with high confidence, ν τ are produced through threeflavor oscillations over cosmic scale distances (Section 3.1).The identification of a ν τ relies on the extrapolation on macroscopic scales of the principleused by OPERA, namely, the displacement between the point where the tau lepton is produced(by a CC ν τ interaction) and the point where the charged tau decays. There are two differentimplementations of this principle. In the first one, different regions of a neutrino telescope (namely,different strings or set of phototubes) see the two interaction vertexes. In the second one, using thefast time response of each individual phototube, the experiment is able to distinguish light emissionoccurred in two successive processes (the ν τ interaction, the τ decay). These two principles areknown as double bang [62] and double pulse [63] respectively—and collectively are called double coreevents in the present review paper. An exciting possibility is the observation of events caused by ¯ ν e interacting with atomic electrons,and producing an on-shell W boson via ¯ ν e + e → W . The cases when the W decay in a pair ofquarks yields the whole energy of the initial neutrino, amounting to E Glashow = m W m e = 6 . ν e . An events at a suchenergy, yet unseen, is called Glashow resonance [64].Seeing events due to Glashow resonance would be an excellent way to probe of the extensionof the cosmic neutrinos spectrum at high energies, and in the long run, also a test of the type ofneutrino source (whether pp or pγ ). See Reference [65] for an updated, quantitative discussion. For each event topology, the calculation of the expected number of neutrino signals N i , given a fluxof neutrinos of type (cid:96) , is usually performed by means of effective areas A (cid:96) → i . If the flux is constantin time and the observation time is T , it is possible to write symbolically: N i = 4 πT (cid:90) dE ν A (cid:96) → i ( E ν ) Φ (cid:96) (26)The effective area incorporates the neutrino cross section, the number of target particles in thedetector, the angular and the energy response, the detector inefficiencies, the cuts implementedin the analysis. Usually, it is a growing function of the energy of the incoming neutrino. In theIceCube detector the effective areas for the main classes of events, the passing (muon) events andthe contained events, are about some tens of m in the relevant energies. The effective area forcontained events at high-energies increases mostly because of the cross section growth with neutrinoenergy, σ ∼ E . − . ν ; see Reference [66] for a useful and accurate discussion. The cosmic neutrino sky as seen on Earth is not background free, due to the presence of theatmospheric neutrinos and secondary atmospheric muons.
In the region of energy where atmospheric neutrino oscillations have been discovered, E ν ∼ GeV,the spectrum of the neutrinos is distributed as E − αν with α ∼ .
7. In fact, due to the mentionedproperty of scaling of the hadron-hadron interactions, atmospheric neutrinos have (approximatively)the same power-law index of the primary cosmic rays at the corresponding energies. Neutrinotelescopes have been able to measure the flux and energy spectrum of atmospheric ν µ [67, 68] andatmospheric ν e [69].This behavior changes at the higher energies of interest for the search of cosmic neutrinos,because most secondary muons in Equation (3), will touch ground before decaying. This reducesthe number of atmospheric ν µ and depletes electron neutrinos: indeed, the electron/muon neutrinofraction decreases from 1/2 to 1/30, because the muon is not allowed to decay freely. Pions of similarenergy travel 100 times less before decaying; however, they have a nuclear interaction cross sectionof the order of σ π ∼ π × fm with nucleons, which implies an interaction length m n / ( σ π × ρ air )17 E ν e (GeV) − − − − − − E ν e d N / d E ν e ( G e V c m − s − s r − ) promptconventional + astrototal E ν µ (GeV) − − − − − − E ν µ d N / d E ν µ ( G e V c m − s − s r − ) promptconventional + astrototal Figure 6: The expected electron (left panel) and muon neutrino (right) flux components in theenergy range from 1 TeV to 1 PeV. Prompt neutrinos are shown separately and summed with allother components. From Reference [47].of comparable size for a density of ρ air ∼ − g/cm . For this reason, spectrum of atmosphericneutrinos from pion interactions becomes steeper, E − αν with α ∼ .
7, since only a fraction of pionsis free to decay before interacting. This is the behavior of the atmospheric component shown inFigure 4.It is important to recall that at some 10–100 TeV one expects the onset of a new component (todate unobserved) due to the production of charmed mesons, that, having a very short lifetime, decayimmediately after production leading to a spectrum as E − αν with α ∼ . non-muonic neutrinos inthe region of 10-few 10 of TeV, as discussed in Reference [47]. In this paper one finds a descriptionof the model of atmospheric neutrinos, of the one of cosmic neutrinos (based on the hypothesisof pp-collisions and upgraded thanks to IceCube through-going muon data), and an assessment oftheir uncertainties. For an illustration of the principle, see Figure 6. Atmospheric muons can penetrate the atmosphere and up to several kilometers of ice/water,and they represent the bulk of reconstructed background events in any large volume neutrinodetector [70, 71, 72]. Neutrino detectors must be located deep under a large amount of shield-ing in order to reduce the background. The flux of down-going atmospheric muons exceeds theflux induced by atmospheric neutrino interactions by many orders of magnitude, decreasing withincreasing detector depth, as shown in Figure 7. 18igure 7:
Flux as a function of the cosine of the zenith angle θ of: (i) atmospheric muons for two differentdepths; (ii) muons induced by CC interactions of atmospheric ν µ , for two different muon energy thresholds E µ . Upgoing (down-going) events have cos θ < >
0) [74].
Atmospheric muons can be used for a real-time monitoring of the detector status and for detectorcalibration [73]. However, they represent a major background source: downward-going particleswrongly reconstructed as upward-going and simultaneous muons produced by different cosmic rayprimaries could mimic high-energy neutrino interactions, see [74] for a discussion.In general, atmospheric neutrinos are indistinguishable from astrophysical neutrinos. The pres-ence of a muon can help to classify a contained interaction as due to atmospheric ν µ instead of acosmic ν µ . This occurs when neutrino energy is sufficiently high and the zenith angle sufficientlysmall that the muon produced in the same decay as the neutrino has a high probability to reachthe detector [75, 76]. In this case, the atmospheric neutrino provides its own self-veto. In general,the atmospheric neutrino passing rate can be evaluated with simulations by including other high-energy muons produced in the same cosmic-ray shower as the neutrino. In this way, the methodcan be extended to ν e ’s [77]. In practice, the passing rate is significantly reduced for zenith angles θ < ◦ and E ν >
100 TeV. This method was used first by the IceCube collaboration to select thehigh energy starting events (Section 5.2). 19
The Observational Status of High-Energy Neutrinos As-tronomy
The IceCube experiment has observed neutrinos of astrophysical origin in different ways [78, 79]—first with the
High Energy Starting Event (HESE) sample; then with passing events; finally with acoincidence with electromagnetic signals.
