Evaluation of the potential of a gamma-ray observatory to detect astrophysical neutrinos through inclined showers

Abstract

We assess the capabilities of a ground-based gamma-ray observatory to detect astrophysical neutrinos with energies in the 100 TeV to 100 PeV range. The identification of these events is done through the measurement of very inclined extensive air showers induced by downward-going and upward-going neutrinos. The discrimination of neutrino-induced showers in the overwhelming cosmic-ray background is achieved by analyzing the balance of the total electromagnetic and muonic signals of the shower at the ground. We demonstrate that a km2-scale wide-field-of-view ground-based gamma-ray observatory could detect a couple of very-high- to ultrahigh-energy neutrino events per year with a reasonable pointing accuracy, making it an interesting facility for multimessenger studies with both photons and neutrinos.

Full text

Evaluation of the potential of a gamma-ray observatory to detect
astrophysical neutrinos through inclined showers
Jaime Alvarez-Muñiz
Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela,
15782 Santiago de Compostela, Spain
Ruben Conceição ,*Pedro J. Costa , Mário Pimenta , and Bernardo Tom´e
Laboratório de Instrumentação e Física Experimental de Partículas (LIP)—Lisbon,
Av. Prof. Gama Pinto 2, 1649-003 Lisbon, Portugal
and Instituto Superior T´ecnico (IST), Universidade de Lisboa,
Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
(Received 24 August 2022; accepted 23 September 2022; published 3 November 2022)
We assess the capabilities of a ground-based gamma-ray observatory to detect astrophysical neutrinos
with energies in the 100 TeV to 100 PeV range. The identification of these events is done through the
measurement of very inclined extensive air showers induced by downward-going and upward-going
neutrinos. The discrimination of neutrino-induced showers in the overwhelming cosmic-ray background is
achieved by analyzing the balance of the total electromagnetic and muonic signals of the shower at the
ground. We demonstrate that a km2-scale wide-field-of-view ground-based gamma-ray observatory could
detect a couple of very-high- to ultrahigh-energy neutrino events per year with a reasonable pointing
accuracy, making it an interesting facility for multimessenger studies with both photons and neutrinos.
DOI: 10.1103/PhysRevD.106.102001
I. INTRODUCTION
The multimessenger approach to astroparticle physics
has the potential to address fundamental problems, such as
those related to physics in extreme phenomena, the origin
of ultrahigh-energy cosmic rays, the nature of dark matter,
the possibility of Lorentz invariance violation, and even the
existence of undiscovered particles.
Numerous experiments resort to extensive air shower
(EAS) arrays to study very-high-energy gamma rays, such
as HAWC [1], LHAASO [2], and the Southern Wide-field
Gamma-ray Observatory (SWGO) [3] currently in its
planning stage. The recent observation of gamma rays
with energies above 1 PeV by LHAASO [4] puts pressure
on the construction of a facility surveying the Southern
Hemisphere sky. This experiment should have an effective
area of the order of km2and excellent gamma/hadron
discrimination capabilities to cope with the low fluxes
reported by LHAASO. On the other hand, experiments
such as IceCube have been successfully operating over the
years, demonstrating the presence of a very-high-energy
neutrino flux of astrophysical origin. This flux has been
seen to extend up to a few PeV with no sign of a cutoff [5].
The simultaneous measurement of gamma rays and
neutrinos coming from the same astrophysical source
known as multimessenger measurements is highly aspired,
and it has in the last years been reshaping the experimental
panorama with the addition of new, more ambitious
upgrades and new experiments (see, for instance, [6–8]).
In this work, we use shower simulations to determine
whether ground-based gamma-ray EAS arrays can be used
to detect neutrinos and estimate their expected sensitivity.
Our study is restricted to neutrinos with energies ranging
from 100 TeV to 100 PeV. Signal events correspond to an
inclined EAS (zenith angle θ>60°) induced by down-
ward- and upward-going neutrinos. The main background
source for this measurement is a very inclined EAS
resulting from the interaction of cosmic rays with the
atmosphere.
The article is organized as follows: In Sec. II, the
experimental strategy employed to distinguish showers
induced by neutrinos from the cosmic-ray background is
presented. Next, in Sec. III, the simulation framework and
the sets of simulated showers are given. In Sec. IV, the
discrimination methodology is presented. In Sec. V,we
discuss the method to estimate the sensitivity of a ground
array observatory to astrophysical neutrinos, focusing on
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PHYSICAL REVIEW D 106, 102001 (2022)
2470-0010=2022=106(10)=102001(12) 102001-1 Published by the American Physical Society

electron neutrinos νe. Our results on the sensitivity obtained
for downward-going and upward-going neutrino-induced
events are given in Secs. VI and VIII, respectively. In
Sec. VI, the impact of the density of detector units in the
array (fill factor) of experimental reconstruction resolution
and of simulations statistics are studied. Finally, in Sec. VII,
an estimate of the sensitivity considering all neutrino
flavors is presented. We end the article in Sec. IX with
some final remarks and conclusions.
II. EXPERIMENTAL STRATEGY
In this work, we investigate the sensitivity of a ground-
based wide-field-of-view gamma-ray observatory, such as
the LHAASO experiment [2] or the future SWGO [3], for
the detection of astrophysical neutrinos in the energy range
of hundreds of TeV up to hundreds of PeV. These experi-
ments cover large effective areas of ∼1km2with a relatively
high fill factor [9] (∼4% for LHAASO) to boost the
detection of the very low photon fluxes at >PeV energies.
The main source of background for these observatories is
the overwhelming cosmic-ray flux that supersedes the
gamma-ray flux by a factor ∼104above 100 TeV energy.
