# Sensitivity for point sources with KM3NeT/ARCA and ANTARES neutrino telescopes

Barbara Caiffi, Vladimir Kulikovskiy, Vittorio Parisi, Matteo Sanguineti, Sandra Zavatarelli, Sergio Alves Garre, Julien Aublin, Damien Dornic, Thijs van Eeden, Aart Heijboer, et al.

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Barbara Caiffi, Vladimir Kulikovskiy, Vittorio Parisi, Matteo Sanguineti, Sandra Zavatarelli, et al. Sensitivity for point sources with KM3NeT/ARCA and ANTARES neutrino telescopes. 13th Cosmic-Ray International Studies and Multi-messenger Astroparticle Conference, Jun 2024, Trapani, Italy. pp.012023, 10.1088/1742-6596/3053/1/012023. [hal-05237037](https://hal.science/hal-05237037v1)

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# Sensitivity for point sources with KM3NeT/ARCA and ANTARES neutrino telescopes

Barbara Caiffi<fnref n="1" />, Vladimir Kulikovskiy<fnref n="1" />, Vittorio Parisi<fnref n="2" />,<fnref n="1" />, Matteo Sanguineti*<fnref n="2" />,<fnref n="1" />, Sandra Zavatarelli<fnref n="1" />, Sergio Alves Garre<fnref n="3" />, Julien Aublin<fnref n="4" />, Damien Dornic<fnref n="5" />, Thijs van Eeden<fnref n="6" />, Aart Heijboer<fnref n="6" />, Giulia Illuminati<fnref n="7" /> and Rasa Muller<fnref n="7" />

E-mail: matteo.sanguineti@unige.it

on behalf of the KM3NeT and ANTARES collaborations

**Abstract.** In recent years, the adoption of a multi-messenger approach in astrophysics has significantly advanced our understanding of the high-energy Universe, allowing researchers to study cosmic phenomena from multiple observational perspectives. Neutrino telescopes, in particular, have become indispensable tools in this framework, enabling the detection of high-energy neutrinos and shedding light on the hadronic components of astrophysical events such as gamma-ray bursts and active galactic nuclei. By analyzing these neutrinos, scientists are able to test and refine existing models of gamma-ray sources, further expanding our knowledge of the most extreme and energetic processes in the cosmos. In this contribution, we present the combined analyses of the data collected with two neutrino telescopes located in the depths of the Mediterranean Sea: the ANTARES detector, operational for over 15 years off the coast of Toulon (France), and KM3NeT/ARCA, one of the two detectors constituting the next-generation neutrino telescope KM3NeT. ARCA is optimized for astrophysical neutrinos exceeding 1 TeV in energy and is presently collecting data while being under construction near Portopalo di Capo Passero (Italy). The goal is to derive the sensitivity of the detectors for point-like sources as a function of the declination.

<figure><img src="image_2.png" /></figure>

<footnote n="1">¹INFN, Sezione di Genova, Via Dodecaneso 33, Genova, 16146 Italy</footnote>

<footnote n="2">²Università di Genova, Via Dodecaneso 33, Genova, 16146 Italy</footnote>

<footnote n="3">³IFIC - Instituto de Física Corpuscular (CSIC - Universitat de València), c/Catedrático José Beltrán, 2, 46980 Paterna, Valencia, Spain</footnote>

<footnote n="4">⁴Université Paris Cité, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France</footnote>

<footnote n="5">⁵Aix Marseille Univ, CNRS/IN2P3, CPPM, 163, avenue de Luminy, Marseille, France</footnote>

<footnote n="6">⁶Nikhef, National Institute for Subatomic Physics, PO Box 41882, Amsterdam, 1009 DB Netherlands</footnote>

<footnote n="7">⁷INFN, Sezione di Bologna, v.le C. Berti-Pichat, 6/2, Bologna, 40127 Italy</footnote>
# 1 Introduction

In 2013, the IceCube Neutrino Observatory [1] made a landmark discovery by identifying a flux of high-energy astrophysical neutrinos. This was followed by the detection of a cosmic neutrino from the blazar TXS 0506+056 in 2018 [2] and from Messier 77 in 2022 [3]. Despite these advancements, the origin of these neutrinos remains mysterious for most sources. The KM3NeT/ARCA detector [4], currently under construction with data collection already underway, is expected to significantly advance in this investigations. KM3NeT will study and investigate neutrino sources already measured by IceCube, but thanks to its complementary visibility, it will also be able to explore new sources that are not in a favorable position for IceCube. For this reason, this contribution examines the sensitivity of KM3NeT as a function of declination.