The first detailed observation of an excess of high-energy astrophysical neutrinos over the expectedbackground has been reported by IceCube using data collected from May 2010 to May 2012 andwith 662 days live time [80]. This sample is continuously updated, and as of this writing (afterICRC 2019), results up to early 2018 are available for a total live time of 2635 days of live time.The high-energy neutrino candidates have been selected with the requirement that the interactionvertex is contained within the instrumented ice volume, without any signal on the PMTs locatedon the top or sides of the detector. In such a way, the edges of IceCube are used as a veto fordown-going atmospheric muons and atmospheric neutrinos, Section 6.2.The deposited energy E dep in the detector is derived from the number of photoelectrons (p.e.)in the optical modules and, in turns, the true energy E ν of the neutrino is estimated with the helpof Monte Carlo simulation techniques. An event with 6000 p.e. corresponds to a deposited energyof ∼
30 TeV.Figure 8 shows the distribution of the deposited energy (left plot) and of the cos(declination)(right plot) for HESE in the 7.5-year sample. The additional contribution in the data sample withrespect to the background corresponds to a diffuse astrophysical signal, with topologies compatiblewith neutrino flavor ratio ν e : ν µ : ν τ ∼ ν means the sum over neutrino andantineutrinos of all flavors), d Φ ν dE = (6 . +1 . − . ) · − (cid:18) E
100 TeV (cid:19) − (2 . ± . GeV − cm − s − sr − . (27)Most of the signal originates primarily from the Southern hemisphere, where neutrinos with E ν (cid:29)
100 TeV are not absorbed by Earth. The poor angular resolution ( ∼ ◦ ) of showering eventsprevents the possibility of accurate localization in the sky of the parent neutrino’s direction. Toidentify any bright neutrino sources in the data, the usual maximum-likelihood clustering searchhas been used, as well as searches for directional correlations with TeV γ -ray sources. No hypothesistest has yielded statistically significant evidence of clustering or correlations. A second IceCube sample that evidences a diffuse presence of cosmic neutrinos corresponds to CCupgoing muon neutrino events [83, 84]. The field of view for these events is restricted to the Northernhemisphere. This analysis has recently been extended with data collected up to December 2018,equivalent to 10 y of live time [85]. This last sample contains ∼ Deposited energies E dep (left panel) and arrival directions (right panel) of observed IceCubeHESE (crosses), compared with predictions. The sample refers to 7.5 years of data. The best-fit expectationis shown as a stacked histogram with each color specifying a flux component—astrophysical (golden),conventional atmospheric (red), and penetrating muons (purple); the best fit prompt normalization is zeroand is not shown. Events below 60 TeV (light blue vertical line) are not included in the fit, but one seesgood data-MC agreement extending into this energy range. From the arXiv version of [82]. For these events, the reconstructed energy E irec of each individual neutrino i is a poor proxyof the true neutrino energy, E ν . Thus, the reconstructed neutrino energy is used to produce aresponse matrix P ( E irec ; E ν ), which must be inverted to produce the posterior probability densityfunction P ( E ν ; E irec ) [84]. Figure 9 shows the distribution of the observable energy for the eight-year sample. A clear excess above ∼
100 TeV is visible and is not compatible with the atmosphericbackground expectation.When the atmospheric neutrino background is removed, the best fit to the full data-set resultsin an astrophysical power-law flux for one neutrino flavor (i.e., ν µ + ¯ ν µ ) [85]: d Φ ν dE = (1 . +0 . − . ) · − (cid:18) E
100 TeV (cid:19) − (2 . ± . GeV − cm − s − sr − . (28) On 22 September 2017 (the month following the first observation of the coalescence of the twoneutron stars with gravitational waves), the IceCube collaboration detected a track event inducedby a ∼
300 TeV ν µ . The detection generated an automatic alert that caused related searches fromthe direction of the event by many experiments. The Fermi-LAT satellite telescope reported thatthe direction of the neutrino was coincident with a known gamma-ray source, the active galaxyknown as TXS 0506 + 056 (object classified as a blazar), that was in a particularly active stateat the time of the neutrino detection. In addition, the MAGIC gamma ray telescope (locatedat the Canary Islands) also observed a significant photon flux of energies up to 400 GeV from thedirection of the blazar; the study of the astronomical object was completed by observations at other21igure 9: Unfolded ν µ event distribution from the passing muon sample in IceCube. The data (crosses)are compared to the best-fit fluxes for atmospheric and astrophysical neutrinos. From the arXiv versionof [85]. wavelengths: radio, optical and X-ray. These observations are compatible with the position of aknown blazar at redshift z = 0 . ± . ◦ below the horizon. A possible neutrino candidate would thus be de-tected as an up-going event. A time-integrated study performed by the collaboration over a periodfrom 2007 to 2017 fits 1.03 signal events, which corresponds to a probability that the backgroundsimulates this signal of 3.4% (not considering trial factors) [89]. Due to their relative proximity, the possibility of studying Galactic sources is particularly intriguing.The ANTARES detector in the Northern hemisphere can measure upgoing events , exploiting,with respect to IceCube, its complementing field-of-view, exposure, and lower energy threshold [90].22igure 10:
Upper limits at 90% C.L. on the ν µ + ¯ ν µ neutrino flux normalization from 57 neutrinocandidate sources (green dots) studied by the ANTARES and IceCube collaborations, as a function of thesource declination [91]. Such kind of plots depends strongly on the assumption of the neutrino energyspectrum and on the differential sensitivity of the detectors. The present plot is computed assuming anunbroken neutrino spectrum, with spectral index γ = 2 .
0. For this spectrum, most of signal is due toneutrinos with E ν >
10 TeV. The green line indicates the sensitivity of the combined analysis. The dashedcurves indicate the sensitivities for the IceCube (blue) and ANTARES (red) individual analyses. Referringto Figure 2, the limit corresponding to the SNR RXJ1713.7-3946 is indicated (when comparing the twoplots, remember that the y-axis of this figure must be multiplied by 10 − to have the same units). In particular, ANTARES is sensitive at a level compatible with the larger IceCube detector topossible sources located in the Galactic plane. Although a sizable neutrino flux from individualsources is expected to be observable only with a km -scale detector (see Figure 2), detailed searchesfor point-like and extended sources of cosmic neutrinos from the Galactic region have recently beenperformed using data collected by the ANTARES and IceCube neutrino telescopes [91]. Theycombined all the track-like and shower-like events pointing in the direction of the Southern Skyincluded in a previous nine-year ANTARES point-source analysis, with the through-going track-like events used in a seven-year IceCube point-source search. The advantageous field of view ofANTARES and the large size of IceCube are exploited to improve the sensitivity in the SouthernSky by a factor of ∼ Combined upper limits from ANTARES and IceCube (at 90% confidence level, blue lines)on the three-flavor neutrino flux of the model of Galactic cosmic ray propagation (the black lines showstwo values of the knee position). The boxes represent the diffuse astrophysical neutrino fluxes measured byIceCube using an isotropic flux template with starting events (yellow) and upgoing tracks (green) [92].
