Search for dark matter towards the Galactic Centre with 11 years of ANTARES data

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Search for dark matter towards the Galactic Centre with

11 years of ANTARES data

A. Albert, M. André, M. Anghinolfi, G. Anton, M. Ardid, J.-J. Aubert, J.

Aublin, B. Baret, S. Basa, B. Belhorma, et al.

To cite this version:

A. Albert, M. André, M. Anghinolfi, G. Anton, M. Ardid, et al..

Search for dark matter

to-wards the Galactic Centre with 11 years of ANTARES data. Phys.Lett.B, 2020, 805, pp.135439.

�10.1016/j.physletb.2020.135439�. �hal-02431461�

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

dark

matter

towards

the

Galactic

Centre

with

11 years

of

ANTARES

data

A. Albert

a

,

b

,

M. André

c

,

M. Anghinolﬁ

d

,

G. Anton

e

,

M. Ardid

f

,

J.-J. Aubert

g

,

J. Aublin

h

,

B. Baret

h

,

S. Basa

i

,

B. Belhorma

j

,

V. Bertin

g

,

S. Biagi

k

,

M. Bissinger

e

,

J. Boumaaza

l

,

S. Bourret

h

,

M. Bouta

m

,

M.C. Bouwhuis

n

,

H. Brânza ¸s

o

,

R. Bruijn

n

,

p

,

J. Brunner

g

,

J. Busto

g

,

A. Capone

q

,

r

,

L. Caramete

o

,

J. Carr

g

,

S. Celli

q

,

r

,

s

,

M. Chabab

t

,

T.N. Chau

h

,

R. Cherkaoui El Moursli

l

,

T. Chiarusi

u

,

M. Circella

v

,

A. Coleiro

h

,

M. Colomer

h

,

w

,

R. Coniglione

k

,

H. Costantini

g

,

P. Coyle

g

,

A. Creusot

h

,

A.F. Díaz

x

,

G. de Wasseige

h

,

A. Deschamps

y

,

C. Distefano

k

,

I. Di Palma

q

,

r

,

A. Domi

d

,

z

,

C. Donzaud

h

,

aa

,

D. Dornic

g

,

D. Drouhin

a

,

b

,

T. Eberl

e

,

I. El Bojaddaini

m

,

N. El Khayati

l

,

D. Elsässer

ab

,

A. Enzenhöfer

e

,

g

,

A. Ettahiri

l

,

F. Fassi

l

,

P. Fermani

q

,

r

,

G. Ferrara

k

,

F. Filippini

u

,

ac

,

L. Fusco

h

,

ac

,

P. Gay

ad

,

h

,

H. Glotin

ae

,

R. Gozzini

w

,

∗

,

R. Gracia Ruiz

a

,

K. Graf

e

,

C. Guidi

d

,

z

,

S. Hallmann

e

,

H. van Haren

af

,

A.J. Heijboer

n

,

Y. Hello

y

,

J.J. Hernández-Rey

w

,

J. Hößl

e

,

J. Hofestädt

e

,

G. Illuminati

w

,

C.W. James

ag

,

M. de Jong

n

,

ah

,

P. de Jong

n

,

M. Jongen

n

,

M. Kadler

ab

,

O. Kalekin

e

,

U. Katz

e

,

N.R. Khan-Chowdhury

w

,

A. Kouchner

h

,

ai

,

M. Kreter

ab

,

I. Kreykenbohm

aj

,

V. Kulikovskiy

d

,

ak

,

R. Lahmann

e

,

R. Le Breton

h

,

D. Lefèvre

al

,

am

,

E. Leonora

an

,

G. Levi

u

,

ac

,

M. Lincetto

g

,

D. Lopez-Coto

ao

,

S. Loucatos

ap

,

h

,

G. Maggi

g

,

J. Manczak

w

,

M. Marcelin

i

,

A. Margiotta

u

,

ac

,

A. Marinelli

aq

,

ar

,

J.A. Martínez-Mora

f

,

R. Mele

as

,

at

,

K. Melis

n

,

p

,

P. Migliozzi

as

,

M. Moser

e

,

A. Moussa

m

,

R. Muller

n

,

L. Nauta

n

,

S. Navas

ao

,

E. Nezri

i

,

C. Nielsen

h

,

A. Nuñez-Castiñeyra

g

,

i

,

B. O’Fearraigh

n

,

M. Organokov

a

,

G.E. P˘av˘ala ¸s

o

,

C. Pellegrino

u

,

ac

,

M. Perrin-Terrin

g

,

P. Piattelli

k

,

C. Poirè

f

,

V. Popa

o

,

T. Pradier

a

,

L. Quinn

g

,

N. Randazzo

an

,

G. Riccobene

k

,

A. Sánchez-Losa

v

,

A. Salah-Eddine

t

,

D.F.E. Samtleben

n

,

ah

,

M. Sanguineti

d

,

z

,

P. Sapienza

k

,

F. Schüssler

ap

,

M. Spurio

u

,

ac

,

Th. Stolarczyk

ap

,

B. Strandberg

n

,

M. Taiuti

d

,

z

,

Y. Tayalati

l

,

T. Thakore

w

,

S.J. Tingay

ag

,

A. Trovato

k

,

B. Vallage

ap

,

h

,

V. Van Elewyck

h

,

ai

,

F. Versari

u

,

ac

,

h

,

S. Viola

k

,

D. Vivolo

as

,

at

,

J. Wilms

aj

,

D. Zaborov

g

,

A. Zegarelli

q

,

r

,

J.D. Zornoza

w

,

J. Zúñiga

w

a_Université_de_Strasbourg,_CNRS,_IPHC_UMR_7178,_F-67000_Strasbourg,_France b_Université_de_Haute_Alsace,_F-68200_Mulhouse,_France

