KM3NET DETECTORS4是在地中海深处安装的三维光传感器阵列。传感器检测通过相对论带电颗粒在海水中诱导的Cherenkov辐射。它们位于光学模块中，该光学模块是44厘米至直径抗压玻璃球，每个球体都有31个3英寸PMT。每个光学模块都包含数据收购电子设备和校准仪器。位于地中海的西西里岛的3,450 m近海Portopalo di Capo Passero的深度为3,450 m的ARCA检测器的模块，将其链接在一起，沿着700 m长的垂直检测线固定在36 m的范围内，将其固定在36 m的间隔内，并通过Optical Modules和Top buoys和Top Puoys和Top Puoys和Top top buoyancy固定在海底上。电流电缆沿检测线运行，为光学模块提供动力并通过光纤传输数据。将检测线放在海底，平均水平间距为95 m。事件发生时，ARCA检测器由21个检测线组成。仪器体积，即包含所有光学模块的最小圆柱体，约为0.15 km3。在最终配置中，该数组将包括230个检测线。
数据收购系统基于“全数据对”概念：来自某个可调阈值的PMT的所有模拟信号均已数字化，并将所有数字数据发送到岸上，并将其实时处理。数据包含前缘的时间戳和阈值信号的脉冲长度，共同称为“命中”。阈值的时间与PMT上转换的光电子的数量成正比。尽管线性行为对于多达几十个光电子的脉冲（以上30个光电子）的脉冲相对较好，但观察到饱和效应，从而产生了随着电荷增加的时间的延迟阈值测量值9。
触发算法搜索与空间和时间相关的命中簇。在25 ns的时间窗口内的每个光学模块上都标识了局部命中的局部巧合。然后，假设命中是根据可能的轨道或淋浴起源传播的三种不同聚类算法。在250 m之内的五个模块上的至少五次命中之间的时空巧合，这是从点样源扩展的，这构成了标称淋浴扳机的簇，从而使25 ns的延迟延迟到水中的光传播。轨道触发器也适用了类似的条件，但是这次考虑到光源是以真空速度在光速中移动的轨道，并在半径120 m的圆柱体中搜索命中。还采用了低阈值淋浴扳机，需要在110 m内的三个模块上进行八次击球。当找到一个或多个集群时，将记录来自时间窗口的所有数据作为离线校准和处理的事件。触发标准旨在检测较低能源阈值的事件。在KM3-230213A的情况下，在时间窗口中发现了3,659个单独的（重叠）触发簇，并且PMTS参与形成至少一个触发簇中的一个。记录了命中但不参与任何触发群集的PMT主要是由非常遥远和/或与物理事件相关的光学背景引起的。因此，可以用作能量估计的可观察到。
数据质量标准用于拒绝分析样本中检测器不稳定性的时期。
高能中微子事件（100 GEV< Eν < 100 EeV) were simulated with gSeaGen v7.4.3 (refs. 48,49), using GENIE50 to simulate the neutrino interaction by means of the HEDIS package51,52. The deep-inelastic scattering model CSMS11 (ref. 53) was used. PROPOSAL54 and TAUSIC55 were used by gSeaGen to propagate muons and taus up to the detector.
The accurate simulation of the light produced by a muon of a given energy is crucial to the muon energy estimate. KM3NeT uses proprietary code, which simulates the continuous and stochastic energy losses owing to bremsstrahlung, pair production, photonuclear interactions, delta rays and ionization, as well as the multiple Coulomb scattering and deep-inelastic scattering. Differential cross-sections for the main processes are extracted from refs. 56,57. The light produced by the muon and the secondary particles is simulated by sampling photon tables that contain the probability density functions of the arrival time of Cherenkov light on a PMT as a function of the distance from the emission point and the PMT orientation with respect to the particle58. For secondary particles, equivalent tabulated values for electromagnetic shower light are used. The amount of photons generated depends on the type and energy of the particle and has been adjusted according to Geant4 simulations59.
