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Combined search in dwarf spheroidal galaxies for
branon dark matter annihilation signatures with the
MAGIC telescopes
To cite this article: S. Abe et al JCAP03(2025)020
 
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ournal of Cosmology and Astroparticle Physics
An IOP and SISSA journalJ
Received: August 16, 2024
Accepted: December 21, 2024
Published: March 12, 2025
Combined search in dwarf spheroidal galaxies for branon
dark matter annihilation signatures with the MAGIC
telescopes
The MAGIC collaboration
S. Abe et al.
Full author list at the end of the paper
E-mail: contact.magic@mpp.mpg.de
Abstract: Massive brane fluctuations, called branons, behave as weakly interacting massive
particles, which is one of the most favored class of candidates to fulfill the role of the dark
matter (DM), an elusive kind of matter beyond the Standard Model. We present a multi-
target search in dwarf spheroidal galaxies for branon DM annihilation signatures with a total
exposure of 354 hours with the ground-based gamma-ray telescope system MAGIC. This
search led to the most constraining limits on branon DM in the sub-TeV and multi-TeV DM
mass range. Our most stringent limit on the thermally-averaged annihilation cross-section (at
95% confidence level) corresponds to ⟨σv⟩ ≃ 1.9×10−24 cm3s−1 at a branon mass of ∼ 1.5TeV.
Keywords: dark matter experiments, gamma ray experiments, cosmology of theories
beyond the SM
ArXiv ePrint: 2408.08009
© 2025 The Author(s). Published by IOP Publishing
Ltd on behalf of Sissa Medialab. Original content from
this work may be used under the terms of the Creative Commons
Attribution 4.0 licence. Any further distribution of this work must
maintain attribution to the author(s) and the title of the work,
journal citation and DOI.
https://doi.org/10.1088/1475-7516/2025/03/020
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Contents
1 Introduction 1
2 Gamma rays from branon annihilation 2
3 dSph observations by the MAGIC telescopes 3
4 Analysis technique 4
4.1 Data reduction 4
4.2 Likelihood analysis 5
5 Results 6
6 Discussion and conclusions 7
The MAGIC collaboration 15
1 Introduction
The nature of dark matter (DM) is still an open question for modern physics. This non-
baryonic and non-relativistic kind of matter is suggested to be accountable for 84% of the
matter density of the Universe [1]. Among many other DM candidates [2], massive brane
fluctuations (branons) emerging from the brane-world theory [3] have been proposed as DM
candidates, since their characteristics match the ones of weakly interacting massive particles
(WIMPs) [4]. Gamma-ray telescopes could potentially detect DM, in particular branons,
indirectly by observing photons, e.g. via quark hadronization or final state radiation from
charged particles, in the very-high energy (VHE, ≳ 50GeV) domain of astrophysical regions
presenting large DM densities.
Dwarf spheroidal galaxies (dSphs) are preferred targets for indirect DM searches. Contrary
to the Galactic Center (GC) and galaxy clusters, also very prominent targets for DM
searches [5, 6], dSphs are not expected to host any strong conventional gamma-ray emitter
that may hinder the detection of a subdominant DM signal. In addition, dSphs are not as
extended targets as the GC or galaxy clusters, with source angular extension presenting a
challenge for ground-based gamma-ray telescopes due to their angular resolution. Nevertheless,
the determination of the DM content in those objects remains the most uncertain ingredient
in most DM analyses. Previous work, the first branon DM search in the VHE domain with
the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes [7, 8], utilized the
deepest exposure on any single dSph to date, namely Segue 1. Being an interesting target
for DM searches, the DM content of Segue 1 has been an active subject of debate [9]. A
refined analysis was carried out in [9, 10] with a more accurate determination of member
stars in Segue 1, leading to a lower and more uncertain value for its DM content than
previously determined in [11]. With the aim of providing more robust and more constraining
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results, in this work we performed a multi-target branon DM search using two independent
determinations of the DM content from the literature.
The present article provides a search for branon DM with gamma rays by combining
MAGIC observations of dSphs with a total accumulation of 354 hours leading to the most
stringent and robust branon DM limits in the sub-TeV and multi-TeV DM mass range to date.
In section 2, we briefly review the brane-world theory and we present the expected photon
flux from branon DM annihilation. The observational campaigns on dSphs by the MAGIC
telescopes and the adopted estimations of the DM content in those objects are summarized
in section 3. The analysis methodology is explained in section 4, while the final results in
terms of upper limits (ULs) on the annihilation cross section of branon DM particles and
the tension of the brane are presented in section 5. Finally, we discuss the ULs and compare
them with the model-independent ULs from MAGIC [12] in section 6.