To mitigate this background, experimental data are often
analyzed to extract the muon content of the shower, which is
higher for hadron-induced showers. However, the distinction
between vertical (zenith angle θ≲60°) neutrino-induced and
cosmic-ray-induced showers is complicated, as the events
exhibit similar signatures. The discrimination is enhanced for
inclined showers (θ≳60°) due to the larger depth of
atmosphere between the point of first interaction and the
ground [10]. As the proton-air interaction cross section is 7
orders of magnitude larger than the neutrino-air one, protons
typically interact in the upper layers of the atmosphere, and a
proton-induced inclined shower has to cross a large amount
of matter before reaching the ground level. As a consequence,
most of the electromagnetic component gets absorbed, and
only muons can reach the ground. As a result, ground-based
array detectors sample what is commonly called an old
shower. Neutrinos, on the other hand, can interact much
closer to the detector stations, and both the electromagnetic
and muonic components will be detected, what is commonly
called a young shower. Thus, the balance between the
amount of measured signal due to muons and electromag-
netic particles can be used to discriminate neutrino from
cosmic-ray-induced showers. This strategy has also been
used by the surface detector array of the Pierre Auger
Observatory to place limits on the neutrino flux at EeV
energies [11,12]. Hence, the neutrino signatures that we
investigate in this work are those of very inclined showers (θ
in the range 60° to 88°) initiated close to the ground.
Neutrinos with energies in the 100 TeV–100 PeV range
are taken as signal, while the background ismainly attributed
to the very inclined EASs induced by cosmic rays. We
initially focus on studying the detection of electron neutrinos
νeonly. When these particles interact with the atmosphere,
they can generate both a hadronic and an electromagnetic
shower, maximizing the detection probability. Upon reach-
ing the ground, the inclined cascade may have undergone a
substantial development producing a large footprint and
facilitating its detection with a surface detector array.
The key observables to discriminate between neutrino-
and proton-induced showers are the total amount of signal
produced by electromagnetic particles (Sem) and by muons
(Sμ). The existing and planned gamma-ray experiments
should be able to access both quantities. The electromagnetic
signal is essential to estimate the primary energy, while Sμis
typically used to discriminate gamma- from proton-induced
showers. In this work, we assume that both quantities are
readily available instead of performing a dedicated experi-
ment-dependent reconstruction (see, for instance, the
LHAASO experiment [2] to see how these quantities can
be accessed). Afterward, in Sec. VI B, the impact of a
possible reconstruction uncertainty on the sensitivity to
very-high-energy (VHE) neutrinos is discussed. This study
allows for the extraction of the experimental resolution
needed to allow the detection of neutrino events.
III. SIMULATION FRAMEWORK
AND DATA ANALYSIS
We have simulated the development of air showers with
dedicated Monte Carlo codes, and assumed a flat EAS
array composed of cylindrical water Cherenkov detector
(WCD) units with area ∼12 m2spanning over an area of
1km2. The response of the station unit is modeled using a
parametrization of the average signal as a function of the
energy of the particle crossing the detector. An example of
the average air-shower footprint at the ground is displayed
in Fig. 1.
FIG. 1. Average footprint of the signal generated by 1000
proton-induced showers of energy Ep¼100 TeV, zenith angle
θ¼75°, and azimuthal angle ϕ¼0° on a WCD array. The array
spans an area of 1km2with an 80% fill factor. Each WCD station
covers an area of 12.6m2. The x¼0and y¼0correspond to the
projection to the ground of the initial cosmic-ray direction.
JAIME ALVAREZ-MUÑIZ et al. PHYS. REV. D 106, 102001 (2022)
102001-2

CORSIKA
(Cosmic Ray Simulations for Kascade version
7.7410) [13] was used to generate downward-going exten-
sive air showers initiated by protons and neutrinos.
Neutrino-induced air showers were simulated at fixed
interaction points from the ground level up to 12 000 m
in vertical height, while for proton-induced showers, the
starting points were sampled taking into account the
proton-air cross section. Showers generated by upward-
going neutrinos interacting within Earth’s crust and devel-
oping in the ground were simulated using the
AIRES
framework version 2.8.4a [14]. Simulations were per-
formed at fixed values of energy and zenith angle, while
the azimuth angle (ϕ) was sampled from a 2πuniform
distribution. The magnetic field and the observation level of
the WCD array remained unchanged in all simulations. The
ground was placed 5200 m above sea level, corresponding
to the approximate altitude of some of the sites being
considered for SWGO [3]. Earth’s magnetic field was fixed
to the value at the ALMA site in Chile.
The response of the WCD stations was emulated with a
parametrization of the signal as a function of the particle
energy obtained with the
GEANT
4toolkit [15]. The signals
induced by shower particles were obtained by injecting
them at the center of the detector in the vertical direction. A
sketch of a WCD unit is shown in Fig. 2. The single-layered
WCD unit with multiple photosensors at the bottom is one
of the candidate designs for the stations being considered
for SWGO [16]. The parametrization of the average
response of the WCD is obtained for electrons, muons,
and protons representative of the electromagnetic, muonic,
and hadronic components of the shower, respectively. It is
important to note that the discrimination shall be done
through two shower quantities: Sμand Sem. As such, the
lack of fluctuations on the parametrization due to light
collection and particle trajectories would have an impact on
the resolution of the reconstructed Sμand Sem. The impact
of the experimental resolution on the reconstruction of
these shower parameters will be discussed in Sec. VI B.
With these simulations, we have computed Sem and Sμ
for each simulated neutrino and background proton shower
at the ground array. The simulated values of Sem and Sμfor
signal and background events are fed into
ROOT
’s Toolkit
for Multivariate Data Analysis [17] to separate the two
classes of events as described in the next section.
IV. DISCRIMINATING SIGNAL
AND BACKGROUND
The aim of this work was to minimize the background so
that any neutrino candidate would be significant, at the
expense of a smaller neutrino identification efficiency.
This was achieved with a Fisher linear discriminant
analysis performed in the parameter space of log10ðSμÞ
vs log10ðSemÞ. The cut in the Fisher discriminant is derived
independently for each simulated zenith angle considering
all the simulated proton energies (10 TeV–10 EeV) and
neutrinos with fixed energy from 100 TeV to 10 PeV. An
example is shown in Fig. 3for the case of θ¼70°. It was
found that the optimal Fisher cut varies with the zenith
angle, but not with the primary energy.