The photon tables account for light absorption, scattering and chromatic dispersion. Absorption is modelled on the basis of in situ measurements14; the scattering model for seawater accounts for pure-water scattering, following the Einstein and Smoluchowski description60,61, and particle scattering, accounting for the wavelength dependence using the Kopelevich parameterization62 and considering the Petzold data63 for the angular dependence. The angular acceptance and average quantum efficiency of the PMTs are also accounted for in the tables, as derived from detailed simulations of the PMT and the structure of the optical module64, and from laboratory measurements65.
The simulation of the stochastic energy losses has been cross-checked by comparing the total simulated amount of energy lost by the muon over a given distance with the same quantity computed using the PROPOSAL software54. Agreement at better than the 10% level was found over the whole energy range of interest. Moreover, PROPOSAL has also been used to check that varying the theoretical models used to describe energy losses66,67,68,69 yields differences that are within the stochastic fluctuations of the energy-loss processes.
Because no external data are available in this energy range to validate the simulation procedure, the particle-propagation and light-simulation code has also been compared with state-of-the-art Geant4-based59 simulation and with a custom GPU-based photon-tracking code (https://github.com/PLEnuM-group/PhotonPropagation.jl) in which the same water model and detector response have been implemented in an independent way. The output of these simulations are in good agreement; when using the alternative simulations for the energy measurement, the result is within 10% of the nominal value.
After light simulation, the readout is simulated. The conversion from photoelectrons on the cathode of the PMT to a time-over-threshold measurement and the transit-time distributions of the PMTs reproduce laboratory measurements65. The gain, gain spread and relative PMT efficiencies come from in situ measurements70. Afterpulses in the PMTs are at present not simulated. Optical background rates and the status of each PMT in the detector are simulated using the rates measured in the detector, following the run-by-run approach pioneered by the ANTARES Collaboration71,72. Subsequently, the simulated data are subjected to the same trigger and reconstruction algorithms that are applied to the data. Comparisons between data and Monte Carlo simulations are provided in Extended Data Fig. 1 for a loose event selection in which the sample is dominated by atmospheric muons. Wrongly reconstructed atmospheric muons that appear as upgoing events in the zenith distribution are completely removed once the selection on the reconstruction log-likelihood is applied.
The directional reconstruction of the muon track is performed with the standard algorithm, which is based on the arrival time of the Cherenkov photons at the PMTs73. Under the hypothesis that a muon travelling in direction is at position at time t0, the arrival time of the Cherenkov light at position is
in which D is the distance of closest approach of the muon to and z is the distance the muon travels before emitting a photon under angle θC, ; vg is the group velocity of light at a reference wavelength of 460 nm.
The reconstruction algorithm maximizes the likelihood of the arrival time residuals
in which p denotes the probability density function of the arrival time residual ri, obtained from interpolated photon tables, at a distance di from the emission point. The angles ϕi and θi describe the orientation of the PMT with respect to the track direction. The photon tables are the same as those that have been described above for the simulation of light from the muon trajectory. They include the contribution of optical background.
The algorithm uses only the first hit on each PMT, as they carry most of the information on the muon direction. As a result of this choice, the reconstruction is robust against PMT afterpulses and other details of modelling of later hits. For the likelihood maximization, only the first hits in a cylinder of radius 175 m and axis defined by the prefit direction are used. This is the standard setting, which was chosen as it optimizes the speed of the algorithm. In the case of KM3-230213A, there are hits outside this cylinder, but it was tested that including them alters the reconstructed track by less than the statistical uncertainty on the direction.
To mitigate the effect of local minima on the likelihood function, the maximization is preceded by a prefit, scanning in 4π sr over assumed track directions. This procedure generates a set of starting points for the likelihood maximization. The track with the largest likelihood is retained.
For ascertaining the quality of the events, the log-likelihood ratio, is used, with the likelihood computed for the case of only optical background hits. This quantity effectively quantifies the number of hits whose arrival time matches the expectation from the track hypothesis. Typical well-reconstructed muons have a value 50, with a tail of larger values resulting from well-reconstructed events with many hits. KM3-230213A has a log-likelihood ratio of 1,415.2, which is the highest value observed in the 21-line ARCA data.