In this figure, the upper limit corresponding to the SNR RXJ1713.7-3946 is highlighted in ordercompare it with the predictions reported in Figure 2. The predicted flux at E ν >
10 TeV is of theorder of few × − GeV cm − s − , which is still slightly below the combined ANTARES (9 years)and IceCube (7 years) sensitivities.In addition to individual sources, the existence of a diffuse Galactic neutrino production isexpected from cosmic-ray interactions with Galactic gas and radiation fields. These interactionsare also the dominant production mechanism of the diffuse high-energy γ -rays in the Galactic plane,which have been measured by the Fermi-LAT. Different models propagating charged cosmic raysdiffusively in the interstellar medium producing γ -rays and neutrinos via interactions with theinterstellar radiation field and interstellar gas have been developed. The ANTARES and IceCubecombined their analyses to test [92] a specific neutrino production model (Figure 11). As a result,their estimate yields a non-zero diffuse Galactic neutrino flux for a p -value of 29% for the mostconservative model.The result of this analysis limits the total flux contribution of diffuse Galactic neutrino emissionto the total astrophysical signal reported by IceCube above 60 TeV to be less than 10%.24 What Are the Main Sources of Cosmic Neutrinos?
The diffuse extraterrestrial flux of high-energy neutrinos, highlighted by IceCube and discussedabove, has characteristics that suggest significant extragalactic contributions. This seems to beconfirmed by the observation concerning TXS 0506 + 056. In spite of that particular association,the individual sources of IceCube neutrino events remain unidentified [93].At present, the IceCube and ANTARES collaborations manage a series of alert and follow-upprograms, which react in real time to events due to neutrino interactions classified as particularlyinteresting. In this case, a short message is automatically sent to the Gamma-ray burst CoordinatesNetwork (the GCN network) [94], which activates the radio, optical, X-ray and gamma telescopes.Conversely, particular transient phenomena observed with other probes can be immediately studiedwith the network of neutrino telescopes.Although we do not have yet a clear theoretical idea on which the sources of cosmic neutrinosare and how intense they are, there are several ideas on the subject. In this section, largely based onReference [23], we discuss a few cases when cosmic neutrinos are directly connected to the (sourcesof the) cosmic rays.
Consider an astrophysical site where cosmic rays are produced and confined for some time, andsuppose that the same region also contains a ‘thin’ target— much more diffuse than in Earth’satmosphere. As described in Section 2.1, we might imagine that this site will be particularlybrilliant in neutrinos and γ -rays, and that the shape of these secondary particles will reflect theproduction spectra of cosmic rays. The cosmic ray spectrum in the source is unknown a priori ,however, general theoretical arguments are in support of the idea that the spectrum behaves as ∼ E − , both for γ -rays and for neutrinos. (1) First, such a spectrum is expected for primarycosmic rays in the Fermi acceleration mechanism. (2) Second, if the target for the cosmic raycollisions is composed by protons or other nuclei, but–differently from the atmosphere–the targetlayer is thin and there is no significant absorption of the mesons, the spectra of the secondaryparticles reflect closely the shape of the primary cosmic ray spectrum. (3) Third, it is not plausiblethat neutrinos suffer absorption in the source - while for gamma rays, this is possible. In theseconditions, the spectrum of the secondary neutrinos (and possibly of the associated γ -rays) tillsome maximum energy, is expected to be distributed as Φ ν ∝ E − ν . This spectrum would stand outover the atmospheric neutrino background at sufficiently high energies - see again Figure 4. Nowadays, extragalactic sources are believed to give the dominant contribution to the high energyneutrino flux. Assuming that the highest energy cosmic rays that we observe on Earth are typicalof the entire cosmos and are of extragalactic origin, we estimate that they have an energy density of ρ uhecr = 3 × − erg/cm above 1 EeV. Considering the typical evolution time of T H = 10 billionyears, the corresponding energy losses of the universe are W = ρ uhecr /T H = 9 × erg / (Mpc yr).This cosmic ray population will be in equilibrium if, in the reference volume of 1 Gpc , there is apopulation of 900 γ -ray bursts and each one injects suddenly 10 erg in cosmic rays; an alternative25ould be that there is a population of 150 active galactic nuclei, and each one radiates continuously2 × erg/s. Interestingly, in both cases, the number of sources is reasonable and the presumedamount of energy emitted in cosmic rays corresponds to the visible electromagnetic output.There are many potential astrophysical sources of high energy neutrinos and below we providea brief summary of the most significant ones, examining AGNs, blazars, starburst galaxies andGamma-Ray Bursts (GRBs). An active galactic nucleus (AGN) is a compact region at the center of a galaxy whose luminosityis much higher than the normal one over some portion of the electromagnetic spectrum, with char-acteristics indicating that the excess luminosity is not produced by stars. This excess (in thenon-stellar emission) has been observed in the radio, microwaves, infrared, optical, ultra-violet, X-ray and gamma ray wavebands. The radiation from an AGN is believed to be a result of accretionof matter by a supermassive black hole at the center of the host galaxy [95]. The central engine canaccelerate protons up to very high energies, while the accretion disc is an emitter of hot thermalradiation, which gives prominent feature in the observed AGN spectra, usually refereed to as a“Big Blue Bump”. Accelerated particles move along two jets perpendicular to the accretion discand crossing this radiation field. AGNs are characterized by a strong positive cosmic evolution,meaning that these objects were much more abundant in the past.AGNs are considered potential sites for high energy neutrino production since 30 years [96,97, 98]. High energy neutrino appear in charged pion decays created in proton- γ interactions,Equation (5), due to the collision between protons and the blue bump photons. Protons can beaccelerated up to ∼ EeV energies and absorbed in the radiation field contained in the disk, that hasa temperature of the order of 10 TeV and a black hole mass of ∼ M (cid:12) . Therefore the resultingneutrino flux is expected to be relevant in the sub-PeV and in the PeV region. One clarification isneeded: as explained in Section 2.2, neutrinos from pp or pγ interactions takes 5% of the primaryproton energy. However, during the propagation, neutrinos looses energy adiabatically, reaching theEarth with an energy equal to ( E p / / (1 + z ), where E p is the primary proton energy. Since thedistribution of AGNs is strongly positive, the larger contribution to the neutrino emission is providedby sources having redshift between z = 1 and z = 2. It means that most of high energy neutrinosreaching Earth, will have an energy ∼
50 times lower than the energy of the primary proton.Nowadays it is not possible to exclude (or confirm) the AGNs as potential sources of a part ofthe IceCube signal. The increasing of the statistics can help in this game, although it is hard toconstrain certain class of abundant sources (such as low luminosity AGNs).