c_Technical_University_of_Catalonia,_Laboratory_of_Applied_{Bioacoustics,}_Rambla_Exposició,₀₈₈₀₀_Vilanova_i_la_Geltrú,_Barcelona,_Spain d_INFN_{- Sezione}_di_Genova,_Via_Dodecaneso_33,₁₆₁₄₆_Genova,_Italy

e_{Friedrich-Alexander-Universität}_{Erlangen-Nürnberg,}_Erlangen_Centre_for_{Astroparticle}_Physics,_{Erwin-Rommel-Str.}_1,₉₁₀₅₈_Erlangen,_Germany f_Institut_{d’Investigació}_per_a_la_Gestió_Integrada_de_les_Zones_Costaneres_(IGIC)_{- Universitat}_Politècnica_de_València,_C/_Paranimf_1,₄₆₇₃₀_Gandia,_Spain g_Aix_Marseille_Univ,_CNRS/IN2P3,_CPPM,_Marseille,_France

h_APC,_Univ_Paris_Diderot,_CNRS/IN2P3,_CEA/Irfu,_Obs_de_Paris,_Sorbonne_Paris_Cité,_France i_Aix_Marseille_Univ,_CNRS,_CNES,_LAM,_Marseille,_France

j_National_Center_for_Energy_Sciences_and_Nuclear_Techniques,_B.P._1382,_R.P.₁₀₀₀₁_Rabat,_Morocco k_INFN_{- Laboratori}_Nazionali_del_Sud_(LNS),_Via_S._Soﬁa_62,₉₅₁₂₃_Catania,_Italy

l_University_Mohammed_V_in_Rabat,_Faculty_of_Sciences,₄_av._Ibn_Battouta,_B.P._1014,_R.P.₁₀₀₀₀_Rabat,_Morocco m_University_Mohammed_I,_Laboratory_of_Physics_of_Matter_and_Radiations,_B.P._717,_Oujda_6000,_Morocco n_Nikhef,_Science_Park,_Amsterdam,_the_Netherlands

o_Institute_of_Space_Science,_RO-077125_Bucharest,_M˘agurele,_Romania

p_Universiteit_van_Amsterdam,_Instituut_voor_Hoge-Energie_Fysica,_Science_Park_105,₁₀₉₈_XG_Amsterdam,_the_Netherlands q_INFN_{- Sezione}_di_Roma,_P.le_Aldo_Moro_2,₀₀₁₈₅_Roma,_Italy

*

Correspondingauthor.

E-mailaddress:srgozzini@km3net.de(R. Gozzini).

https://doi.org/10.1016/j.physletb.2020.135439

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2 A. Albert et al. / Physics Letters B 805 (2020) 135439

r_Dipartimento_di_Fisica_{dell’Università}_La_Sapienza,_P.le_Aldo_Moro_2,₀₀₁₈₅_Roma,_Italy s_Gran_Sasso_Science_Institute,_Viale_Francesco_Crispi_7,₀₀₁₆₇_L’Aquila,_Italy

t_LPHEA,_Faculty_of_Science_{- Semlali,}_Cadi_Ayyad_University,_P.O.B._2390,_Marrakech,_Morocco u_INFN_{- Sezione}_di_Bologna,_Viale_Berti-Pichat_6/2,₄₀₁₂₇_Bologna,_Italy

v_INFN_{- Sezione}_di_Bari,_Via_E._Orabona_4,₇₀₁₂₆_Bari,_Italy

w_IFIC_{- Instituto}_de_Física_Corpuscular_(CSIC_{- Universitat}_de_València),_c/_Catedrático_José_Beltrán,_2,_E-46980_Paterna,_Valencia,_Spain x_Department_of_Computer_Architecture_and_{Technology/CITIC,}_University_of_Granada,₁₈₀₇₁_Granada,_Spain

y_Géoazur,_UCA,_CNRS,_IRD,_Observatoire_de_la_Côte_d’Azur,_Sophia_Antipolis,_France z_Dipartimento_di_Fisica_{dell’Università,}_Via_Dodecaneso_33,₁₆₁₄₆_Genova,_Italy aa_Université_Paris-Sud,₉₁₄₀₅_Orsay_Cedex,_France

ab_Institut_für_Theoretische_Physik_und_Astrophysik,_Universität_Würzburg,_Emil-Fischer_Str._31,₉₇₀₇₄_Würzburg,_Germany ac_Dipartimento_di_Fisica_e_Astronomia_{dell’Università,}_Viale_Berti_Pichat_6/2,₄₀₁₂₇_Bologna,_Italy