Two additional cuts were introduced to achieve a back-
ground-free discrimination. Neutrino events have Fisher
values predominantly above ∼0.5. However, also a small
fraction of low-energy proton events typically characterized
by small values of Sem can fulfill the Fisher cut. For all
values of zenith angle, a cut in log10ðSem=p:e:Þ>5.3, with
Sem given in photoelectrons (p.e.), removes the majority of
FIG. 2. Sketch of the WCD unit employed in this study. The
cylindrical tank is filled with water, and four photomultiplier
tubes are placed at the bottom of the structure. Taken from [16].
0246810
/p.e.)
em
(S
10
log
0
5
10
/p.e.)
μ
(S
10
log
° = 70θ
p
100 TeV,,
e
ν
1 PeV, 10 PeV
10 TeV
100 TeV
1 PeV
10 PeV
100 PeV 1 EeV 10 EeV
Fisher Cut
FIG. 3. Fisher cut (solid line) applied in the discrimination
between neutrino- and proton-induced showers for θ¼70°. Red
dots represent neutrino events, while blue dots represent proton-
induced showers. The dotted vertical (horizontal) line corre-
sponds to the cut in log10 Sem (log10 Sμ) to reject all background
proton events (see text for details). Only events that do not fall in
the shaded gray region are considered neutrino candidate events.
All signals are given in terms of photoelectrons (p.e.)
EVALUATION OF THE POTENTIAL OF A GAMMA-RAY …PHYS. REV. D 106, 102001 (2022)
102001-3

these background events, while minimizing the loss of
neutrino events. An example is shown in Fig. 3.
A second, zenith-dependent cut on Sμwas introduced to
remove the contamination due to the highest-energy proton
background showers. Cascades induced by protons with
energies above 1 PeV produce larger muonic signals than
those induced by neutrinos with energies in the 100 TeV to
10 PeV range. By limiting the maximum value of Sμ, these
background events are eliminated with minimal loss of
neutrino events, as can be seen in the example in Fig. 3.
Within the squared region defined by the Sem and Sμcuts,
the value of the Fisher cut can be further adjusted to remove
all background events.
V. SENSITIVITY OF A GROUND ARRAY
TO NEUTRINOS
To estimate the sensitivity of a gamma-ray ground-based
observatory to neutrinos, we have calculated the expected
neutrino event rate dNν=dtgiven by the following equation:
dNν
dt¼ZEν;max
Eν;min
dΦν
dEν
ðEνÞ1
mσðEνÞMeffðEνÞdEν;ð1Þ
where dΦν=dEνdenotes the differential flux of incoming
neutrinos, mis the mass of an air nucleon, and σðEνÞis the
neutrino-nucleon cross section. MeffðEνÞis the effective mass
of the detector (see below), while Eν;min and Eν;max denote the
integration limits used for the sensitivity calculation.
In this section, we study the sensitivity to electron
neutrinos only. The sensitivity to all neutrino flavors will
be addressed in Sec. VII.
A. Electron neutrino flux
An astrophysical flux of VHE electron neutrinos and
antineutrinos was measured at the IceCube neutrino
observatory up to a few PeV [5]. The flux of νeand ¯
νe
can be approximated by
dΦν
dEν
ðEνÞ¼k0Eν
E0−2.53
;ð2Þ
where E0¼105GeV and k0¼kE−2.53
0≡4.98 ×
10−18 GeV−1cm−2s−1sr−1. In this work, we discuss the
detection of neutrinos with energy above 100 TeV, where
the flux of astrophysical neutrinos dominates over the one
by atmospheric neutrinos. As such, we will use for electron
neutrinos the flux given in Eq. (2) reduced by a factor of 2,
assuming an equal content of νeand ¯
νeat Earth. Moreover,
as in this work we intend only to have an estimate of the
number of neutrinos that could be detected by a generic
gamma-ray observatory through the use of inclined show-
ers, we consider only the mean values reported by IceCube;
i.e., we neglect for the upcoming calculations the claimed
experimental errors.
B. Neutrino-nucleon cross section
In Eq. (2) we use the values of the neutrino-nucleon cross
section as a function of the energy from [18], distinguishing
between charged-current (CC) and neutral-current (NC)
neutrino interactions, as shown in Fig. 4.
C. Neutrino efficiency and effective mass
The effective mass represents the amount of matter
within which an interacting neutrino can be identified.
Equation (3) gives the effective mass as a function of the
zenith angle θand the energy of the incoming neutrino Eν:
Mθ
effðEν;θÞ¼2πAsin θcos θZD
ενðEν;θ;DÞdD: ð3Þ
The function ενðθ;D;E
νÞdenotes the probability of iden-
tifying a neutrino considering the cuts introduced in
Sec. IV. It is a function of the slant depth of the point
of first interaction of the neutrino D(expressed in g cm−2
and measured from ground), the energy of the neutrino Eν
(given in GeV), and the angle of incidence θ(in radians).
The surface area of the array is denoted as Aand was fixed
at a value A¼1km2.
The neutrino identification efficiency ενðEν;θ;DÞis
obtained as the ratio of the number of neutrino points
within the area delimited by the cuts (white region in Fig. 3)
and the total number of simulated neutrino points for a
given zenith angle, energy, and interaction depth. An
example is depicted in Fig. 5for Eν¼1PeV and several
zenith angles as a function of D. As expected, the neutrino
identification efficiency decreases for showers initiated far
from the ground since those are more similar to showers
induced by protons that typically interact in the upper
layers of the atmosphere.
For each primary neutrino energy, five values of θare
considered: 60°, 70°, 75°, 80°, and 88°. The integration in D
of Eq. (3) is done using a cubic spline interpolation to the
456789
/ GeV)
ν
(E
10
log
35−
34−
33−
32−
)
2
/ cmσ(
10
log
Total
CC
NC
FIG. 4. Neutrino-nucleon charged-current (CC), neutral-current
(NC), and total (CC þNC) cross sections as a function of the
neutrino energy Eν. Values taken from [18].
JAIME ALVAREZ-MUÑIZ et al. PHYS. REV. D 106, 102001 (2022)
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discrete values of ενðEν;θ;DÞ[19]. This results in the
effective mass values for each value of θreported in Table I.