Blazars are AGNs with the emitted jet pointing toward the Earth. They are divided in two classes:BL Lacertae (BL Lac) and Flat Spectrum Radio Quasar (FSRQ). FSRQs are characterized by thepresence of a broad line region and by emission lines in the optical spectrum, while BL Lacs are char-acterized by featureless optical spectra (i.e., lacking strong emission/absorption lines). A completereview of the processes occurring in blazars is provided in Reference [99].The Fermi-LAT satellite proved that the blazars are the brightest extragalactic sources above260 GeV. Many more of these blazars are not visible as point sources, being too faint and/or toofar from us. They contribute to the unresolved γ -ray radiation, again observed by Fermi-LAT.The sum of resolved and unresolved blazars almost saturates the observed diffuse emission, providing ∼
80% of the Extragalactic Gamma-ray Background (EGB) above 100 GeV [100], with a marginof uncertainty of some ten percents, that should be attributed to other sources.Since blazars dominate the γ emission, it is natural to consider them also as high energy neutrinoemitters [101, 102, 103, 104, 106, 105]. Particularly, FSRQs are expected to be very efficient in theneutrino production, due to the interaction that can occur in the broad line region. Moreover,as discussed in Section 7.3, up to now the only confirmed sources of one high energy neutrino isa blazar.However FSRQs (and high luminosity blazars in general) are not abundant in the universe.To have an idea, blazars having a gamma-ray luminosity larger than L γ = 10 erg/s have a localdensity of 10 sources per Gpc − . For these reasons if high luminosity blazars were the sources,at least two or more neutrinos from the one FSRQ would be expected. This is not observed inthe present neutrino data, meaning that blazars cannot contribute more than 20% to the observedhigh energy neutrino flux [106]. It is important to remark that this result does not say anythingon the possible contribution of blazars at higher energies. For example, blazars may dominatethe emission in the multi PeV-EeV energy range, but nowadays we do not have the technologyto observe such a flux, since the flux decreases with the increasing of the energy in any plausibleproduction mechanism.In Figure 12 the problem due to the absence of multiplets is clearly shown. A multiplet is definedas two or more events from the same source (within the angular resolution of track-like events,order of 1 ◦ ) during the time window in which data have been collected by IceCube. Up to now nomultiplets are present in the IceCube measurements. The purple region represents the local powerdensity required to match the flux measured by IceCube. The blue regions denote the parameterspace excluded from the absence of multiplets in the neutrino data. We see in the left panel thatsources that are brilliant but rare (like FSRQs) are excluded by the present measurements. The starburst galaxies are a subset of star forming galaxies (SFGs) that undergo an episode ofvigorous star formation in their central regions. The gas density is much higher than what isobserved in quiescent galaxies and for this reason the pp interaction is a plausible mechanism toproduce high energy neutrinos. Particularly the star formation rate can be 10–100 times higherthat the one of Milky Way. Diffusion in starburst galaxies might also become weaker due to strongmagnetic turbulence, while advective processes might be enhanced. Since the losses by inelasticcollisions and advection are nearly independent of energy, the hadronic emission of starburst isexpected to follow more closely the injected cosmic ray nucleon spectrum, E − α , with α (cid:39) . γ -ray spectrum in the GeV to TeV energy range, with a spectralindex between 2.1 and 2.3. Especially the γ -ray spectrum of NGC 253 has been well measured byboth Fermi-LAT and H.E.S.S. experiments. Due to the harder emission spectrum and a higher pionproduction efficiency, the starburst subset is predicted to dominate the total diffuse γ -ray emission27igure 12: Figure from Reference [107]. The purple bands show the power required to interpret the fluxof astrophysical neutrinos detected by IceCube (steady sources on the left, transient sources on the right).The blue regions show the parameter space excluded by the absence of multiplets in the neutrino data (i.e.,two or more events from the same source). Sources that are abundant and faint (top left of the panels) arefavorite by the data. of SFGs beyond a few GeV, while above 10 GeV the contribution of blazars becomes dominant.Provided that the cosmic ray accelerators in starburst galaxies are capable of reaching energies of ∼
10 PeV per nucleon, the hadronic emission can also contribute significantly to the diffuse neutrinoemission at PeV energies. However a problem related to the Multimessenger connections betweenneutrinos and γ -rays comes out in this scenario.Indeed, in proton-proton ( pp ) interaction an about equal amount of π + , π and π − is produced.Taking into account also the sub-dominant contribution of kaons, the emitted all flavor neutrinoflux is almost equal to the emitted γ -ray flux. After the propagation the two fluxes become verydifferent, because neutrinos lose energy only adiabatically while γ -rays at TeV scale interact withthe Extragalactic Background Light (EBL) and the energy is redistributed in the 1–100 GeV energyrange approximately with a E − spectrum. However, it is possible to connect the measured neutrinoflux with the associated expected γ -ray, taking into account the effect of the propagation. Thishas been done in two works, finding different results. If one relies on the IceCube HESE sample(Section 7.1), the measured neutrino spectrum is very soft and the associated gamma-ray fluxwould be too high [111], overshooting the possible contribution to the extragalactic backgroundexpected from Starburst Galaxies ( ∼
20% above 50 GeV). Following this result, the contributionof starburst galaxies would be at level of 10% (see left panel of Figure 13). However if one relieson the through-going muon flux, starburst galaxies are still perfectly compatible with astrophysicalneutrinos [112] (see right panel of Figure 13). Moreover the absence of multiplets in neutrinodata suggests that high energy neutrinos are produced by abundant and faint sources; followingthis argument, starburst galaxies would be an ideal candidate. Future detections are required toimprove the knowledge of the origin of astrophysical neutrinos.28igure 13:
Multimessenger comparison between the flux of astrophysical neutrinos and the associatedflux of γ -rays. In the left panel, High Energy Starting Events for the neutrino flux are used (figure fromReference [111]). In the right panel through-going muons are used (figure from Reference [112]). The present status of neutrino astrophysics is extremely exciting, with very intriguing perspectives.The first general remark is that the total number of cosmic neutrinos is small. Due to the not nullbackground from atmospheric neutrinos, usually each neutrino candidate is tagged with an eventsignalness . This is a parameter (used firstly by the IceCube collaboration to classify their neutrinocandidates) defined as the ratio of the astrophysical expectation over the sum of the atmosphericand astrophysical expectations for a given energy proxy and a specific neutrino flux. Events withhigh signalness ( > >
60 TeV. The features of the energy flux for the two samples are in good agreement athigh energy. The plausible interpretation of the flux supports strongly the view that extragalactichigh-energy cosmic neutrinos have been observed. This emission is diffuse emission: probably, thisdiffuse emission is, at least in part, due simply to still unresolved emission.Although smaller than IceCube, the ANTARES detector studied the diffuse emission from theSouthern sky using both track- and shower-like events. They found, using data collected in nineyears, a mild excess of high-energy events over the expected background; the excess is compatiblewith the IceCube findings [113].The distribution that fits the data-set of passing-events collected, Equation (28), fits also the highenergy subset of the HESE, Equation (27); however the low energy part of the HESE does not agreewith Equation (28). In order to explain the discrepancy, the hypothesis of an additional componentpresent in the HESE, but not in the passing-event data-set, has been considered [114, 115, 116,117]. If (most of) the cosmic neutrinos have an extragalactic origin, an isotropic distribution isto be expected. This is in first approximation in agreement with the observations of IceCube. Acontribution due to a Milky Way emission cannot be excluded, and a value of the order of ∼ E ν >
60 TeV is not incompatible with observations [92].The identification of sources of the high energy neutrinos relies on the possible correlation ofobserved events with specific objects in the sky and/or by self-correlating the events themselves. A29art with the relevant exception of the coincidence between the direction of a very-high energy ν µ and the position of a blazar, as discussed in Section 7.3, searches of correlations among neutrinocandidates and classes of astrophysical objects contained in gamma-ray catalogs did not reveal asignificant amount of coincidences [106, 118, 119].From theoretical models, the timescale of the neutrino emission depends dramatically upon thetype of sources. The hypothesis that the gamma ray burst are associated to a prompt neutrinoemission (lasting a few hours or less) has been tested: the non-detection of coincident events be-tween neutrinos and GRBs with IceCube [120, 121] and ANTARES [122] data has led to importantconstraints on cosmic-ray acceleration in GRBs. Other episodic events of intense neutrino emissioncould at least in principle occur in AGN, and be associated, for example, also to accretion phenom-ena. On the contrary, it is unlikely that stationary populations of cosmic rays (as, say, the onesthat presumably exist in a starburst galaxy) may lead to this type of phenomenology.The current status of experimental results is not inconsistent with expectations, namely thatthere exist astronomical sites where cosmic rays distributed as E − CR collide with surrounding hadronsleading to intense neutrino fluxes, whose distribution reflects closely the cosmic ray spectra. How-ever, it is quite evident the interest in probing accurately the shape and the extent of the observedspectrum, checking it at very high energies, observing events at the Glashow resonance energy,tau neutrinos.A key role will be also the observation of cosmic events below few tens of TeV against thebackground of atmospheric events, using the improved angular resolution of incoming detectors. Inthe quest for the identification of (some of) the sources, the muon events (that induced by ν µ CCinteractions) have the best angular resolution and offer the best chances. The improved angularresolution is one one of the main motivation for large volume neutrino telescope in water, as foreseenby the KM3NeT project. Other reasons are the need to verify the current findings/discoveries andthe wish to explore new patches of the sky - including the central regions of the Milky Way. Lastbut not least, when reliable observational information will be available, it will be possibly to studyinteresting and possibly important sites for cosmic ray production and the environment where theyinteract. For this, the role of Multimessenger astronomy is of paramount importance.