2 Gamma rays from branon annihilation
Standard Model (SM) fields could exist on a tridimensional brane embedded in a higher
dimensional spacetime, where gravity propagates. These extra-dimensional models [13–16]
were originally proposed as a potential solution to the hierarchy problem. However, they
also provide us with natural DM particle candidates. In the context of the brane-world
scenario with low1 brane tension f , massive brane fluctuations (branons) in the direction
of the N extra-dimensions are natural DM candidates [3, 18]. The lowest-order effective
Lagrangian for branon DM reads [19, 20]
L = 12g
µν∂µπ
α∂νπ
α − 12m
2
χπ
απα + 18f4
(
4∂µπα∂νπα −m2χπαπαgµν
)
TµνSM, (2.1)
where π is the branon field and α runs over the N extra-dimensions, mχ is the particle mass
of the branon, and TµνSM is the energy-momentum tensor of the SM fields. The coupling of
the branons to the SM particles is suppressed by the fourth power of the tension of the
brane, rendering them as WIMPs.
The expected differential photon flux produced by branon DM annihilation [20] is
composed of the two terms: (i) the astrophysical factor (J -factor; see section 3), which
depends on both the distance l to the target, and the DM distribution ρDM at the source
region denoted by its subtended solid angle ∆Ω, and (ii) the particle physics factor, which
includes the branon DM annihilation photon yield. It reads as
dΦ
dE (⟨σv⟩) =
1
4π
∫
∆Ω
dΩ′
∫
l.o.s.
dl ρ2DM(l,Ω′)︸ ︷︷ ︸
J -factor
· ⟨σv⟩2m2χ
n∑
i=1
Bri
dNi
dE︸ ︷︷ ︸
DM annihilation
, (2.2)
where ⟨σv⟩ is the thermally-averaged annihilation cross section and l.o.s. stands for line-of-
sight. The branon branching ratios Bri as a function of mχ have been calculated following
the prescriptions in [20] including annihilation into the SM pairs W+W−, ZZ, hh, e+e−,
tt¯, cc¯, µ+µ−, τ+τ− and bb¯. However, the W+W−, ZZ and hh channels are the dominant
1The low brane tension regime refers to when the tension of the branon is greater than the mass of the
branon, where the branon dynamic is given by the Nambu-Goto action added to the usual SM action [17].
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contributors in our search for TeV branon DM. The differential photon yields per annihilation
dNi/dE, including electroweak (EW) corrections, are taken from the PPPC 4 DM ID
distribution for this work [21]. The resulting differential photon yield per branon annihilation
for a set of branon DM masses can be found in [7, 8, 22, 23].
3 dSph observations by the MAGIC telescopes
The Florian Goebel Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes2
are two 17-m diameter reflector imaging atmospheric Cherenkov telescopes (IACTs) situated
at an altitude of 2200 m a.s.l. at the Roque de los Muchachos Observatory (28.8◦ N, 17.9◦ W)
on the Canary Island of La Palma, Spain. MAGIC inspects the VHE gamma-ray sky (above
≳ 30GeV) with a 3.5◦ field of view probing the most extreme astrophysical environments in
our universe. The point-source 5σ sensitivity above 220GeV of MAGIC is ∼ 0.7% of the Crab
Nebula flux for 50 h of observations near zenith with an associated energy resolution of ∼ 16%
and a 0.07◦ angular resolution measured as the 68% containment radius of the gamma-ray
excess. A detailed performance study of the MAGIC telescopes can be found in [24].
The MAGIC Collaboration has carried out extensive observational campaigns on dSphs
in the Northern Hemisphere throughout the years, motivated by the search for DM signals in
these objects. At first, MAGIC observed the dSphs Draco, Willman 1, and Segue 1 with the
MAGIC-I telescope in single telescope mode around 2009 [25, 26]. Those data have not been
used in this work because of the superseding sensitivity by the additional MAGIC-II telescope.
After upgrading MAGIC to a stereoscopic IACT system, Segue 1 was observed between 2011
and 2013 with an exposure of 158 hours [27, 28]. This is still the deepest observation of
any dSph by an IACT to date. Additionally, MAGIC observed Ursa Major II between 2014
and 2016 [29], Draco in 2018, and Coma Berenices in 2019 leading to a total accumulation
of 354 hours of dSph observations [12]. The observation of Triangulum II by the MAGIC
telescopes [30] has been excluded due to the statistical uncertainty on the determination of
the DM distribution in this object [31]. The dSph observations by the MAGIC telescopes
included in this combined search for branon DM are summarized in table 1. No effects of
the extragalactic background light absorption [32] are considered in our analysis, since the
observed dSphs are positioned only a few tens of kpc away from us (see table 2).
The driving factor of the search for DM annihilation signatures in dSphs is the estimation
of the DM content in those objects. This is a challenging task resulting in rather large
uncertainties, which are dominant in our analysis. Therefore, this work includes a systematic
study on the impact of the estimation of the J -factors to our derived constraints by performing
the same likelihood analysis (see section 4.2) with two different sets of the J -factors from the
literature, i.e. Geringer-Sameth et al. [11] (henceforth referred to as GS15) and Bonnivard
et al. [10] (henceforth referred to as B16). The derivation of the two J -factor sets was
carried out in [10, 11] using a Jeans analysis [34] of the same kinematic stellar data for
Segue 1, Ursa Major II, and Coma Berenices (a detailed description can be found in [11]).