The total effective mass for a given neutrino energy is
obtained by integrating the effective mass in the zenith
angle θ∈½60°;89°. The integration in the zenith angle is
achieved by applying a cubic spline interpolation to
the Mθ
effðθ;E
νÞvalues listed in Table Ifor the case of
Eν¼1PeV. This yields a total effective mass for the
reference energy Eν¼1PeV of Meff ≃2.97 ×1014 gsr.
D. Electron neutrino interactions
The neutrino detection efficiency and the effective mass
depend on the neutrino interaction channel. In Fig. 5and
Table I, the interaction channel, either CC or NC, was
randomly chosen according to their relative weights in the
total cross section. However, in
CORSIKA
simulations, the
interaction can be chosen so that neutrinos only interact via
CC or NC, allowing the estimation of the sensitivity for
each interaction channel. An example of the resulting
neutrino identification efficiency is presented in Fig. 6
for Eν¼1PeV and θ¼80°.
As seen in Fig. 6, the electron neutrino identification
efficiency considering only CC interactions has nonzero
values at a larger distance from the ground than the one
obtained using only NC interactions. This happens
because, in CC interactions, the total energy of the νeis
transferred to an electromagnetic shower from the energetic
electron produced in the interaction, and a hadronic shower
from the collision with the nucleon of the atmosphere.
In NC interactions, instead of an electron, an electron
neutrino will be produced. Hence, only the typically less-
energetic hadronic shower can be detected reducing the
efficiency. In Fig. 6, it is also shown the more realistic case
of the efficiency when CC and NC interactions are chosen
at random depending on their relative weight in the total
neutrino-nucleon cross section. As expected, the curve
NC þCC is in between the CC and NC curves.
Integrating Eq. (3) in the zenith angle for a fixed
energy yields the effective masses reported in Table II for
Eν¼1PeV.
VI. SENSITIVITY TO DOWNWARD-GOING νe
Equation (1) can be integrated over energy to obtain the
electron neutrino event rate. This is achieved by applying a
cubic spline interpolation to estimate the effective mass
values for neutrino energies between 100 TeV and 10 PeV.
The effective mass for energies outside this range is
approximated via extrapolation. The estimated electron
neutrino event rates are given in Table III. Different values
of Eν;min and Eν;max were used in Eq. (1) to study the
dependence of the event rate on both the minimum energy
above which the flux can be considered to be purely
astrophysical with a negligible contamination from
FIG. 5. Neutrino identification efficiency as a function of the
neutrino interaction slant depth (measured from the ground),
for simulated neutrino-induced showers of Eν¼1PeV, and
θ¼60°, 70°, 75°, 80°, and 88°.
FIG. 6. Neutrino identification efficiency obtained for showers
induced by 1 PeV neutrinos with θ¼80°. Interactions are either
selected at random between CC and NC according to their
relative weight in the total cross section (curve labeled as
NC þCC), or set to only CC or only NC interactions.
TABLE I. Effective mass as given in Eq. (3) for neutrino-
induced showers with Eν¼1PeV and several values of θ.
θMθ
eff ðEν¼1PeV;θÞ(g)
60° 9.73 ×1012
70° 1.27 ×1013
75° 1.65 ×1013
80° 9.09 ×1012
88° 2.21 ×1012
TABLE II. Effective mass for the different neutrino interaction
channels CC and NC with Eν¼1PeV. Total corresponds to the
case where CC or NC are chosen randomly.
Interaction Meff ðEν¼1PeVÞ(g sr)
CC 3.60 ×1014
NC 2.27 ×1014
Total 2.97 ×1014
EVALUATION OF THE POTENTIAL OF A GAMMA-RAY …PHYS. REV. D 106, 102001 (2022)
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atmospheric neutrinos, and on the maximum energy to
which the astrophysical flux could extend without a cutoff.
As can be seen in Table III, a rate of 0.3 electron neutrinos
per year can be detected.
The estimates of sensitivity given in Table III can be
extrapolated linearly to other values of detector surface area
A. In Fig. 7, we depict the electron neutrino event rates as a
function of Afor different values of Eν;min and Eν;max.
A. Impact of the array fill factor
The fill factor is defined as the ratio between the sum of
the area of individual detectors and the total area of the
array A. To infer the impact of the fill factor on the event
rate, the procedure described previously is applied to a
detector array of equal surface area (1km2) and variable fill
factor. In this work, we have studied the sensitivity for fill
factors of 1%, 3%, 5%, 10%, 50%, and 80%, yielding the
results in Fig. 8. All the cuts described in Sec. IV were
recomputed to ensure that all the simulated proton back-
ground events were rejected.
Taking as a reference LHAASO’s fill factor of 4% [2],
the estimated neutrino event rate decreases by a factor of
≈3when compared to the initially assumed 80% fill factor.
It is interesting to see that the event rate increases rather
slowly for fill factors between 1% and ∼5% and more
rapidly between ∼10% and ∼50%.
B. Impact of experimental resolution
We have also studied the impact of experimental
resolution on the expected event rate. Gaussian smearings
denoted as σSem and σSμwere applied to both electromag-
netic (Sem) and muonic (Sμ) signals of the neutrino and
background events, respectively.
After applying the smearing, the previously derived cuts
on the Fisher discrimination described in Sec. IV were
recomputed to ensure that all simulated background events
were rejected. Assuming again an array area of A¼1km2
with an 80% fill factor, the resulting neutrino event rates are
presented in Fig. 9. Larger values of σSμand/or σSem result
in progressively lower event rates and hence lower sensi-
tivity, as would be expected. Degradation of the expected
number of neutrinos by a factor of 2 is only achieved when
the smear applied to the electromagnetic or muonic signal
reaches an extreme value of about 200%. However, at PeV
energy, the reconstruction resolutions of Sem and Sμare
expected to be a few tens of percent. The reduced impact on
the event rate reflects the robustness of this methodology to
a possible degradation of the signal due to reconstruction.