Acknowledgments
This work was partially supported by the research grant number 2017W4HA7S “NAT-NET: Neu-trino and Astroparticle Theory Network” under the program PRIN 2017 funded by the ItalianMinistero dell’Istruzione, dell’Universit`a e della Ricerca (MIUR); it has received funding from theEuropean Research Council (ERC) under the European Union’s Horizon 2020 research and inno-vation programme (Grant No. 646623). Figures 6 and 13 are reproduced by permission of IOPPublishing: c (cid:13)
IOP Publishing Ltd and Sissa Medialab, all rights reserved.We are grateful to three anonymous reviewers for the excellent feedback we received. F.V. thanksF. Aharonian, A. Capone, S. Celli, M.L. Costantini, E. Esmaili, A. Gallo Rosso, P.L. Ghia, C. Mas-caretti, E. Roulet and V. Zema for precious discussions.30
How to Estimate Neutrinos from Gamma-Rays
After the discussion and the caveats, we give various practical recipes to connect high energy gammarays and neutrinos: In order, to be definite we focus on pp collisions and quantify the connectionbetween neutrinos and gamma rays in various levels of approximation.( i ) The simplest procedure is just to recall that the leading pion carries about 1/5 of the initialproton, and that the energy partition in its subsequent decay leads to a similar sharing of energy.Therefore, each neutrino carries about 1/20 of the initial proton energy whereas the gamma rays(from neutral pion) have twice this energy.( ii ) A very practical recipe, that can be adopted in the case when the cosmic ray spectra obeythe exponential cutoff distribution, is the following one [123] dN p dE = A p E − α exp (cid:18) − E(cid:15) p (cid:19) ⇒ dN γ/ν dE = A γ/ν E − Γ γ/ν exp (cid:32) − (cid:115) E(cid:15) γ/ν (cid:33) where A ν ≈ (0 . − . α ) A γ , Γ ν ≈ Γ γ ≈ α − , , (cid:15) ν ≈ . (cid:15) γ ≈ (cid:15) p / iii ) Finally an accurate approximation allows us to find the neutrino flux F ν from the gammaray flux F γ in the same assumptions, simply by performing one integral with a known kernelthat accounts for the kinematics of the decay as shown in Reference [124], based on the resultsof Reference [30], and as further improved in Reference [39]. For example, the sum of the muonneutrinos and antineutrinos is given byΦ ν µ ( E ν ) + Φ ¯ ν µ ( E ν ) = 0 .
66 Φ γ (cid:18) E ν − r π (cid:19) + 0 .
02 Φ γ (cid:18) E ν − r K (cid:19) + (cid:90) κ ( x ) Φ γ (cid:18) E ν x (cid:19) dx where the first term comes from pion decay ( r π = ( m µ /m π ) ), the second from kaon decay ( r K =( m µ /m K ) ), the third from the muons, and κ ( x ) = x (33 . − . x ) , if x < r K (1 − x ) ( − .
63 + 12 . x ) , if x > r π .
04 + 0 . x + 7 . x − . x otherwiseSee Reference [47] for the other flavors and for the most updated expression of the kernels. Notethat in the last method, the assumption of a power law distribution is not necessary. Of course,in all of these cases the gamma ray flux is supposed to be fully due to ‘hadronic’ origin and to beunperturbed from propagation, as discussed just above.31 eferences [1] Greisen, K. Cosmic ray showers. Ann. Rev. Nucl. Part Sci. , , 63.[2] Markov, M.A.; Zheleznykh, I.M. On high energy neutrino physics in cosmic rays. Nucl. Phys. , , 385.[3] Zheleznykh, I.M, Early years of high-energy neutrino physics in cosmic rays and neutrinoastronomy (1957–1962). Int. J. Mod. Phys. A , , 1.[4] Morrison, P. On Gamma-Ray Astronomy. Il Nuovo Cimento Vol VII , , 858.[5] Reines, F.; Kropp, W.R.; Sobel, H.W.; Gurr, H.S.; Lathrop, J.; Crouch, M.F.; Sellschop,J.P.F.; Meyer, B.S. Muons produced by atmospheric neutrinos: Experiment. Phys. Rev. D , , 80.[6] Chen, H.H.; Kropp, W.R.; Sobel, H.W.; Reines, F. Muons produced by atmospheric neutrinos:Analysis. Phys. Rev. D , , 99.[7] Krishnaswamy, M.R.; Menon, M.G.K.; Narasimham, V.S.; Hinotani, K.; Ito, N.; Miyake, S.;Osborne, J.L.; Parsons, A.J.; Wolfendale, A.W. The Kolar Gold Fields Neutrino Experiment.1. the Interactions of Cosmic Ray Neutrinos. Proc. R. Soc. Lond. A , , 489.[8] Aartsen, M.G.; et al. [IceCube Collaboration]. First observation of PeV-energy neutrinos withIceCube. Phys. Rev. Lett. , , 021103.[9] Suzuki, A.; Koshiba, M. History of neutrino telescope/astronomy. Exper. Astron. , ,209.[10] Spiering, C. Towards High-Energy Neutrino Astronomy. A Historical Review. Eur. Phys. J. H , , 515.[11] Proceedings of the International Conference on History of the Neutrino: 1930–2018. Availableonline: Http://inspirehep.net/record/1760351 (accessed on 8 February 2020).[12] Pontecorvo, B. Neutrino Experiments and the Problem of Conservation of Leptonic Charge.