To illustrate the quality of the reconstruction, Extended Data Fig. 2 presents the photon arrival time residuals, which represent the difference between the measured time and the expected time from the reconstructed muon trajectory hypothesis, shown here for the first hits on the PMTs. Many hits are compatible with the muon hypothesis with nanosecond accuracy, even for PMTs located far from the track. Hits arriving after the main peak are because of photons that have scattered in the water and/or that were emitted under some angle other than θC from the muon track. These contributions are accounted for in the reconstruction and the large log-likelihood ratio value reflects the agreement of these residuals with the detailed expectation.
The directional uncertainty on the event is dominated by uncertainty on the absolute orientation of the detector on Earth.
Compasses and accelerometers in the optical modules allow for an estimation of their orientation. The detection lines move with the sea current, which can displace the top modules by . The continuous monitoring of the optical module positions is therefore mandatory. For this purpose, a system of autonomous acoustic emitters is used, located in and up to 1 km outside the detector on the seabed74. The acoustic signals are recorded by piezoelectric sensors in the optical modules. A χ2 fit of the arrival times of the sound is used to determine the orientation and shape of the detection line as parameterized by a mechanical model. In this way, the relative positions of the optical modules can be determined to within 0.15 m. Acoustic signals are processed at 10-min intervals; the results of the fit are interpolated to provide the relative positions of the optical modules over time75. At the time of the event, the string tilts changed steadily by about 2° over a time span of 2 h, corresponding to less than 0.1° in 10 min. The uncertainty on the position of the detector elements owing to the interpolation of the acoustic data is thus negligible.
The acoustic system measures distances between the optical modules and acoustic emitters but this does not constrain the absolute orientation of the telescope on Earth. During sea campaigns, the positions of the detection lines and acoustic emitters are measured. The emitter positions are used to determine the nominal absolute orientation. These data are at a present accurate to approximately 10 m. This is supported by comparisons with two bathymetry datasets (for the vertical positions) and internal cross-checks with the acoustic system (for the horizontal positions). The position uncertainty translates, after conservatively rounding the result, to an uncertainty of 1° on rotations of the detector around each of the three axes.
An independent cross-check of the pointing was performed by means of a measurement of the directional deficit of atmospheric muons owing to the absorption of cosmic rays in the Moon, similar to ref. 76. This anti-signal of the Moon was studied in 335 days of data when the detector consisted of 19 and 21 detection lines. The Moon shadow signal was found at a significance of 3.2σ. In evaluating the Moon shadow for different assumed rotations around the vertical axis, in the range ±3° in steps of 0.25°, the largest significance was found for the nominal orientation. The corresponding uncertainty is evaluated by means of simulations to 0.24°.
A comparison of detector-line depths determined with the acoustic system and the two bathymetry datasets yields further evidence that the system is aligned to within 1°.
Propagating the 1° uncertainty to the celestial coordinates of the event yields a circular 68% confidence region on the sky with a radius of 1.5°. This uncertainty is the dominant source of (systematic) uncertainty in the determination of the celestial coordinates of KM3-230213A.
Simulations of muons in the same location as KM3-230213A were performed at energies from 1 to 1,000 PeV to evaluate the statistical uncertainty on the direction estimation. At 100 PeV, 50% (90%) of the muons are reconstructed within 0.12° (0.28°) from the nominal direction. The azimuthal uncertainty increases with energy, so that, for an energy of 500 PeV, 50% (90%) of the muons were reconstructed within 0.17° (0.38°). These uncertainties are negligible with respect to the 1.5° 68% confidence region and are mentioned here only to indicate the future potential of a fully aligned detector.
We foresee upgrading the detector in the next sea campaign by using new acoustic emitters whose absolute position will be measured with <1-m accuracy in each direction. This, as well as the extra collected data for the Moon shadow analysis, will allow for a recalibration of the data and a more precise determination of the celestial origin of KM3-230213A.