B16 [10] adopted the kinematic stellar data for the classical dSph Draco from [35], which
differs from the data used by [11]. The main differences between the two approaches are the
2https://magic.mpp.mpg.de.
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Name zd [◦] Tobs [h] E [TeV] θ [◦] SLi&Ma[σ]
Coma Berenices 5− 37 49 0.06− 10 0.17 0.8
Draco 29− 45 52 0.07− 10 0.22 −0.7
Segue 1 13− 37 158 0.06− 10 0.12 −0.5
Ursa Major II 35− 45 95 0.12− 10 0.30 −2.1
Table 1. Summary of the considered dSph observations by the MAGIC telescopes [12]. We report
the zenith distance (zd) range, the total observation time (Tobs), and the energy range (E). We also
list the angular radius (θ) of the signal region and the significance of detection (SLi&Ma) calculated by
following Li&Ma [33]. Please note that the significance of detection is not reported for Coma Berenices
and Draco in [12], but no gamma-ray excess has been found.
Name Distance l, b log10 J(θmax) {GS15} log10 J(θmax) {B16}
[kpc] [◦] [log10(GeV2cm−5sr)] [log10(GeV2cm−5sr)]
Coma Berenices 44 241.89, 83.61 19.02+0.37−0.41 20.13+1.56−1.08
Draco 76 86.37, 34.72 19.05+0.22−0.21 19.42+0.92−0.47
Segue 1 23 220.48, 50.43 19.36+0.32−0.35 17.52+2.54−2.65
Ursa Major II 32 152.46, 37.44 19.42+0.44−0.42 20.60+1.46−0.95
Table 2. Summary of the dSph properties. We report the heliocentric distance and Galactic
coordinates of each dSph, as well as the total J -factor values and its ±1σ uncertainties from GS15 [11]
and B16 [10] used in the present work. The maximum angular distance θmax is the angular distance
from the center to the outermost member star considered in the J -factor calculation.
selection of the DM density, velocity anisotropy, and light profiles, as well as the inclusion
of systematic uncertainties in [10]. The J -factor values and its uncertainties are listed in
table 2 and visualized in figure 1. The largest discrepancy is found for the J -factor of
Segue 1, since the Jeans analysis in B16 [10] is extremely sensitive on the determination of
the member stars. The contamination of the dSph stellar sample by a foreground population
with different velocity properties complicates membership determination [9] leading to an
artificially inflated J -factor estimation in GS15 [11], where the foreground population is
wrongly included in the Jeans analysis.
4 Analysis technique
4.1 Data reduction
The low-level data reduction of the four dSph observations was performed in [12] using the
standard MAGIC analysis software MARS [36]. We re-analyse the resulting high-level data
of four dSph observations [12] in the context of brane-world extra-dimensional theories using
the same open-source analysis software tools [37] for multi-instrument and multi-target DM
searches gLike3 [38] and LklCom4 [39].
3https://github.com/javierrico/gLike.
4https://github.com/TjarkMiener/likelihood_combiner.
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Coma Berenices Draco Segue 1 Ursa Major II
15
16
17
18
19
20
21
22
J-f
ac
to
r [
lo
g 1
0(
Ge
V2
cm
5 s
r)]
Geringer-Sameth et al. (2015)
Bonnivard et al. (2016)
Figure 1. Comparison of the J -factor values and its uncertainties from GS15 [11] (green dots) and
B16 [10] (blue stars) for all considered dSphs.
4.2 Likelihood analysis
In this work, we used the same likelihood analysis as [12], which was originally proposed in [40],
further utilized in [28, 29] and discussed in [41]. In order to obtain the expected branon DM
signal for the MAGIC telescopes, the theoretical branon DM flux (eq. 2.2) is convolved with
the instrument response functions (IRFs) for the signal (ON) region IRFON (E,E′) including
the morphology of the dSph via the “Donut” MC method [29], which can be described by the
PDF for the energy estimator and the effective collection area. The Donut MC method is the
procedure to build the IRFs with a specific MC sample representing the source morphology
rather than using MC for an assumed point-like source. The specific MC samples are produced
by selecting events from the diffuse MC resulting in a donut-shaped distribution. E and E′
are the true and estimated energy of the gamma-ray photon, respectively. The expected
number of signal events in the i-th energy bin yields
si(⟨σv⟩) = Tobs
∫ Emax,i
Emin,i
dE′
∫ ∞
0
dΦ(⟨σv⟩)
dE IRFON
(
E,E′
)
dE, (4.1)
where Tobs is the total observation time and Emin,i and Emax,i are the lower and upper
limits of the i-th energy bin. The thermally-averaged annihilation cross section ⟨σv⟩ is our
parameter of interest and therefore the only free parameter in our likelihood analysis.