Sov. Phys. JETP , , 984.[13] The Nobel Prize in Physics 2015. Available online: (accessed on 30 December 2019).[14] Spurio, M. Probes of Multimessenger Astrophysics - Charged cosmic rays, neutrinos, γ -raysand gravitational waves. Springer: Cham, Switzerland, 2018.[15] Capone, A.; Lipari, P.; Vissani, F. Neutrino Astronomy. In Multiple Messengers and Chal-lenges in Astroparticle Physics ; Aloisio, R., Coccia, E., Vissani, F., Eds.; Springer: Cham,Switzerland, 2018.[16] Halzen, F.; Hooper, D. High-energy neutrino astronomy: The Cosmic ray connection.
Rept.Prog. Phys. , Phys. Rev. D , Eur. Phys. J. C , Science , Mod. Phys. Lett. , A24,
Ann.Rev. Nucl. Part Sci. , Prog.Part. Nucl. Phys. , Eur. Phys. J. Plus , , 267.[24] Berezinsky, V.S.; Bulanov, S.V.; Ginzburg, V.L.; Dogiel, V.A.; Ptuskin, V.S. Astrophysics ofCosmic Rays. North-Holland: Amsterdam, Netherlands, 1990.[25] Gaisser, T.K.; Engel, R.; Resconi, E. Cosmic Rays and Particle Physics ; Cambridge UniversityPress: Cambridge, UK, 2016.[26] Stecker, F.W. Cosmic Physics: The High Energy Frontier.
J. Phys. G , , R47.[27] Matthiae, G. The cosmic ray energy spectrum as measured using the Pierre Auger Observatory. New J. Phys. , , 075009.[28] Berezinsky, V.S.; Volynsky, V.V. Generation Function Of High-energy Cosmic Neutrinos.I. PP-Neutrino. Available online: Http://adsabs.harvard.edu/full/1979ICRC...10..326B (accessed on 6 February 2020).[29] Kelner, S.K.; Aharonian, F.A.;. Bugayov, V.V. Energy spectra of gamma-rays, electrons andneutrinos produced at proton-proton interactions in the very high energy regime.
Phys. Rev.D , , 034018.[30] Volkova, L.V. Energy Spectra and Angular Distributions of Atmospheric Neutrinos. Sov. J.Nucl. Phys. , , 784.[31] Yen, E. New scaling variable and early scaling in single-particle inclusive distributions forhadron-hadron collisions. Phys. Rev. D , , 836.[32] Allard, D. Extragalactic propagation of ultrahigh energy cosmic-rays. Astropart. Phys. , , 39–40.[33] Celli, S.; Palladino, A.;. Vissani, F. Neutrinos and γ -rays from the Galactic Center Regionafter H.E.S.S. multi-TeV measurements. Eur. Phys. J. C , , 66.[34] Simple Quantum Integro Differential Solver (SQiIDS). Available online: (accessed on 30 December 2019).[35] Aharonian, F.; O’Drury, L.; Volk, H.J. GeV/TeV gamma-ray emission from dense molecularclouds overtaken by supernova shells. Astron. Astroph. , , 645.3336] Drury, L.O.; Aharonian, F.A.; Volk, H.J. The Gamma-ray visibility of supernova remnants: ATest of cosmic ray origin. Astron. Astrophys. , , 959.[37] Naito, T.; Takahara, F. High-energy gamma-ray emission from supernova remnants. J. Phys.G , , 477.[38] Alvarez-Muniz, J.; Halzen, F. Possible high-energy neutrinos from the cosmic accelerator RXJ1713.7-3946. Astrophys. J. , , L33.[39] Villante, F.L.; Vissani, F. How precisely neutrino emission from supernova remnants can beconstrained by gamma ray observations? Phys. Rev. D , , 103007.[40] Vissani, F.; Aharonian, F.; Sahakyan, N. On the Detectability of High-Energy Galactic Neu-trino Sources. Astropart. Phys. , , 778.[41] Aiello, S.; et al. [The KM3NeT collaboration]. Sensitivity of the KM3NeT/ARCA neutrinotelescope to point-like neutrino sources. Astropart. Phys. , , 100–110.[42] Gribov, V.N.; Pontecorvo, B. Neutrino astronomy and lepton charge. Phys. Lett. B , ,493.[43] Berezinsky, V.S.; Gazizov, A.Z. Cosmic neutrino and the possibility of Searching for W bosonswith masses 30-100 GeV in underwater experiments. JETP Lett. , , 254.[44] Bilenky, S.M.; Pontecorvo, B. Lepton Mixing and Neutrino Oscillations. Phys. Rept. , ,225.[45] Esteban, I.; Gonzalez-Garcia, M.C.; Hernandez-Cabezudo, A.; Maltoni, M.; Schwetz, T. Globalanalysis of three-flavour neutrino oscillations: Synergies and tensions in the determination of θ , δ CP , and the mass ordering. J. High Energy Phys. , , 106.[46] Palladino, A.; Vissani, F. The natural parameterization of cosmic neutrino oscillations. Eur.Phys. J. C , , 433.[47] Mascaretti, C.; Vissani, F. On the relevance of prompt neutrinos for the interpretation of theIceCube signals. J. Cosmol. Astropart. Phys. , , 004.[48] Palladino, A.; Mascaretti, C.; Vissani, F. The importance of observing astrophysical tau neu-trinos. J. Cosmol. Astropart. Phys. , , 004.[49] Bugaev, E.; Montaruli, T.; Shlepin, Y.; Sokalski, I. Propagation of tau neutrinos and tauleptons through the Earth and their detection in underwater/ice neutrino telescopes. Astropart.Phys. , , 491–509.[50] Dziewonski, A.M.; Anderson. D.L. Preliminary reference Earth model. Phys. Earth Planet.Inter. , , 297–356.[51] Murase, K.; Bartos, I. High-Energy Multimessenger Transient Astrophysics. Ann. Rev. Nucl.Part. Sci. , , 477.[52] Halzen, F.; Kheirandish, A. Multimessenger Search for the Sources of Cosmic Rays UsingCosmic Neutrinos. Front. Astron. Space Sci. , , 32.3453] Achterberg, A.; et al. [IceCube Collaboration]. First Year Performance of The IceCube NeutrinoTelescope. Astropart. Phys. , , 155–173.[54] Aartsen, M.G.; et al. [IceCube Collaboration]. The Design and Performance of IceCube Deep-Core. Astropart. Phys. 2012 , J. Instrum. , P03012.[56] Ageron, M.; et al. [ANTARES Collaboration]. ANTARES: The first undersea neutrino tele-scope.
Nucl. Instrum. Meth. , A656 , 11.[57] Albert, A.; et al. [ANTARES Collaboration]. Long-term monitoring of the ANTARES opticalmodule efficiencies using 40K decays in sea water.