Situated in the Mediterranean Sea off the coast of Sicily at a depth of 3500 meters, ARCA will consist of two building blocks. Each block will feature 115 strings, with each string containing 18 digital optical modules. Each module will house 31 three-inch photomultiplier tubes (PMTs). This setup is primarily designed for neutrino astrophysics, offering exceptional sub-0.2° pointing accuracy for muon neutrinos with energies above 10 TeV. ARCA sensitivity extends across a broad energy range, from hundreds of GeV to PeV, and it provides a unique observational perspective that complements the IceCube observatory, especially with its excellent view of the Galactic Center.

ANTARES [5], the predecessor of KM3NeT, operated from May 2008 until February 2022 in the Mediterranean Sea near Toulon, France. It consisted of 12 detection strings, each with 25 floors, and each floor housed three 10-inch PMTs enclosed in pressure-resistant glass spheres.

The detection mechanism for neutrinos in these observatories is the same. Neutrinos interacting within or near the detectors produce charged particles. These particles travel faster than light in the water medium emitting Cherenkov radiation. The PMTs detect this radiation, and their signals are digitized using a time-over-threshold (ToT) method, which records both the time at which the signal crosses a predefined threshold and the duration it remains above that threshold. This approach preserves essential timing and amplitude information while optimizing data transmission. The digitized signals are then sent to shore via optical fibers for further processing, that allows for the reconstruction of the particle direction and energy based on the timing and spatial information of the detected signals. This enables the determination of the sky region where the neutrino originated.

To identify cosmic neutrino signals amidst the background noise of atmospheric muons and neutrinos, statistical methods using Monte Carlo simulations are required. The analysis framework is based on a binned likelihood analysis which evaluates the sensitivity of the detectors as a function of source declination.

# 2 Data samples and Monte Carlo simulation

To seamlessly integrate the diverse detector data into the developed analysis framework, we introduce the dataset with specific considerations. Each dataset refers to a distinct detector period and dedicated event selection, ensuring no event overlaps. In KM3NeT, neutrino interactions can produce two main event topologies: tracks, which arise from charged-current interactions of muon neutrinos and result in elongated, well-defined trajectories, and showers, which originate from electron and tau neutrino charged-current interactions or neutral-current interactions, producing more spherical, point-like energy deposits. The datasets used in this analysis include:

1. ANTARES tracks: Data from ANTARES point source analysis, focusing on track events from 2007 to 2022 (4541 days) [6].

2. ANTARES showers: Data from ANTARES point source analysis, focusing on shower events from 2007 to 2022 (4541 days) [6].

3. ARCA6 tracks: Data from ARCA period with 6 working lines (92 days) [7];

4. ARCA8 tracks: Data from ARCA period with 8 working lines (210 days) [7].

5. ARCA19 tracks: Data from ARCA period with 19 working lines (53 days) [8].

6. ARCA21 tracks: Data from ARCA period with 21 working lines (70 days) [8].

Each dataset is paired with its instrument response functions (IRF) necessary for signal and background modeling. The Instrumented Response Functions (IRFs), described in Section 3, are derived from the official Monte Carlo simulation of the KM3NeT collaboration.
High-energy neutrino events (100GeV < $E_ν$ < 100EeV) are simulated using gSeaGen v7.4.3 [9], with GENIE [10] simulating neutrino interactions through the HEDIS package [11]. The CSMS11 [12] deep-inelastic scattering model is applied, and PROPOSAL [13] and TAUSIC [14] are used to propagate muons and taus up to the detector. The simulation of light is implemented employing proprietary code to model energy losses (bremsstrahlung, pair production, photonuclear interactions, etc.) and the scattering processes. The light produced by muons and secondary particles is simulated using photon tables, accounting for Cherenkov light arrival time, distance, and PMT orientation. Electromagnetic shower light of secondary particles is similarly modeled. Photon generation is adjusted using Geant4 simulations [15]. After light simulation, the readout is modeled, simulating the conversion from photoelectrons to time-over-threshold measurements and replicating PMT transit-time distributions based on laboratory measurements. Subsequently, the simulated data are subjected to the same trigger and reconstruction algorithms that are applied to the data.

### 3 Signal and background models and likelihood formalism

After applying some preliminary cuts to reject poorly reconstructed and downgoing events, several IRF histograms are produced for signal and background modelling.