The ability to reconstruct the geometry (arrival direction
and core position) of the neutrino-induced shower events
was also investigated using a simple reconstruction algo-
rithm. The reconstruction is performed by fitting the arrival
times of the first particles reaching each WCD station to a
conic shower front. The curvature of the front was taken
from [20] without any further optimization. This test was
done considering an array of A¼1km2and a fill factor
of 5%.
In Fig. 10, we show a density plot for the angular
reconstruction resolution σθas a function of the neutrino
interaction slant depth and the number of active stations.
The resolution σθis defined as the 68% containment of the
TABLE III. Even rate given by Eq. (1) for electron neutrinos
only in a wide-field ground-based gamma-ray observatory
(A¼1km2) for different ranges of Eν. The rates are obtained
in different ranges of Eν;min and Eν;max in Eq. (1).
Eν;min −Eν;max dN
dt ðEνÞðyr−1Þ
100 TeV–1 PeV 1.30 ×10−1
100 TeV–10 PeV 2.06 ×10−1
100 TeV–100 PeV 3.01 ×10−1
1–10 PeV 1.06 ×10−1
1–100 PeV 1.72 ×10−1
1−
10 1 10
2
Area/km
3−
10
2−
10
1−
10
1
-1
/ yr
dt
ν
dN
100 TeV - 100 PeV
1-100 PeV
100-200 TeV
1-2 PeV
FIG. 7. Number of electron neutrinos expected to be detected
and identified per year as a function of the area of the detector.
Three curves are presented corresponding to different values of
Eν;min and Eν;max ranging from 1 to 2 PeV and 100 PeV, as well as
from 100 to 200 TeV and 100 PeV. For reference, the LHAASO
ground array has an area of A¼1km2.
1 10
Fill factor/%
0.1
0.2
0.3
-1
/ yr
dt
ν
dN
FIG. 8. Estimated electron neutrino event rate as a function of
the fill factor of the WCD array; see text for details. The event rate
is obtained with Eq. (1) for Eν;min ¼100 TeV and Eν;max ¼
100 PeV for an array with A¼1km2.
JAIME ALVAREZ-MUÑIZ et al. PHYS. REV. D 106, 102001 (2022)
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difference between the simulated and reconstructed angle.
From this figure, it can be seen that the precision of the
shower axis reconstruction depends both on the distance of
the neutrino interaction point to the ground and on the
number of triggered stations. If the interaction happens
close to the ground, the shower footprint is small, leading to
a poor reconstruction. However, if the interaction happens
at ≳100 gcm
−2it is possible to achieve angular resolutions
better than ∼1°.
Experimentally, one could apply a cut on the number of
active stations. For instance, it was seen that requiring at least
∼30 active stations would allow having a reconstruction
resolution better than ∼5°. The introduction of such a
condition would lead to a small ∼10% decrease in the
neutrino identification efficiency and effective mass, result-
ing in a proportionately lower neutrino event rate.
In Fig. 10, it can also be seen that for showers with large
slant depths (D≳1000 gcm
−2), the number of active
stations can have significant variations being intrinsically
connected to the shower development. However, the plot
also displays the median and the standard deviation of the
number of events, evidencing that most of the showers will
lead to a large number of active stations. It should also be
pointed out that while the number of active stations affects
the quality of the reconstruction, better resolutions can be
attained for neutrino-induced showers that interact higher
in the atmosphere. This happens because even though
fewer particles are reaching the ground, the shower foot-
print is more extended due to the longer shower develop-
ment through the atmosphere, easing the reconstruction of
the geometry.
It was verified that the order of magnitude of the claimed
geometric reconstruction resolution was the same for all the
energies and angles considered in this work.
Finally, it is important to note that the provided values on
the reconstruction resolutions should be taken as upper
limits. Dedicated reconstructions of inclined showers are
expected to improve the angular resolution [21].
C. Impact of the limited simulation statistics
The flux of background proton-induced showers greatly
exceeds the expected flux of neutrinos, implying that a
reliable observation of neutrino events requires a large
background rejection factor. Simulations are needed to
establish the cuts and assess a possible contamination by
proton showers in order to get a significant detection in case
a neutrino candidate is observed. However, the available
simulations are limited in statistics due to limited computa-
tional resources and computing time.
To overcome this difficulty, we have applied the follow-
ing procedure. For all sets of simulated proton showers at
fixed energy and zenith angle, we have obtained the Fisher
distributions for proton showers within the region of
interest delimited by the cuts on Sem and Sμas defined
in Sec. IV (see also Fig. 3). The cumulative of these
distributions (number of events above a Fisher value) is
then obtained and normalized to 1. This procedure gives the
proton background selection efficiency εpor the proton
contamination fraction as a function of the Fisher value.
A few examples are shown in Fig. 14 in the Appendix. An
exponential fit to the tail of the cumulative proton dis-
tributions is performed and used to extrapolate to higher
background rejection factors (smaller contamination frac-
tions εp) where the limited statistics of the proton simu-
lations did not populate the tails of the distributions. The
Fisher value cumulative distribution for each zenith angle is
then obtained by combining the cumulative distributions
for all proton energies, weighting according to their relative
contribution to the cosmic-ray flux assuming a power-law
E−3spectrum. For each proton selection efficiency εp, the
matching Fisher value is extracted from the cumulative of
the corresponding zenith angle and taken as the Fisher cut
value. In this way, the neutrino event rate above the Fisher
FIG. 9. Electron neutrino event rate as a function of the
experimental resolution on the discriminating variables Sem
and Sμassumed to follow a Gaussian distribution of width σSμ
and σSem . The rate was obtained with Eq. (1) for the range of
energies Eν;min ¼100 TeV and Eν;max ¼100 PeV, assuming a
detector surface area A¼1km2.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
)
-2
(Slant Depth/g cm
10
log
0
1
2
3
4
(Active Stations)
10
log
1−
10
1
10
°/
θ
σ
FIG. 10. Angular reconstruction resolution as a function of the
neutrino interaction slant depth (measured from the ground) and
of the number of active stations for neutrinos with Eν¼1PeV
and θ¼75°. Red points denote the median, and the error bars the
standard deviation of the event distribution within each slant
depth bin.