Eur. Phys. J. C , , 669.[58] Adrin-Martnez, S.; Ageron, M.; Aharonian, F.; Aiello, S.; Ameli, F.; Anassontzis, E.; Andre,M.; Androulakis, G.; Anghinolfi, M.; et al. Letter of intent for KM3NeT 2.0. J. Phys. G Nucl.Part. Phys. , , 084001.[59] Adrin-Martnez, S.; et al. [The KM3NeT collaboration]. Intrinsic limits on resolutions in muon-and electron-neutrino charged-current events in the KM3NeT/ORCA detector. J. High EnergyPhys. , , 008.[60] Aynutdinov, V.; Avrorin, V.A.; Aynutdinov, V.M.; Bannasch, R.; Belolaptikov, I.A.; Bogorod-sky, D.Yu.; Brudanin, V.B.; Budnev, N.M.; Danilchenko, I.A.; Domogatsky, G.V.; et al. Theprototyping/early construction phase of the BAIKAL-GVD project. Nucl. Instrum. MethodsPhys. Res. Sect. A , , 82–88.[61] Avrorin, A.D.; et al. [Baikal-GVD Collaboration]. Search for cascade events with Baikal-GVD.Available online: Https://arxiv.org/abs/1908.05430 (accessed on 6 February 2020).[62] Learned, J.G.; Pakvasa, S. Detecting Nutau Oscillations as PeV Energies.
Astropart. Phys. , , 267.[63] Aartsen, M.G.; et al. [IceCube Collaboration]. Search for high-energy neutrinos from gravita-tional wave event GW151226 and candidate LVT151012 with ANTARES and IceCube. Phys.Rev. D , , 022001.[64] Glashow, S.L. Resonant Scattering of Antineutrinos. Phys. Rev. , , 316.[65] Palladino, A.; Pagliaroli, G.; Villante, F.L.; Vissani, F. Double pulses and cascades above 2PeV in IceCube. Eur. Phys. J. C , , 52 .[66] Gandhi, R.; Quigg, C.; Reno, M.H.; Sarcevic, I. Ultrahigh-energy neutrino interactions. As-tropart. Phys. , , 81.[67] Abbasi, R. et al. [IceCube Collaboration]. Measurement of the atmospheric neutrino energyspectrum from 100 GeV to 400 TeV with IceCube. Phys. Rev. D , , 012001.[68] Adrian-Martinez, S.; et al. [ANTARES Collaboration]. Measurement of the atmospheric ν µ energy spectrum from 100 GeV to 200 TeV with the ANTARES telescope. Eur. Phys. J. C , , 2606. 3569] Aartsen, M.G.; et al. [IceCube Collaboration]. Measurement of the Atmospheric ν e Spectrumwith IceCube.
Phys. Rev. D , , 122004.[70] Aartsen, M.G.; et al. [IceCube Collaboration]. Characterization of the Atmospheric Muon Fluxin IceCube. Astropart. Phys. , , 1.[71] Aiello, S.; et al. [NEMO Collaboration]. Measurement of the atmospheric muon depth intensityrelation with the NEMO Phase-2 tower. Astropart. Phys. , , 1.[72] Aguilar, J.A.; et al. [ANTARES Collaboration]. Zenith distribution and flux of atmosphericmuons measured with the 5-line ANTARES detector. Astropart. Phys. , , 179.[73] Adrin-Martnez, S.; et al. [ANTARES Collaboration]. Time calibration with atmospheric muontracks in the ANTARES neutrino telescope. Astropart. Phys. , , 43.[74] Becherini, Y.; Margiotta, A.; Sioli, M.; Spurio, M. A Parameterisation of single and multiplemuons in the deep water or ice. Astropart. Phys. , , 1–13.[75] Sch¨onert, S.; Gaisser, T.K.; Resconi, E.; Schulz, O. Vetoing atmospheric neutrinos in a highenergy neutrino telescope. Phys. Rev. D , , 043009.[76] Arg¨uelles, C.A.; Palomares-Ruiz, S.; Schneider, A.; Wille, L.; Yuan. T. Unified atmosphericneutrino passing fractions for large-scale neutrino telescopes. J. Cosmol. Astropart. Phys. , , 047.[77] Gaisser, T.K.; Jero, K.; Karle, A.; van Santen, J. Generalized self-veto probability for atmo-spheric neutrinos. Phys. Rev. , D90 , 023009.[78] Halzen, F. IceCube: Opening a new window on the universe from the South Pole.
Int. J. Mod.Phys. D , , 1930007.[79] Ahlers, M.; Halzen, F. Opening a New Window onto the Universe with IceCube. Prog. PartNucl. Phys. , , 73.[80] Aartsen, M.G.; et al. [IceCube Collaboration]. Evidence for high-energy extraterrestrial neu-trinos at the IceCube detector. Science , , 1242856.[81] Aartsen, M.G. et al. [IceCube Collaboration]. Flavor Ratio of Astrophysical Neutrinos above35 TeV in IceCube. Phys. Rev. Lett. , , 171102.[82] Schneider, A. [The IceCube Collaboration]. Characterization of the Astrophysical Diffuse Neu-trino Flux with IceCube High-Energy Starting Events. Available online: Https://arxiv.org/abs/1907.11266 (accessed on 6 February 2020).[83] Aartsen, M.G.; et al. [IceCube Collaboration]. Evidence for Astrophysical Muon Neutrinosfrom the Northern Sky with IceCube.
Phys. Rev. Lett. , , 081102.[84] Aartsen, M.G.; et al. [IceCube Collaboration]. Observation and Characterization of a CosmicMuon Neutrino Flux from the Northern Hemisphere using six years of IceCube data. Astrophys.J. , , 3. 3685] Stettner, J. [The IceCube Collaboration]. Measurement of the Diffuse Astrophysical Muon-Neutrino Spectrum with Ten Years of IceCube Data. Available online: Https://arxiv.org/abs/1908.09551 (accessed on 6 February 2020).[86] Paiano, S.; Falomo, R.; Treves, A.; Scarpa, R. The redshift of the BL Lac object TXS 0506+056.
Astrop. J. , , L32.[87] Aartsen, M.G.; et al. [IceCube and Fermi-LAT and MAGIC and AGILE and ASAS-SN andHAWC and H.E.S.S. and INTEGRAL and Kanata and Kiso and Kapteyn and Liverpool Tele-scope and Subaru and Swift NuSTAR and VERITAS and VLA/17B-403 Collaborations]. Mul-timessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A. Science , , 6398.[88] Aartsen, M.G.; et al. [IceCube Collaboration]. Neutrino emission from the direction of theblazar TXS 0506+056 prior to the IceCube-170922A alert. Science , , 147.[89] Albert, A.; et al. [ANTARES Collaboration]. The Search for Neutrinos from TXS 0506+056with the ANTARES Telescope. Astrophys. J. , , L30. doi:10.3847/2041-8213/aad8c0.[90] Albert, A.; et al. [ANTARES Collaboration]. First all-flavor neutrino pointlike source searchwith the ANTARES neutrino telescope. Phys. Rev. D , , 082001.[91] Albert, A.; et al. [ANTARES and IceCube Collaborations]. ANTARES and IceCube Com-bined Search for Neutrino Point-like and Extended Sources in the Southern Sky. arXiv ,arXiv:2001.04412.[92] Albert, A.; et al. [ANTARES and IceCube Collaborations].Joint Constraints on Galactic Dif-fuse Neutrino Emission from the ANTARES and IceCube Neutrino Telescopes. Astrophys. J.Lett. , , L20.[93] Murase, K.; Waxman, E. Constraining High-Energy Cosmic Neutrino Sources: Implicationsand Prospects. Phys. Rev. D , , 103006.[94] GCN: The Gamma-Ray Coordinates Network. Available online: Https://gcn.gsfc.nasa.gov/ (accessed on 30 December 2019).[95] Urry, C.M.; Padovani, P. Unified schemes for radio-loud active galactic nuclei.