The effective area, defined as the ratio between the rate of detected events and the total flux, is stored as a 3D histogram as a function of true neutrino energy $E_{true}$ and sky direction. The Point Spread Function (PSF), defined as the angle $α$ between the true neutrino direction and that of the best reconstructed track, is stored as a 3D histogram as a function of primary neutrino energy $E_{true}$ and sky direction. Finally, the energy resolution is evaluated via a 3D histogram where the energy of the reconstructed event $E_{rec}$, the true primary neutrino energy $E_{true}$ and sky direction are stored.

The source neutrino flux is convoluted with the previous IRFs to obtain 2D distributions for expected signal ($S$) and background ($B$). An arbitrary flux normalisation $Φ_0$ is scaled with a varying signal strength $μ$ to study the sensitivity of the detector.

For the estimation of the signal $S$, a 2D histogram is computed as a function of the angular distance $α$ and the logarithm of the reconstructed energy $E_{rec}$ at each declination $δ$. In particular, at a given declination $δ$ and bin $i$ in the 2D($α$, $log 10(E_{rec})$ histogram:

$$S_i(α, log 10(E_{rec})) = \sum_{E_{true}} rate(δ, E_{true}) \cdot f_α(E_{true}, α_{min}, α_{max}) \cdot f_E(E_{true}, δ, E_{rec min}, E_{rec max}) \quad (1)$$

where $rate(δ, E_{true})$ is derived from the effective area of the detector, $f_α(E_{true}, α_{min}, α_{max})$ is computed from the detector point spread function and is the fraction of events in the PSF histogram within $α_{min}$ and $α_{max}$ and $f_E(E_{true}, δ, E_{rec min}, E_{rec max})$ is the fraction of the events within $E_{rec min}$ and $E_{rec max}$ in the energy resolution histogram.

For the estimation of the background $B_i$ two different approaches have been implemented. In the case of low statistics samples (<1000 data events) the 2D histogram is computed as a function of the angular distance $α$ and the logarithm of the reconstructed energy $E_{rec}$. In particular, at a given declination $δ$ and bin $i$ in the 2D($α$, $log 10(E_{rec})$ histogram:

$$B_i(α, log 10(E_{rec})) = n \cdot f(δ) \cdot f(logE) \quad (2)$$

where $f(δ)$ and $f(logE)$ are two independent 1D distributions of energy and declination fitted from data. For larger statistics samples (>1000 data events) the Kernel Density Estimation (KDE) approach [16] is used:

$$B_i(α, log 10(E_{rec})) = n \cdot KDE(δ, logE) \quad (3)$$

using several $sin(δ)$ functions for the different energy bins. Depending on the statistics, the KDE functions may be derived from data (if more than 1000 events are included in the corresponding energy bin) or Monte Carlo simulation. The KDE function derived for several data sample are provided in Fig. 1 showing a good agreement between the data sample, the MC simulations and the computed KDE functions.

For each dataset, three histograms are produced: $N$ with the number of observed or simulated events, $S$ with expected number of signal events for the arbitrary flux normalisation $Φ_0$, and $B$ with the number of background events. The $S$ and $B$ histograms computed for ARCA19 and ARCA21 are shown in Fig. 2.
<figure><img src="image_3.png" /><figcaption>Figure 1: KDE functions for various samples and energy ranges. Top left: KM3NeT/ARCA 6 (first period); top right: KM3NeT/ARCA 6 (second period); bottom: KM3NeT/ARCA 8. In each plot, the MC atmospheric muon and MC atmospheric neutrino histograms are shown in green and orange respectively, with the data marked by black crosses. Different colours are used for the KDE functions: MC atmospheric muon (green), MC atmospheric neutrino (orange), total MC (blue), hybrid KDE combining data and MC that are used in this analysis (black).</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 2: Signal and background 2D histograms for KM3NeT/ARCA19 (top) and KM3NeT/ARCA21 (bottom) as a function of the logarithm of the reconstructed energy and the angular distance from the source.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 3: Sensitivity fluxes of ANTARES (red), ARCA (green) and of the combination (black) of the two neutrino telescopes (top). Ratio of combined sensitivity over ANTARES (solid line) and over ARCA (dotted line) (bottom).</figcaption></figure>

The log-likelihood function is derived from the Poisson probability of the bin contents of the S and B 2D($\alpha$, log 10($E_{rec}$)) histograms, as follows:

$$ \log L = \sum_{\text{bins}} \log[\exp(-B_i - \mu S_i)(B_i + \mu S_i)^{N_i/N_i!}] \quad (4) $$

where $N_i$ is the number of data events in bin i, and $\mu$ is the “signal strength”, which is the scaling factor of the arbitrary flux normalisation $\Phi_0$. Omitting all terms that do not depend on $\mu$:

$$ \log L = \sum_{\text{bins}} N_i \log(B_i + \mu S_i) - (B_i + \mu S_i) \quad (5) $$

For a given data-set $\hat{\mu}$ is determined by maximizing $\log L$.