The binned (Nbins = 30) likelihood function of the dataset D′ with nuisance parameters
ν reads as:
Lbin
(⟨σv⟩;ν | D′) = Nbins∏
i=1
[
P(si(⟨σv⟩) + bi | NON,i) · P(τbi | NOFF,i)
]
× T (τ | τo, στ ) (4.2)
where P(x|N) stands for a Poisson distribution with mean x and measured value N , while
NON,i, NOFF,i are the total number of observed events in the i-th energy bin in the signal
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(ON) and background (OFF) regions, respectively. The background events in the 30 bin
in energy and the normalization between background and signal regions τ are nuisance
parameters, which leads to a total of 31 nuisance parameters in eq. 4.2. The likelihood
function T (τ | τo, στ ) is a Gaussian with mean τo = 1.0 and variance σ2τ , which include
statistical and systematic uncertainties on τ following στ =
√
σ2τstat + σ2τsyst . Based on
a dedicated performance study of the MAGIC telescopes [24], we typically considered a
systematic uncertainty of στsyst = 1.5% · τ on the estimate of the residual background.
The joint likelihood function L is a nested product of the binned likelihood function
Lbin,kl (eq. 4.2) for each dSphs (NdSphs = 4) and their distinct observational datasets Dkl
with individual set of IRFs due to different observational conditions or hardware setup of
the instrument. It reads as:
L (⟨σv⟩) =
NdSphs∏
k=1
Nobs,k∏
l=1
[
Lbin,kl (⟨σv⟩,νkl | Dkl)
]
× Jk
(
Jk | Jo,k, σlog10 Jk
)
(4.3)
where Nobs,k is the number of observations for the k-th dSph and νkl represents the set of
nuisance parameters different from the J -factor affecting the analysis of dataset Dkl. Given
the importance of the J -factors and their uncertainties (see section 3), we treat the J -factors
as nuisance parameters using the likelihood Jk for the J -factor of the k-th dSph (ignoring
index k in the following for the sake of clarity)
J (J | Jo, σlog10 J) = 1ln (10)Jo√2πσlog10 J exp
(
−(log10 J − log10 Jo)
2
2σ2log10 J
)
, (4.4)
where J is the true value of the J -factor and Jo is the observed J -factor with error σlog10 J [42].
In the absence of a branon DM signal, ULs on ⟨σv⟩ for all datasets D are set using
a test statistic defined as
TS = −2 ln
L
(
⟨σv⟩; ̂̂ν | D)
L
(
⟨̂σv⟩; ν̂ | D
)
, (4.5)
where ⟨̂σv⟩ and ν̂ are the values that globally maximize L, and ̂̂ν is the set of values that
maximize L for a particular value of ⟨σv⟩. In particular, the ULs on ⟨σv⟩ are computed
by solving TS = 2.71, where 2.71 corresponds to a one-sided 95% confidence level [43]. No
additional boosts from the presence of substructures [44] or quantum effects [45] entered
the computation of the final results.
5 Results
Our likelihood analysis is coherent with all previously reported results [26–28, 46] in that
no gamma-ray signal has been detected (see also table 1). Thus, we present the 95%
confidence level upper limits (ULs) on the thermally-averaged cross-section ⟨σv⟩ for branon
DM annihilation in a particle mass range from 100GeV to 100TeV. The ULs are obtained
with the before-mentioned combined analysis of multiple dSph observations with the MAGIC
telescopes for two different sets of J -factors (see figure 2). We include systematic uncertainties
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in the residual background intensity and statistical uncertainties in the J -factor in our
likelihood analysis. Our strongest limit is ⟨σv⟩ ≃ 1.9× 10−24 cm3s−1 for a ∼ 1.5TeV mass
branon DM particle.
We obtain the two-sided 68% and 95% containment bands as well as the median from
the distribution of ULs performing the same analysis of 300 fast simulations of the source
and background regions assuming no DM signal (⟨σv⟩ = 0). As expected, our constraints
are located within the 68% containment band for both sets of J -factors. The ULs from
each individual dSph observation are also depicted in figure 2. For GS15, the combined
analysis is dominated by Ursa Major II and Segue 1, while the latter target does not have
any substantial contribution in the combination for B16. Given the rather huge negative
fluctuation of the Ursa Major II observation (−2.1σ for a conventional IACT analysis; see
table 1) and Ursa Major II being the most dominant dSph in the analysis for B16, the combined
limit for B16 locates significantly below the median. The estimated branon sensitivity for
300 h observation on the dSph Draco with the future Cherenkov Telescope Array (CTA) [22]
lays an order of magnitude below the median of both presented analyses, as expected.