Publ. Astron.Soc. Pac. , , 803.[96] Stecker, F.W.; Done, C.; Salamon, M.H.; Sommers, P. High-energy neutrinos from activegalactic nuclei. Phys. Rev. Lett. , , 2697.[97] Stecker, F.W. PeV neutrinos observed by IceCube from cores of active galactic nuclei. Phys.Rev. D , , 047301.[98] Kalashev, O.; Semikoz, D.; Tkachev, I. Neutrinos in IceCube from active galactic nuclei. J.Exp. Theor. Phys. , , 541.[99] Boettcher, M.; Reimer, A.; Sweeney, K.; Prakash, A. Leptonic and Hadronic Modeling ofFermi-Detected Blazars. Astrophys. J. , , 54.37100] Ackermann, M.; et al. [Fermi-LAT Collaboration]. Resolving the Extragalactic γ -Ray Back-ground above 50 GeV with the Fermi Large Area Telescope. Phys. Rev. Lett. , ,151105.[101] Keivani, A.; Murase, K.; Petropoulou, M.; Fox, D.B.; Cenko, S.B.; Chaty, S.; Coleiro, A.;DeLaunay, J.J.; Dimitrakoudis, S.; Evans, P.A.; et al. A Multimessenger Picture of the FlaringBlazar TXS 0506+056: Implications for High-Energy Neutrino Emission and Cosmic RayAcceleration. Astrophys. J. , , 84.[102] Murase, K.; Oikonomou, F.; Petropoulou, M. Blazar Flares as an Origin of High-EnergyCosmic Neutrinos? Astrophys. J. , , 124.[103] Palladino, A.; Rodrigues, X.; Gao, S.; Winter, W. Interpretation of the diffuse astrophysicalneutrino flux in terms of the blazar sequenc. Astrophys. J. , , 41.[104] Kadler, M.; Krau, F.; Mannheim, K.; Ojha, R.; Mller, C.; Schulz, R.; Anton, G.; Baumgart-ner, W.; Beuchert, T.; Buson, S.; et al. Coincidence of a high-fluence blazar outburst with aPeV-energy neutrino event. Nat. Phys. , , 807.[105] Murase, K.; Inoue, Y.; Dermer, C.D. Diffuse Neutrino Intensity from the Inner Jets of ActiveGalactic Nuclei: Impacts of External Photon Fields and the Blazar Sequence. Phys. Rev. D , , 023007.[106] Padovani, P.; Resconi, E.; Giommi, P.; Arsioli, B.; Chang, Y.L. Extreme blazars as counter-parts of IceCube astrophysical neutrinos. Mon. Not. R. Astron. Soc. , , 3582.[107] Ackermann, M.; Ahlers, M.; Anchordoqui, L.; Bustamante, M.; Connolly, A.; Deaconu, C.;Grant, D.; Gorham, P.; Halzen, F.; Karle, A.; et al. Astrophysics Uniquely Enabled by Obser-vations of High-Energy Cosmic Neutrinos. Bull. Am. Astron. Soc. , , 185.[108] Tamborra, I.; Ando, S.; Murase, K. Star-forming galaxies as the origin of diffuse high-energybackgrounds: Gamma-ray and neutrino connections, and implications for starburst history. J.Cosmol. Astropart. Phys. , , 043.[109] Chang, X.C.; Wang, X.Y. The diffuse gamma-ray flux associated with sub-PeV/PeV neutrinosfrom starburst galaxies. Astrophys. J. , , 131.[110] Loeb, A.; Waxman, E. The Cumulative background of high energy neutrinos from starburstgalaxies. J. Cosmol. Astropart. Phys. , , 003.[111] Bechtol, k.; Ahlers, M.; Di Mauro, M.; Ajello, M.; Vandenbroucke, J. Evidence against star-forming galaxies as the dominant source of IceCube neutrinos. Astrophys. J. , , 47.[112] Palladino, A.; Fedynitch, A.; Rasmussen, R.W.; Taylor, A.M. IceCube Neutrinos fromHadronically Powered Gamma-Ray Galaxies. J. Cosmol. Astropart. Phys. , , 004.[113] Albert, A.; et al. [ANTARES Collaborations]. All-flavor Search for a Diffuse Flux of CosmicNeutrinos with Nine Years of ANTARES Data. Astrophys. J. Lett. , , L7.[114] Spurio, M. Constraints to a Galactic Component of the Ice Cube cosmic neutrino flux fromANTARES. Phys. Rev. D , , 103004.38115] Chen, C.-Y.; Bhupal Dev, P.S.; Soni, A. Two-component flux explanation for the high energyneutrino events at IceCube. Phys. Rev. D , , 073001.[116] Palladino, A.; Vissani, F. Extragalactic plus Galactic model for IceCube neutrino events. Astrophys. J. , , 185.[117] Vincent, A.C.; Palomares-Ruiz, S.; Mena, O. Analysis of the 4-year IceCube high-energystarting events. Phys. Rev. , D94 , 023009.[118] Aartsen, M.G.; et al. [IceCube Collaboration]. The contribution of Fermi-2LAC blazars to thediffuse TeV-PeV neutrino flux.
Astrophys. J. , , 45.[119] Palladino, A.; Vissani, F. Can BL Lacertae emission explain the neutrinos above 0.2 PeV? Astron. Astrophys. , , A18.[120] Abbasi, R.; et al. [IceCube Collaboration] An absence of neutrinos associated with cosmic-rayacceleration in γ -ray bursts. Nature , , 351.[121] Aartsen, M.G.; et al. [IceCube Collaboration] Search for Prompt Neutrino Emission fromGamma-Ray Bursts with IceCube. Astrophys. J. , , L5.[122] Albert, A.; Andr, M.; Anghinolfi, M.; Anton, G.; Ardid, M.; Aubert, J.-J.; Avgitas, T.; Baret,B.; Barrios-Mart, J.; Basa, S.; Bertin, V.; et al. Search for high-energy neutrinos from brightGRBs with ANTARES. Mon. Not. R. Astron. Soc. , , 906.[123] Kappes, A.; Hinton, J.; Stegmann, C.; Aharonian, F.A. Potential Neutrino Signals fromGalactic Gamma-Ray Sources. Astrophys. J. , , 870.[124] Vissani, F. Neutrinos from galactic sources of cosmic rays with known γ -ray spectra. Astropart.Phys. , , 310. 39 ontents pp and pγ Mechanisms of Neutrino Production . . . . . . . . . . . . . . . . . . . . . . . 32.3 Connection of Neutrino and Gamma-Ray Astronomies . . . . . . . . . . . . . . . . . . . . . 59 Discussion and Prospects 29A How to Estimate Neutrinos from Gamma-Rays 31