The energy of a muon above a few TeV can be estimated by measuring its energy loss. Radiative energy losses produce showers of charged particles along the muon trajectory that induce excess Cherenkov photons along the track. The photons arrive on the PMTs very close in time, producing a large number of photoelectrons that translate into hits with a large time-over-threshold. In the case of KM3-230213A, the large number of photons induced by the muon saturates most of the PMTs within about 100 m from the track, and hits are recorded even up to a distance of 300 m. This saturation effect is visible in more than 25% of the PMTs that participated in the triggering of KM3-230213A and is reproduced in simulations. Several subsequent hits are observed on the PMTs and at least some of them could be attributed to afterpulses, which are not modelled in the Monte Carlo simulations. The number of PMTs that participate in the triggering of the event, , is used as an observable in the energy estimation to overcome this possible issue. This observable does not exploit the full information from the event, as it does not account for the time-over-threshold information, but is robust against the limitations of the simulations because PMTs are only counted once if several hits are recorded.
Simulations of muons of various energies traversing the detector in the same direction and location as the reconstructed event were used to estimate the energy of KM3-230213A. The optical properties of water (scattering and absorption lengths) and the detection efficiency of the optical modules were varied in the simulation to account for systematic uncertainties, within the known limits for these parameters. The estimate of the muon energy Eμ is derived from the likelihood , in which are nuisance parameters that affect the distribution. The likelihood is estimated from the aforementioned Monte Carlo simulations at discrete combinations of Eμ and the three nuisance parameters. A Gaussian term is added to the likelihood to constrain each of the nuisance parameters to within 10% (1σ) of the nominal value. The energy estimate is the value that maximizes the constrained likelihood. The maximum-likelihood values for given are shown in Extended Data Fig. 3 left, with the 68% confidence level interval with and without systematic uncertainties, computed from Wilks’ theorem13. The log-likelihood profile for is shown in the right panel of Extended Data Fig. 3, with the 1σ, 2σ and 3σ confidence levels, with and without systematics.
Scattering of light does not influence the energy estimate by more than several percent. Similarly, it was found that the optical module efficiency has a <10% level effect on this estimation. The most relevant effect comes from light absorption: a +10% (−10%) modification of the absorption length yields a −0.21 (+0.25) shift in the logarithm of the estimated energy. Finally, it was checked that modifying the muon direction and location in the simulations, within the estimated systematic uncertainties from the detector calibration, does not affect the energy measurement.
The incoming neutrino energy is estimated using Monte Carlo simulations in which neutrino interactions are simulated over a large volume surrounding the detector. Because the neutrino interaction point is unknown, a flat prior is assumed on the muon propagation length in case the interaction occurred in the sensitive volume of the detector, up to 350 m away from the instrumented volume. If instead the interaction occurred outside the sensitive volume, the muon propagation distance distribution is taken from the large-scale Monte Carlo productions obtained with the standard KM3NeT simulation chain. Neutrino events are weighted according to a power-law spectrum with a spectral index equal to −2 to finally estimate the neutrino energy distribution that would produce muons at the detector distributed according to the energy estimate and its uncertainty.
Atmospheric muons from cosmic-ray extensive air showers constitute most of the events reconstructed in neutrino telescopes. The probability that KM3-230213A is an atmospheric muon is constrained from its reconstructed direction and energy. The muon flux drops rapidly with energy; given that the primary flux of ultra-high-energy cosmic rays extends up to at most several hundred EeV (refs. 77,78), muons at sea level cannot exceed an energy of few tens of EeV, as muons carry on average around 10% of the primary energy. However, the flux of atmospheric muons at high energies is affected by several uncertainties, such as those on the flux and spectrum of primary cosmic rays, on the composition of this flux, on the hadronic interactions of cosmic rays and of their interaction products. For this reason, a conservative estimate of the surviving muon background has been obtained using a toy model in which several muons have been injected on the surface of the sea according to a power-law spectrum with spectral index −2.7 and normalization at 100 PeV equal to 10−17 GeV cm−2 s−1 sr−1. These assumptions yield an overestimation of the muon flux by at least one order of magnitude over the whole energy range of interest, so that a conservative estimate of the rate of muons reaching the detector can be obtained.