We set constraints to the specific parameter space of the branon DM model (see figure 3),
i.e. the tension of the brane f(mχ) versus the branon DM mass ranging from 100GeV to
100TeV, by translating our ⟨σv⟩ ULs to constraints on f [7, 8]. The combined analysis of this
work allows us to exclude a significantly larger portion of the brane tension parameter space
than previous branon ULs in the literature by CMS [47], Cembranos et al. [48] with AMS-02
e+e− data [49], and MAGIC with the observation of Segue 1 [7, 8], for both sets of J -factors,
GS15 and B16. Although, the constraints obtained by Cembranos et al. [48] with AMS-02
data [49] would require an updated analysis including more recent AMS-02 data from [50].
6 Discussion and conclusions
The branon DM exclusion limits are compared with the dominant annihilation mode W+W−,
ZZ, and hh in the branon DM model at VHE. The model-independent ULs in figure 4 are
taken from [12], which rely on the same dSph datasets with the same analysis scheme. In [12],
the J -factor values of GS15 were used to compute the model generic DM exclusion limits.
The ULs for branon DM annihilation are enclosed by the dominant annihilation channels
verifying the correctness of the performed analysis (see figure 4).
In comparison with the model-independent search for DM [12], this work is not only
capable of constraining the thermally-averaged cross-section ⟨σv⟩, but also the brane tension
f(mχ). The tension of the brane can be affected by various factors, such as the curvature
of the spacetime, the number of dimensions in the brane, and the type of matter present
in the brane. It plays a crucial role in theories such as string theory and brane cosmology,
which aim to explain the fundamental nature of our universe. It helps to determine the
dynamics and behavior of branes within a given spacetime.
This work supersedes the exclusion limits from CMS [47] and Cembranos et al. [48] with
AMS-02 data even at the upper edge of the sub-TeV DM mass range leading to the most
constraining branon DM limits above ∼ 700GeV by combining all major dSph observations
of the MAGIC telescopes. Even more stringent and robust exclusion limits of the branon
DM annihilation over a wider range of branon DM masses can be achieved in the framework
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10 1 100 101 102
m [TeV]
10 28
10 26
10 24
10 22
10 20
v
[c
m
3 /s
]
J-factors (Geringer-Sameth et al.)
All dSphs (354 h)
H0 median 
H0 68% containment 
H0 95% containment 
Thermal relic cross section
Segue1 (158 h)
Ursa Major II (95 h)
Coma Berenices (49 h)
Draco (52 h)
Excluded by Cembranos et al.
Excluded by CMS
CTA sensitivity (300 h)  
SKA1-MID sensitivity (1000 h) 
10 1 100 101 102
m [TeV]
10 28
10 26
10 24
10 22
10 20
v
[c
m
3 /s
]
J-factors (Bonnivard et al.)
All dSphs (354 h)
H0 median 
H0 68% containment 
H0 95% containment 
Thermal relic cross section
Segue1 (158 h)
Ursa Major II (95 h)
Coma Berenices (49 h)
Draco (52 h)
Excluded by Cembranos et al.
Excluded by CMS
CTA sensitivity (300 h)  
SKA1-MID sensitivity (1000 h) 
Figure 2. 95% ULs on ⟨σv⟩ for branon DM annihilation from the combined analysis (solid black line)
and the analysis of the individual dSphs (Segue 1 purple, Ursa Major II cyan, Draco lime green, and
Coma Berenices steel blue). The median and the two-sided 68% and 95% containment bands of the
combined analysis are depicted by the dotted black line, green and yellow bands, respectively. The
red dashed line indicates the thermal relic cross-section from [4]. The blue exclusion region represents
the tightest constraints to branons model by colliders obtained from CMS data [47] and the orange
exclusion region was obtained by Cembranos et al. from an analysis [48] of AMS-02 e+e− data [49].
They were translated to the ⟨σv⟩ parameter space from [17]. The estimated branon sensitivity for
300 h observation of Draco with the future CTA is depicted by the purple dashed-dotted line [22].
The yellow dotted line represents the estimated sensitivity for 1000 h observation of Draco with the
planned SKA assuming the W+W− annihilation mode [17].
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10 1 100 101 102
m [TeV]
10 1
100
101
102
f[
Te
V]
All dSphs (354 h) - J-factors (Bonnivard et al.)
All dSphs (354 h) - J-factors (Geringer-Sameth et al.)
MAGIC Segue 1 limits (JCAP05(2022)005)
Thermal relic cross section
m /4
Excluded by Cembranos et al.
Excluded by CMS
CTA sensitivity (300 h)  
SKA1-MID sensitivity (1000 h) 
Figure 3. 95% ULs on f for branon DM annihilation from the combined analysis with the B16
J -factors set (green exclusion region) and the GS15 J -factors set (solid black line). The ULs previously
obtained with the MAGIC observation of Segue 1 are depicted by the dashed black line [7, 8]. The
grey dashed region depicts the model validity limit in the f (mχ) parameter space.
of multi-instrument and multi-messenger DM searches [51, 52] by performing a global branon
DM search with a joint analysis of observational data from different ground/space-based
gamma-ray and neutrino telescopes. Future instruments, such as CTA and SKA, will probe
even a larger fraction of the exclusion region, providing valuable complementary information
in both gamma-ray and radio observations, respectively.