The compatibility of the data with the signal/background hypotheses is tested computing the logarithm of the likelihood ratio:

$$ \lambda = \log L(\mu = \hat{\mu}) - \log L(\mu = 0) \quad (6) $$

For a (true) value of the signal strength $\mu_{true}$, pseudo-experiments (PE) can be generated drawing each $N_i$ from a Poisson distribution with mean $B_i + \mu_{true}S_i$. Each PE undergoes the treatment described above, i.e. a maximum likelihood fit yielding $\hat{\mu}$ which is then used to compute the test statistic $\lambda$ for that PE.

The distributions of $\lambda(\mu_{true})$ are then derived. For convenience the $\mu_{true}$ are chosen in a way that they provide a given number of signal events in the whole data set, $S = \sum_i \mu_{true}S_i$. It is straightforward to see that the conversion $S_{sig} \leftrightarrow \mu_{true}$ is a scaling factor ($S = \sum_i S_i$).

The $\lambda$ distributions are used to extract limits with the Neyman approach [17]. The sensitivity is defined as the median upper limit on S for 90% C.L. $S_{90}$) that can be converted to the flux:

$$ \Phi_{90} = \frac{S_{90}}{S} \Phi_0 \quad (7) $$
## 4 Results

The presented analysis estimated the sensitivities to neutrino point sources for the ARCA 2020-2022 track datasets, the ANTARES 2007-2022 dataset, and their combined analysis. Sensitivity results as a function of declinations are presented in Fig. 3.

Currently ANTARES contributes most significantly to the sensitivity of the combined analysis, however including the ARCA data sample the sensitivity enhances by 10%, as can be appreciated from the ratio between the sensitivity of ANTARES and that of the combined analysis in the bottom panel of Fig. 3. As the ARCA detector configurations expand and more data are collected, the joint analysis will effectively utilise data from both the ARCA and ANTARES detectors. The first ARCA building block (consisting of 115 lines) is expected to be completed before the end of this decade, indicating rapid growth for KM3NET in the near future. The combined analysis will become more and more effective as the KM3NeT data sample will continue to grow.

## References

[1] IceCube Collaboration. Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector. Science 342.6161 (2013)

[2] IceCube Collaboration. Multi-messenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A. Science 361, eaat1378 (2018)

[3] IceCube Collaboration. Evidence for neutrino emission from the nearby active galaxy NGC 1068. Science 378, 6619, 538-543 (2022)

[4] KM3NeT Collaboration, Letter of Intent for KM3NeT 2.0. Journal of Physics G: Nuclear and Particle Physics, 43 (8), 08400 (2016)

[5] ANTARES collaboration. ANTARES: the first undersea neutrino telescope. Nucl. Instrum. Meth. A, 656, 11-38 (2011)

[6] ANTARES collaboration. Searches for Point-like Sources of Cosmic Neutrinos with 15 Years of ANTARES Data. Proceedings of Science, 444, ICRC 2023 (2023)

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[8] B. Caiffi et al. on behalf of the KM3NeT Collaboration. Search for cosmic neutrino point sources and extended sources with 6-21 lines of KM3NeT/ARCA. Proceedings of Science, 444, ICRC 2023 (2023)

[9] KM3NeT Collaboration. gSeaGen: the KM3NeT GENIE-based code for neutrino telescopes. Comput. Phys. Commun. 256, 107477 (2020)

[10] Andreopoulos, C. et al. The GENIE neutrino Monte Carlo generator. Nucl. Instrum. Methods Phys. Res. A 614, 87-104 (2010).

[11] Alvarez-Ruso, L. et al. Recent highlights from GENIE v3. Eur. Phys. J. Spec. Top. 230, 4449-4467 (2021).

[12] Cooper-Sarkar, A. et al. The high energy neutrino cross-section in the Standard Model and its uncertainty. J. High Energy Phys. 2011, 42 (2011).

[13] Koehne, J.-H. et al. PROPOSAL: a tool for propagation of charged leptons. Comput. Phys. Commun. 184, 2070-2090 (2013).

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[15] Agostinelli, S. et al. Geant4—a simulation toolkit. Nucl. Instrum. Methods Phys. Res. A 506, 250-303 (2003).

[16] SUFTware package https://suftware.readthedocs.io/en/latest/index.html

[17] Neyman, J. A selection of early statistical papers of J. Neyman. University of California Press, 1967.