Muons in the EeV range and beyond have a maximal range of about 60 km in water. Requiring that they must reach the detector still with at least an energy of 10 PeV reduces their effective range to about 30 km. Given the curvature of the Earth and the measured zenith angle, a muon should have entered the water at a distance of approximately 140 km from the detector. The direction of the event points towards the Malta Escarpment, a cliff rising above the abyssal plain: an atmospheric muon travelling in this direction should cross it to reach the detector. In Extended Data Fig. 4, bathymetric data have been used to show the path travelled by a particle along the reconstructed direction. Assuming an average density of 2.6 g cm−3 for rock in the seabed, the total amount of matter to be traversed is then on the order of 300 km water-equivalent for the reconstructed direction and becomes smaller than 60 km only if the absolute orientation of the detector is wrong by more than 2° in zenith.
Even assuming a flux that overshoots by one order of magnitude the total flux of atmospheric muons, and including the uncertainties on the zenith angle reconstruction for KM3-230213A, the upper limit on the muon rate is 10−10 events per year when assuming a direction within 2σ of the best-fit value. For a mis-reconstruction at a 5σ level error, the upper limit is still 10−4 events per year for the single-muon hypothesis and 10−3 events per year for muon bundles of low multiplicity in which only a few parallel muons from the same cosmic-ray air shower could reach the detector. This estimation is confirmed when extrapolating the expected rate of events from Monte Carlo simulations16 accounting for muon absorption in water following ref. 79.
Bundles of downgoing (zenith angles smaller than 60°) atmospheric muons, or muons from simultaneous but unrelated cosmic-ray air showers, can produce a large amount of light in the detector. Such events could be mis-reconstructed as a horizontal track. Such coincidences would, however, not have good hit-residuals distributions on all PMTs over many detection lines, in contrast to what is observed for KM3-230213A. This is further corroborated by the detection of several showers along the muon path and their collinearity (as shown in the Supplementary Material): given the good time resolution of the detector elements, a nanosecond-level temporal coincidence between the arrival time of muons at the detector and the emission of showers along their track would be needed to create such a light pattern in the detector, which is extremely unlikely.
Considering the reconstructed arrival direction, neutrinos from cosmic-ray interactions in the atmosphere are not substantially absorbed at least up to some tens of EeV. However, the flux of these atmospheric neutrinos falls steeply with energy. The conventional component, arising from pion and kaon decays in the cosmic-ray extensive air shower, fades away at an energy of about 100 TeV–1 PeV. In that energy range, a prompt component is expected to arise from the