Acknowledgments
T. Miener: Principal investigator, MAGIC data analysis, publication coordination; D. Ker-
szberg: MAGIC data analysis, publication coordination; V. Gammaldi: Branon Dark Matter
theory, interpretation J. Rico: Statistical analysis supervision and software framework devel-
opment; D. Nieto: supervision and coordination, interpretation. The rest of the authors have
contributed in one or several of the following ways: design, construction, maintenance, and
operation of the instrument(s); preparation and/or evaluation of the observation proposals;
data acquisition, processing, calibration and/or reduction; production of analysis tools and/or
related Monte Carlo simulations; discussion and approval of the contents of the draft. We
would like to thank the Instituto de Astrofísica de Canarias for the excellent working condi-
tions at the Observatorio del Roque de los Muchachos in La Palma. The financial support
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10 1 100 101 102
m [TeV]
10 24
10 23
10 22
v
[c
m
3 /s
]
Branon DM (this work)
W+W  (Acciari et al.)
ZZ (Acciari et al.)
hh (Acciari et al.)
Figure 4. Comparison of the 95% ULs on ⟨σv⟩ for branon DM annihilation (black, this work) and
the dominant annihilation mode W+W− (yellow), ZZ (purple), and hh (blue) in the branon DM
model (extracted from [12]).
of the German BMBF, MPG and HGF; the Italian INFN and INAF; the Swiss National
Fund SNF; the grants PID2019-104114RB-C31, PID2019-104114RB-C32, PID2019-104114RB-
C33, PID2019-105510GB-C31, PID2019-107847RB-C41, PID2019-107847RB-C42, PID2019-
107847RB-C44, PID2019-107988GB-C22, PID2022-136828NB-C41, PID2022-137810NB-
C22, PID2022-138172NB-C41, PID2022-138172NB-C42, PID2022-138172NB-C43, PID2022-
139117NB-C41, PID2022-139117NB-C42, PID2022-139117NB-C43, PID2022-139117NB-C44
funded by the Spanish MCIN/AEI/ 10.13039/501100011033 and “ERDF A way of making Eu-
rope”; the Indian Department of Atomic Energy; the Japanese ICRR, the University of Tokyo,
JSPS, and MEXT; the Bulgarian Ministry of Education and Science, National RI Roadmap
Project DO1-400/18.12.2020 and the Academy of Finland grant nr. 320045 is gratefully
acknowledged. This work was also been supported by Centros de Excelencia “Severo Ochoa”
y Unidades “María de Maeztu” program of the Spanish MCIN/AEI/ 10.13039/501100011033
(CEX2019-000920-S, CEX2019-000918-M, CEX2021-001131-S) and by the CERCA insti-
tution and grants 2021SGR00426 and 2021SGR00773 of the Generalitat de Catalunya; by
the Croatian Science Foundation (HrZZ) Project IP-2022-10-4595 and the University of
Rijeka Project uniri-prirod-18-48; by the Deutsche Forschungsgemeinschaft (SFB1491) and
by the Lamarr-Institute for Machine Learning and Artificial Intelligence; by the Polish
Ministry Of Education and Science grant No. 2021/WK/08; and by the Brazilian MCTIC,
CNPq and FAPERJ. This work was supported by the Grant RYC2021-032552-I funded by
MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR.
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VG’s contribution to this work has been supported by Juan de la Cierva-Incorporación
IJC2019-040315-I grant, and by the PGC2018-095161-B-I00, PID2022-139841NB-I00 and
CEX2020-001007-S projects, both funded by MCIN/AEI/10.13039/501100011033 and by
“ERDF A way of making Europe”. VG thanks J.A.R. Cembranos for useful discussions.