EVALUATION OF THE POTENTIAL OF A GAMMA-RAY …PHYS. REV. D 106, 102001 (2022)
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cut is estimated as a function of εpranging from 10−14 to
10−1, as shown in Fig. 11. The plot suggests that an electron
neutrino event rate of ∼0.3per year can be achieved with
proton background contamination smaller than ∼0.005 per
year. The 1-sigma uncertainty of the exponential fit can be
used to evaluate the corresponding uncertainty on the
number of neutrinos as a function of εpshown as a band
in the top panel of Fig. 11. From this exercise, it can be seen
that while the uncertainty on the number of expected
neutrinos increases as εpdecreases, it is at maximum a
factor of 4 for a quasi-background-free (εp→0) experi-
ment. In any case, for values of εplower than ≈10−14, the
neutrino event rate is higher than that of the background.
VII. ESTIMATE OF SENSITIVITY FOR ALL
NEUTRINO FLAVORS
Until this point, this work focused exclusively on the
contribution of electron neutrinos to the estimated event
rate. By neglecting muon- and tau-neutrino flavors, and all
antineutrinos, the estimate presented constitutes a lower
limit to the number of neutrinos a gamma-ray ground-based
array may be capable of detecting. The estimated event rate
for all neutrino and antineutrino flavors presented here is
achieved by taking advantage of the effective mass of the
array for electron neutrinos computed in Sec. V, explicitly
for CC and NC interactions, and denoted here as MνeðCCÞ
and MνeðNCÞ, respectively. Combining these quantities
with the corresponding neutrino-air interaction properties
allows us to conservatively estimate the number of
expected neutrinos for all flavors and interaction channels.
As we are considering astrophysical neutrinos, the expected
number of electron, muon, and tau neutrinos are assumed to
be in the ratio 1∶1∶1after oscillation over cosmological
distances. Moreover, the same amount of antineutrinos is
expected. What might change is the ability to distinguish a
given species of neutrino-induced showers from the back-
ground, i.e., the identification efficiency εand hence the
effective mass, which can be assessed based on some
qualitative arguments on the characteristics of the neutrino
interaction with Earth’s atmosphere.
First, the effective mass of the array when accounting
only for neutral-current interactions is expected to be the
same for all neutrino flavors and hence equal to that of νe
NC interactions. All neutrino flavors produce the same type
of hadronic shower in a NC interaction, carrying on average
the same fraction of the neutrino energy. Moreover, the
only difference in the Feynman diagrams responsible for
the bulk of the cross section is the neutrino mass that can be
considered negligible at the very high energies involved. As
a consequence, for all neutrino flavors the expected event
rate is assumed to be proportional to σNCMνeðNCÞwith σNC
the NC-interaction cross section.
For the case of the muon neutrino, the charged-current
interaction will induce a hadronic shower and an energetic
muon. One single muon is unlikely to be detected in a sparse
array, so we will only consider the hadronic cascade. Again,
given the extreme primary energies, the energy distribution
of the secondaries arising from the hadronic vertex of the
interaction is very similar to the one of an electron neutrino
(and an emerging fast electron) or a neutral-current inter-
action. Hence, conservatively, we will assume that the
effective mass of the array to muon neutrinos for the CC
interaction is the same as the one of the electron neutrinos for
the neutral-current interaction estimated before. This yields
the expected number of CC-interacting muon neutrinos
proportional to σCCMνeðNCÞ, with σCC the CC interaction
cross section. It should be noted again that this is a
conservative assumption, as the muon produced in a CC
interaction could radiate an energetic photon via bremsstrah-
lung leading to the production of an electromagnetic shower
that would increase the detection probability.
The tau-neutrino charged-current interaction produces a
hadronic cascade plus a high-energy tau. In the atmosphere,
the tau lepton will travel on average between ∼5m and
∼5km at energies between 100 TeV and 100 PeV before
decaying. The decay of the tau can either produce hadrons
(∼65% of the time) and electrons (∼17% of the time) that
will lead to young cascades of particles. Muons can also be
produced in the decay (∼17% of the time) that will be
essentially undetectable, as discussed before. In this work,
we have assumed that only the hadronic particles directly
emerging from the collision of the tau neutrino with the
atmosphere will produce a detectable shower; i.e., we
neglect the decay of the τlepton, and assume that the
effective mass of the detector is the same as in the case of
neutral-current interactions, with the expected number
of CC-interacting tau neutrinos being proportional
σCCMνeðNCÞ. We stress that this is conservative and that
a more accurate calculation of the number of expected tau
neutrinos would be clearly above this estimate.
The assumptions above can be applied to antineutrinos ¯
ν
given the high energy of the involved interactions. The ¯
ν-air
14−
10 11−
10 8−
10 5−
10 2−
10
p
ε
1−
10
1
-1
/ yr
dt
ν
dN
Nonextrapolated Extrapolated
FIG. 11. Neutrino event rate as a function of the proton
contamination fraction εpusing only simulated data (green dots
with line) and extrapolating from available data points (orange
dots with line and band).
JAIME ALVAREZ-MUÑIZ et al. PHYS. REV. D 106, 102001 (2022)
102001-8

interaction properties will be similar, leading to air showers
with essentially the same general properties leading to
similar Sem and Sμ, the main parameters of this analysis.
Additionally, above 100 TeV, neutrino-air and antineutrino-
air cross sections are very close. Nonetheless, we have
used the exact values for each energy. Consequently, the
inclusion of antineutrinos would likely increase the
expected event rate for all neutrinos by a factor 2.
The total expected event rate would be additionally
increased due to the resonant channel for the electron
antineutrinos ¯
νe. Around E¯
ν∼6.3PeV, electron antineutri-
nos can interactwith the air atomicelectrons producing a real
W−boson—the so-called Glashow resonance. This reso-
nance has in fact been observed by the IceCube neutrino
observatory [22] and represents an important contribution to
the expected neutrino event rate around such energies.