decay of short-lived charmed hadrons and become the dominant contribution to the atmospheric flux. Reference neutrino conventional and prompt fluxes were computed using the MCEq software80 and the Sibyll 2.3c hadronic interaction model81, for the location of the ARCA detector: the expected event rates above 100 PeV in the detector are on the order of (1–5) × 10−5 events per year, depending on the chosen model of the primary cosmic-ray flux82. Estimations of prompt fluxes are affected by large uncertainties83; even considering the most optimistic estimations, the event rate from prompt atmospheric neutrinos is less 5 × 10−3 events per year. An alternative possibility could be that the detected muon does not come from the interaction of a νμ from the prompt component but rather arises from the decay of a tau lepton from the prompt atmospheric ντ flux. The branching ratio of charmed hadrons to ντ is about a tenth of that to muon neutrinos, hence the expected flux in the atmosphere is one order of magnitude lower. However, above EeV energies, the tau decay length (>50 km）增加了检测这些中微子相互作用的有效体积。尽管如此，迅速通量仍然太低而无法解释观察到的事件，估计的事件速度速度迅速tau中微子≤10-5事件，对于用sibyll 2.3C 2.3c Hadroons相互作用模型估计的通量。
已经分析了ARCA和ORCA检测器的不同配置的数据，以及Antares和Icecube实验的公共数据，以评估接近KM3-230213A的中微子的可能定向过量。在扩展数据表1中给出了有关分析数据集和各自的分析方法的详细信息。根据可用框架，使用了ON/OFF方法或最大样式方法（binned或noted）。在后一种情况下，通过使用HealPix Tool84，将检查的区域分为覆盖相等区域（约0.1°×0.1°）的像素，其值的值为512，并且在每个像素中的可能性最大。结果总结在扩展数据表2中。
已经将四种选择方法应用于天文目录，以构建同行Blazar候选样本。从KM3-230213A（99％的事件误差区域）进行搜索。
方法1。使用档案波长数据来查明大型的同行：第一个ositiata catalogue22的X射线源与无线电NVSS Catalogue24交叉匹配，选择了18个源具有大于10 mjy的无线电源。Wise23收集的红外数据用于进一步完善可能的对应物的列表。选择了“ Wise Blazar Strip” 85的Blazars，将候选人Blazars清单缩小到七个物体。
方法2。遵循参考文献中建议的方法。86使用了很长的基线干涉法（VLBI）的测量值（使用无线电基本目录（RFC 2024B（https://astrogeo.org/rfc/））的测量值。选择了8 GHz处的100 mJY的当前完整性截止，从而导致五个中位VLBI通量密度的物体范围从0.1到大于2 JY，如扩展数据表3所示。
方法3。ROMA-BZCAT25已用于搜索活跃的银河核相关性。该Blazar目录包含3,561个来源，汇总了多频观测的结果。在此目录中发现了三个大麻。
方法4。4FGL-DR4 CATALOGUE17是Fermi-Lat仪器在14年的调查数据中观察到的伽马射线来源的最新汇编，在50 MEV – 1 TEV ENSIL范围内：选择了四个来源。
所选源的主要属性和相应的选择方法在扩展数据表3中描述。
KM3NET/ARCA All-Sky暴露定义为：
其中TKM3NET = 335天（覆盖ARCA的19和21检测线构型），并且是在扩展数据中显示的天空平均有效区域，在图5中显示，中微子和抗肿瘤之间的平均。已经估计了文本中描述的轨道选择的该有效区域（轨道长度超过250 m，轨道重建对数可能比500大于500）。然后，每流风量全套通量φ的预期事件数量很简单：
其中集成边界固定在与KM3-230213A相关的中微子中微子能量范围内固定。
已经使用已发表的材料估算了中微子和抗肿瘤之间的全天空暴露和平均。皮埃尔螺旋钻天文台的有效区域是从参考文献中的数据释放中获取的。87，对于三个分析样本（地球刺激性，低序列，向下，高zenthith向下进行），生计为18年。ICECUBE/EHE全峰有效区域是从9年的分析样本中获取的。
假设单flavour单力量差异中微子通量φ（e）= ϕ（e（e（gev））-2，我们可以使用最大的likikeLikeLikeLiohood估算量估计auger和iCecube/ehe样品中的km3net事件，而在km3net中发生了一个最可能的事件，我们可能会估计最可能的通量归一化事件。
对于这样的通量，在Icecube和螺旋钻中，预期将有0.59和0.40事件，这与它们的无效观测值兼容。KM3NET中相应的预期事件数量约为0.013事件，因此暗示了2.2σ向上波动。这种构型的关节泊松概率（km3net中的一个事件，iCecube和螺旋钻中的一个事件）约为0.5％（2.6σ）。
KM3NET协作的科学目标是对高能宇宙中微子的宇宙中的搜索和观察，以及在地球大气中产生的中微子的特征的测量。为此，合作是在地中海底部建立一个中微子探测器网络。在同一地点，该网络还为地球和海科学研究工具的连接提供了节点。用最多几立方公里的仪器量建造探测器将需要几年的时间。记录数据的科学分析是在协作的监督下进行的；几年后，如KM3NET数据传播计划中所述，将向其他数据提供数据。
KM3NET合作的科学家和工程师之所以融合，是因为它们具有科学兴趣，并且来自不同的背景，文化和国家。这种多样性被认为是协作的优势，也是高质量研究的基础。为了培养多样性，合作制定了基于一组共享价值观并描述良好行为规则的行为守则和道德行为守则。
合作的正式规则是在理解的备忘录（MOU）中描述的，该备忘录由雇用参加KM3NET合作的个人的研究所签署。