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The MAGIC collaboration
S. Abe 1, J. Abhir 2, A. Abhishek3, V. A. Acciari 4, A. Aguasca-Cabot 5, I. Agudo 6,
T. Aniello7, S. Ansoldi 8,40, A. Arbet Engels 9, C. Arcaro 10, K. Asano 1, D. Baack11,
A. Babić 12, U. Barres de Almeida 13, J. A. Barrio 14, I. Batković 10, A. Bautista9, J. Baxter1,
J. Becerra González 15, W. Bednarek 16, E. Bernardini 10, J. Bernete17, A. Berti 9,
J. Besenrieder9, C. Bigongiari 7, A. Biland 2, O. Blanch 4, G. Bonnoli 7, Ž. Bošnjak 12,
E. Bronzini7, I. Burelli 8, A. Campoy-Ordaz 18, R. Carosi 19, M. Carretero-Castrillo 5,
A. J. Castro-Tirado 6, D. Cerasole 20, G. Ceribella 9, Y. Chai 1, A. Cifuentes 17,
E. Colombo 4, J. L. Contreras 14, J. Cortina 17, S. Covino 7, G. D’Amico 21, V. D’Elia7,
P. Da Vela 7, F. Dazzi 7, A. De Angelis 10, B. De Lotto 8, R. de Menezes22, J. Delgado 4,41,
C. Delgado Mendez 17, F. Di Pierro 22, R. Di Tria 20, L. Di Venere 20, D. Dominis Prester 23,
A. Donini 7, D. Dorner 24, M. Doro 10, D. Elsaesser 11, J. Escudero 6, L. Fariña 4,
A. Fattorini11, L. Foffano 7, L. Font 18, S. Fröse11, S. Fukami2, Y. Fukazawa 25,
R. J. García López 15, M. Garczarczyk 26, S. Gasparyan 27, M. Gaug 18,
J. G. Giesbrecht Paiva 13, N. Giglietto 20, F. Giordano 20, P. Gliwny 16, T. Gradetzke11,
R. Grau 4, D. Green 9, J. G. Green 9, P. Günther24, D. Hadasch 1, A. Hahn 9, T. Hassan 17,
L. Heckmann 9, J. Herrera Llorente 15, D. Hrupec 28, R. Imazawa 25, K. Ishio16,
I. Jiménez Martínez 9, J. Jormanainen 29, S. Kankkunen29, T. Kayanoki25, D. Kerszberg 4,47,∗,
G. W. Kluge 21,42, Y. Kobayashi1, P. M. Kouch 29, H. Kubo 1, J. Kushida 30, M. Láinez 14,
A. Lamastra 7, F. Leone7, E. Lindfors 29, S. Lombardi 7, F. Longo 8,43, R. López-Coto 6,
M. López-Moya 14, A. López-Oramas 15, S. Loporchio 20, A. Lorini3, E. Lyard31,
P. Majumdar 32, M. Makariev 33, G. Maneva 33, M. Manganaro 23, S. Mangano 17,
K. Mannheim 24, M. Mariotti 10, M. Martínez 4, M. Martínez-Chicharro17, A. Mas-Aguilar 14,
D. Mazin 1,44, S. Menchiari6, S. Mender 11, D. Miceli 10, T. Miener 14,48,∗, J. M. Miranda 3,
R. Mirzoyan 9, M. Molero González15, E. Molina 15, H. A. Mondal 32, A. Moralejo 4,
D. Morcuende 6, T. Nakamori 34, C. Nanci 7, V. Neustroev 35, M. Nievas Rosillo 15,
C. Nigro 4, L. Nikolić3, K. Nishijima 30, T. Njoh Ekoume4, S. Nozaki 9, A. Okumura36,
J. Otero-Santos 6, S. Paiano 7, D. Paneque 9, R. Paoletti 3, J. M. Paredes 5, M. Peresano 9,
M. Persic 8,45, M. Pihet10, G. Pirola9, F. Podobnik 3, P. G. Prada Moroni 19, E. Prandini 10,
G. Principe8, W. Rhode 11, M. Ribó 5, J. Rico 4, C. Righi 7, N. Sahakyan 27, T. Saito 1,
F. G. Saturni 7, K. Schmidt 11, F. Schmuckermaier 9, J. L. Schubert11, A. Sciaccaluga7,
G. Silvestri10, J. Sitarek 16, V. Sliusar 31, A. Spolon10, D. Sobczynska 16, J. Strišković 28,
D. Strom 9, M. Strzys 1, Y. Suda 25, H. Tajima36, R. Takeishi 1, P. Temnikov 33,
K. Terauchi37, T. Terzić 23, M. Teshima9,46, S. Truzzi3, A. Tutone 7, S. Ubach 18,
J. van Scherpenberg 9, M. Vazquez Acosta 15, S. Ventura 3, G. Verna3, I. Viale 10,
C. F. Vigorito 22, V. Vitale 38, I. Vovk 1, R. Walter31, F. Wersig 11, M. Will 9,
C. Wunderlich3, T. Yamamoto 39, V. Gammaldi 49,50,51,a,∗, D. Nieto 14,a
1 Japanese MAGIC Group: Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa,
277-8582 Chiba, Japan
2 ETH Zürich, CH-8093 Zürich, Switzerland
3Università di Siena and INFN Pisa, I-53100 Siena, Italy
4 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology (BIST),
E-08193 Bellaterra (Barcelona), Spain
5Universitat de Barcelona, ICCUB, IEEC-UB, E-08028 Barcelona, Spain
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6 Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, 18008, Granada, Spain
7National Institute for Astrophysics (INAF), I-00136 Rome, Italy
8Università di Udine and INFN Trieste, I-33100 Udine, Italy
9Max-Planck-Institut für Physik, D-85748 Garching, Germany
10Università di Padova and INFN, I-35131 Padova, Italy
11Technische Universität Dortmund, D-44221 Dortmund, Germany
12Croatian MAGIC Group: University of Zagreb, Faculty of Electrical Engineering and Computing (FER),