In this case, the total number of expected ¯
νe-induced
events can be assumed to be proportional to σNCMνeðNCÞþ
σCCMνeðCCÞþσGM¯
νeðWÞ, where we denote M¯
νeðWÞas
the effective mass for resonant antineutrino interactions,
and σGðE¯νÞis the Glashow resonance cross section, which
is a function of the antineutrino energy. The W-boson
decays into hadronic particles or a lepton. Following the
above considerations, MðWÞcan be approximated as
M¯
νeðWÞ≃1=9MνeðCCÞþ2=3MνeðNCÞþ ð4Þ
1=9ðBRτ→eMνeðCCÞþBRτ→hadMνeðNCÞÞ;ð5Þ
where we have used the approximation that the effective
mass of the array for the produced electron in the decay of
the Wis equal MνeðCCÞ, and for hadronic final states, it
follows MνeðNCÞ. The fractions accompanying the effec-
tive masses in Eq. (5) account for the (approximate)
branching ratios of the W-boson branching ratios (BRs)
to electrons (∼0.11), hadrons (∼0.68), and τ-leptons
(∼0.11) with BRτ→e∼0.17 and BRτ→had ∼0.65 denoting
the tau branching ratios into electron and hadronic par-
ticles, respectively. The decay of the W-boson to a muon is
neglected since the single muon is assumed not to produce
a detectable shower, as explained before.
With all the assumptions and approximations above,
we have estimated the expected number of neutrinos per
year, considering an extensive air shower array with an area
of 1km2and a fill factor of 80%. This is shown in Fig. 12
as a function of the neutrino energy and for the different
neutrino flavors and channels. Accounting for the Glashow
resonance of ¯
νehas a noticeable impact on the total number
of expected neutrinos in the energy region around ≈6PeV.
The integrated number of events per year above a given
energy is also shown in Fig. 12 as a red line. Integrating
from 100 TeV up to 100 PeV, one would conservatively
expect approximately two neutrino events per year. As
discussed before, a more realistic array with a fill factor of
∼5% would reduce the event rates by a factor ≲3.
VIII. SENSITIVITY TO UPWARD-GOING
ELECTRON NEUTRINOS
A study was carried out of the possibility of upward-going
neutrino events contributing to the estimated event rate in a
gamma-ray ground-based array of WCD. The
AIRES
frame-
work was used to simulate the development of upward-
going showers, as the version of
CORSIKA
code used
throughout this work is unable to treat showers in dense
homogeneous media such as Earth’s crust. We simulated
upward-going showers induced by electron neutrinos,
although our conclusions below apply to any type of
upward-going shower. Since an electron neutrino is not a
default primary particle in
AIRES
, we obtained the secondary
products of the νeinteraction with
CORSIKA
, and inject those
in
AIRES
to obtain the longitudinal and lateral development
of the shower underground. The composition of Earth’s crust
in
AIRES
is emulated by setting the atmosphere’s composi-
tion to match that of standard soil. According to [23], this
medium is characterized by ρ¼1.8gcm
−3and effective
atomic number Z¼11. This simulation setup was utilized
for inclined and very inclined upgoing showers, θranging
from 92° to 120° where Earth is not opaque to neutrinos
of PeV energies. We generated neutrinos with energy
Eν¼1PeV. The vertical height of the first interaction
assumed values between 2 and 5 m below the observation
level, as showers were severely attenuated for higher depths
and not sufficiently developed for smaller depths. Under
each set of conditions, 1000 showers were simulated.
The average footprint of the showers was inferred for each
combination of θand vertical depth underground. An
example is presented in Fig. 13 for showers with θ¼
100° initiated at a vertical depth of 3 m. As can be seen in
Fig. 13, the small dimensions of the footprints produced (of
the order of a few tens of m2in all cases) make their detection
at typical gamma-ray observatories such as LHAASO very
difficult, particularly in the sparse array. The detection would
eventually be possible in a compact array with larger filling
6
10 7
10 8
10
/GeV
ν
E
4−
10
3−
10
2−
10
1−
10
1
-1
/ yr
dt
ν
dN
νAll
Cumulative
FIG. 12. Event rates for all neutrino flavors within each energy
bin from 100 TeV to 100 PeV. Each decade in energy is divided
into four bins. The enhancement of the event rate at Eν∼6.3PeV
is due to the Glashow resonant interaction of ¯
νe. The red line
gives the sum of all event rates above Eν.
EVALUATION OF THE POTENTIAL OF A GAMMA-RAY …PHYS. REV. D 106, 102001 (2022)
102001-9

factor of a gamma-ray observatory. For our nominal array
with an 80% filling factor, ∼50% of the simulated events in
the example shown in Fig. 13 have less than five triggered
WCD stations as seen in the inset panel. Even in this case, the
involved effective areas would not be sufficient to perform a
competitive measurement, since the shower has to be
produced at less than ∼10 m vertical depth below the array
for it to develop before attenuating in Earth. This limitation
induces a small effective detection volume in comparison to
other detection techniques such as the observation of an
emerging τdecay in the atmosphere [12]. We conclude that
showers induced by upgoing neutrinos do not contribute
significantly to the estimated event rate in the PeV energy
range explored in this work.
The Earth-skimming tau-neutrino detection method con-
sists of the observation of a shower induced by the decay of
a tau lepton in the atmosphere. The tau is produced by a
quasihorizontal tau neutrino interacting in Earth, with
zenith angle between θ¼90° and typically θ≃93° corre-
sponding to the zenith angle range where the shower can
trigger an array of detectors. At the energies of interest in
this work, ∼PeV, the decay length of a tau lepton is of the
order of 50 m, and for this reason, the production of a tau-
induced shower would be around 10 times more likely at
PeV energies than the generation of a more upward-going
shower inside Earth that needs to initiated between 2 and
5 m depth, as explained above. However, this is partly
compensated by the smaller solid angle where the shower
can trigger the detector ∼0.22 sr for θ∈ð90°;92°Þcom-
pared to ∼2.92 sr for θ∈ð92°;120°Þ. On the other hand,
the tau-decay-induced shower produced in the atmosphere
generates a footprint which will be highly dependent on the
exit angle, altitude of decay, and trigger conditions. One
can roughly estimate a footprint of ∼km length on the array
that would be more efficiently detected than the small and
narrow upward-going shower produced in the larger
density medium inside Earth. As a result, the Earth-
skimming technique would be, in principle, more efficient
in relative terms than the detection of the upward-going
showers discussed here. A more quantitative evaluation of
the impact of the Earth-skimming tau-neutrino channel on
the total neutrino event rate requires a detailed simulation
of the trigger efficiency of the EAS array to quasihorizontal
atmospheric showers, possibly considering the topography
of the site, which is beyond the scope of this work. Our
results in this respect should be regarded as conservative.
IX. FINAL REMARKS AND CONCLUSIONS
In this work, we have investigated the possibility of using
gamma-ray wide-field-of-view observatories to detect show-
ers induced by astrophysical neutrinos in the 100 TeV to
100 PeV energy range. The discrimination from the over-
whelming cosmic-ray-induced background has been
achieved through the detection of inclined showers and
inspecting the balance between their electromagnetic and
muonic content of the shower at the ground, two observables
that are typically accessible in gamma-ray experiments and
used for photon-hadron discrimination. An end-to-end sim-
ulation procedure emulating the detector response has been
applied to electron neutrino events and conservatively
extrapolated for the remaining neutrino and antineutrino
species and interaction channels. The expected number of
neutrinos observed through this method in an array with an
effective area of 1km2for energies above 100 TeV is around
two per year. This is not a considerable number, particularly
when compared with dedicated experiments working in the
same energy range, such as IceCube, which sees a few tens of
events per year. Nonetheless, in the context of multimes-
senger science and the pursuit of these events, it is not
negligible either. Note that gamma-ray observatories are
already operating, or will be in the near future, so the
potential gain of these additional events is essentially for
free. Moreover, this measurement has been performed
assuming a diffusive neutrino background implying that
the detected neutrinos could be used to alert other experi-
ments with a few minutes latency.
In this work, it has also been demonstrated that, while a
very sensitive detection channel at very high energies,
the use of upward-going events does not add much to the
expected neutrino event rate due to the reduced size of
the shower footprint and the relatively shallow depths of
neutrino interaction needed for the shower developing
underground to arrive at the array.
The number of expected neutrinos could benefit from the
topography surrounding the experiments, such as moun-
tains, as suggested in [24,25]. These experiments are
usually placed at high altitudes on plateaus at the foot of
mountains. A shower whose reconstructed direction coin-
cides with emerging from inside a mountain is a clear
evidence of a neutrino-induced event, although the esti-
mated rates are small.
Finally, this work has aimed to be a proof of concept, and
more sophisticated analyses that could lead to higher
30−20−10−010 20 30
x/m
10−
0
10
20
y/m
1
10
2
10
3
10
/p.e〉Signal〈
0 2 4 6 8 10 12 14
Active Stations
0
50
100
150
Entries
FIG. 13. Average footprint produced by a shower induced by an
upgoing electron neutrino with Eν¼1PeV and θ¼100° inter-
acting at a vertical depth below ground of 3 m. The inset panel
shows the histogram of the number of active WCD stations
(stations that register signal above 10 p.e.).
JAIME ALVAREZ-MUÑIZ et al. PHYS. REV. D 106, 102001 (2022)
102001-10

counts are naturally envisaged. These analyses are experi-
ment dependent, and this work has shown that it is a
compelling line of research to be pursued at km2-scale,
gamma-ray, ground-based observatories such as those
pursuing PeV gamma-ray astronomy.
ACKNOWLEDGMENTS
We would like to thank to Sofia Andringa and Enrique
Zas for useful discussions and suggestions, and Ioana Mariş
for carefully reading the manuscript. This work has been
financed by national funds through FCT—Fundação para a
Cincia e a Tecnologia, I. P., under Project No. PTDC/FIS-
PAR/4300/2020. R. C. is grateful for the financial support
by OE—Portugal, FCT, I. P., under Grant No. DL57/2016/
cP1330/cT0002. This work has received financial support
from Xunta de Galicia (Centro singular de investigación
de Galicia accreditation 2019–2022), by European Union
ERDF, and by the “María de Maeztu”Units of Excellence
Program No. MDM-2016-0692 and the Spanish Research
State Agency, and from Ministerio de Ciencia e Innovación
Grants No. PID2019–105544 GB-I00 and No. RED2018-
102661-T (RENATA).
APPENDIX: FITS TO THE PROTON FISHER
CUMULATIVE DISTRIBUTION TAIL
A few examples of the normalized cumulatives of
the Fisher value distributions for proton showers within
the region of interest are presented here. The formula of the
exponential fit performed to the tail of the cumulative is
presented in each figure. The exponential fit is presented
as a solid black line, and the shaded area represents its
1-sigma uncertainty. This fit was used to extrapolate to
higher background rejection factors (smaller contamination
fractions εp).
1−0.8−0.6−0.4−0.2−0
Fisher Value
2−
10
1−
10
1
p
ε
3.32) * F.V. )± 1.35) + (-12.24 ± = exp( (-6.33 ε
(a)
0.6−0.5−0.4−0.3−0.2−0.1−
Fisher Value
4−
10
3−
10
2−
10
1−
10
p
ε
1.05) * F.V. )± 0.47) + (-8.18 ± = exp( (-8.00 ε
(b)
0.8−0.7−0.6−0.5−0.4−0.3−0.2−0.1−0
Fisher Value
4−
10
3−
10
2−
10
1−
10
p
ε
1.62) * F.V. )± 0.42) + (-5.03 ± = exp( (-6.23 ε
(c)
1−0.8−0.6−0.4−0.2−0
Fisher Value
3−
10
2−
10
1−
10
p
ε
1.79) * F.V. )± 0.90) + (-3.44 ± = exp( (-5.71 ε
(d)
FIG. 14. Example of the exponential fits to the tail of the cumulative proton distributions (solid black line) used to extrapolate to higher
background rejection factors (smaller contamination fractions εp). The 1-sigma uncertainty of the fit corresponds to the shaded area.
(a) θ¼60°;E
p¼104GeV. (b) θ¼60°;E
p¼106GeV. (c) θ¼70°;E
p¼107GeV. (d) θ¼75°;E
p¼109GeV.
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