10000 Zagreb, Croatia
13Centro Brasileiro de Pesquisas Físicas (CBPF), 22290-180 URCA, Rio de Janeiro (RJ), Brazil
14 IPARCOS Institute and EMFTEL Department, Universidad Complutense de Madrid, E-28040 Madrid,
Spain
15 Instituto de Astrofísica de Canarias and Dpto. de Astrofísica, Universidad de La Laguna, E-38200, La
Laguna, Tenerife, Spain
16University of Lodz, Faculty of Physics and Applied Informatics, Department of Astrophysics, 90-236 Lodz,
Poland
17Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, E-28040 Madrid, Spain
18Departament de Física, and CERES-IEEC, Universitat Autònoma de Barcelona, E-08193 Bellaterra,
Spain
19Università di Pisa and INFN Pisa, I-56126 Pisa, Italy
20 INFN MAGIC Group: INFN Sezione di Bari and Dipartimento Interateneo di Fisica dell’Università e del
Politecnico di Bari, I-70125 Bari, Italy
21Department for Physics and Technology, University of Bergen, Norway
22 INFN MAGIC Group: INFN Sezione di Torino and Università degli Studi di Torino, I-10125 Torino, Italy
23Croatian MAGIC Group: University of Rijeka, Faculty of Physics, 51000 Rijeka, Croatia
24Universität Würzburg, D-97074 Würzburg, Germany
25 Japanese MAGIC Group: Physics Program, Graduate School of Advanced Science and Engineering,
Hiroshima University, 739-8526 Hiroshima, Japan
26Deutsches Elektronen-Synchrotron (DESY), D-15738 Zeuthen, Germany
27Armenian MAGIC Group: ICRANet-Armenia, 0019 Yerevan, Armenia
28Croatian MAGIC Group: Josip Juraj Strossmayer University of Osijek, Department of Physics, 31000
Osijek, Croatia
29 Finnish MAGIC Group: Finnish Centre for Astronomy with ESO, Department of Physics and Astronomy,
University of Turku, FI-20014 Turku, Finland
30 Japanese MAGIC Group: Department of Physics, Tokai University, Hiratsuka, 259-1292 Kanagawa,
Japan
31University of Geneva, Chemin d’Ecogia 16, CH-1290 Versoix, Switzerland
32 Saha Institute of Nuclear Physics, A CI of Homi Bhabha National Institute, Kolkata 700064, West Bengal,
India
33 Inst. for Nucl. Research and Nucl. Energy, Bulgarian Academy of Sciences, BG-1784 Sofia, Bulgaria
34 Japanese MAGIC Group: Department of Physics, Yamagata University, Yamagata 990-8560, Japan
35 Finnish MAGIC Group: Space Physics and Astronomy Research Unit, University of Oulu, FI-90014 Oulu,
Finland
36 Japanese MAGIC Group: Institute for Space-Earth Environmental Research and Kobayashi-Maskawa
Institute for the Origin of Particles and the Universe, Nagoya University, 464-6801 Nagoya, Japan
37 Japanese MAGIC Group: Department of Physics, Kyoto University, 606-8502 Kyoto, Japan
38 INFN MAGIC Group: INFN Roma Tor Vergata, I-00133 Roma, Italy
39 Japanese MAGIC Group: Department of Physics, Konan University, Kobe, Hyogo 658-8501, Japan
40Also at International Center for Relativistic Astrophysics (ICRA), Rome, Italy
41Also at Port d’Informació Científica (PIC), E-08193 Bellaterra (Barcelona), Spain
42Also at Department of Physics, University of Oslo, Norway
43Also at Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
44Max-Planck-Institut für Physik, D-85748 Garching, Germany
45Also at INAF Padova, Padova, Italy
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46 Japanese MAGIC Group: Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa,
277-8582 Chiba, Japan
47Now at Sorbonne Université, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies,
LPNHE, 4 place Jussieu, 75005 Paris, France
48Now at Département de physique nucléaire et corpusculaire, University de Genève, Faculté de Sciences,
1205 Genève, Switzerland
49Departamento de Física Teórica, Facultad de Ciencias, Mod. 15, Universidad Autónoma de Madrid,
E-28049 Madrid, Spain
50 Instituto de Física Teórica, UAM-CSIC, Calle Nicolás Cabrera 13-15, Campus de Cantoblanco, E-28049
Madrid, Spain
51Now at Department of Information Technology, Escuela Politecnica Superior, Universidad San
Pablo-CEU, CEU Universities, Campus Monteprincipe, Boadilla del Monte, Madrid 28668, Spain
∗Corresponding author
aNot a member of the MAGIC collaboration.
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