ad_Laboratoire_de_Physique_{Corpusculaire,}_Clermont_Université,_Université_Blaise_Pascal,_CNRS/IN2P3,_BP_10448,_F-63000_{Clermont-Ferrand,}_France ae_LIS,_UMR_Université_de_Toulon,_Aix_Marseille_Université,_CNRS,₈₃₀₄₁_Toulon,_France

af_Royal_Netherlands_Institute_for_Sea_Research_(NIOZ)_and_Utrecht_University,_Landsdiep_4,₁₇₉₇_SZ_’t_Horntje_(Texel),_the_Netherlands ag_{International}_Centre_for_Radio_Astronomy_Research_{- Curtin}_University,_Bentley,_WA_6102,_Australia

ah_{Huygens-Kamerlingh}_Onnes_{Laboratorium,}_Universiteit_Leiden,_the_Netherlands ai_Institut_{Universitaire}_de_France,₇₅₀₀₅_Paris,_France

aj_Dr._{Remeis-Sternwarte}_and_ECAP,_{Friedrich-Alexander-Universität}_{Erlangen-Nürnberg,}_{Sternwartstr.}_7,₉₆₀₄₉_Bamberg,_Germany ak

MoscowStateUniversity,SkobeltsynInstituteofNuclearPhysics,Leninskiegory,119991Moscow,Russia

al_{Mediterranean}_Institute_of_Oceanography_(MIO),_{Aix-Marseille}_University,_13288,_Marseille,_Cedex_9,_France am_Université_du_Sud_Toulon-Var,_{CNRS-INSU/IRD}_UM_110,_83957,_La_Garde_Cedex,_France

an_INFN_{- Sezione}_di_Catania,_Via_S._Soﬁa_64,₉₅₁₂₃_Catania,_Italy

ao_Dpto._de_Física_Teórica_y_del_Cosmos_&_C.A.F.P.E.,_University_of_Granada,₁₈₀₇₁_Granada,_Spain ap_IRFU,_CEA,_Université_{Paris-Saclay,}_F-91191_{Gif-sur-Yvette,}_France

aq_INFN_{- Sezione}_di_Pisa,_Largo_B._Pontecorvo_3,₅₆₁₂₇_Pisa,_Italy

ar_Dipartimento_di_Fisica_{dell’Università,}_Largo_B._Pontecorvo_3,₅₆₁₂₇_Pisa,_Italy as_INFN_{- Sezione}_di_Napoli,_Via_Cintia₈₀₁₂₆_Napoli,_Italy

at_Dipartimento_di_Fisica_{dell’Università}_Federico_II_di_Napoli,_Via_Cintia_80126,_Napoli,_Italy

a

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i

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Articlehistory:

Received12December2019 Receivedinrevisedform3April2020 Accepted16April2020

Availableonline21April2020 Editor:H.Peiris

Keywords:

Darkmatterindirectdetection Neutrinotelescope

GalacticCentre ANTARES

Neutrinodetectorsparticipateintheindirectsearchforthefundamentalconstituentsofdarkmatter(DM)inform ofweaklyinteractingmassiveparticles(WIMPs).InWIMPscenarios,candidateDMparticlescanpair-annihilateinto StandardModelproducts,yieldingconsiderableﬂuxesofhigh-energyneutrinos.AdetectorlikeANTARES,locatedin theNorthernHemisphere,isabletoperformacomplementarysearchlookingtowardstheGalacticCentre,wherea highdensityofdarkmatteristhoughttoaccumulate.Boththisdirectionalinformationandthespectralfeaturesof annihilatingDMpairsareenteredintoanunbinnedlikelihoodmethodtoscanthedatasetinsearchforDM-like signalsinANTARESdata.Resultsobtaineduponunblinding3170daysofdatareconstructedwithupdatedmethods arepresented,whichprovidesalarger,andmoreaccurate,datasetthanapreviouslypublished resultusing2101 days.Anon-observationofdarkmatterisconvertedintolimitsonthevelocity-averagedcrosssectionforWIMPpair annihilation.

1. Introduction:darkmattersignalsatneutrinotelescopes

The existence of cold, non-baryonic dark matter (DM), evi-dencedonmacroscopicscalebyastrophysicalobservations[1], en-couragesthesearchesforitspossibleparticleconstituents.Among thosecandidates,mostWIMPscenariosaccommodatetheDMrelic densityreportedbyastrophysicalmeasurementsthrougha freeze-out mechanism. Thiscould implythat typical WIMP interactions of the DMcandidate, especially its annihilation cross section, lie neartheelectroweakscale;beyondthat,otherparameterslikethe candidateWIMPmassorthespeciﬁcdetailsoftheDMmodelare leftunbound.UnderthehypothesisthataWIMPcoincideswithits antiparticle,indirectsearchesforWIMPsarepossiblebydetecting a signature of WIMP annihilation into Standard Model particles. Suchsignalsare thereforesearchedfromthedirectionofmassive astrophysical environments, where WIMPs can be gravitationally attracted.DMbuildsupinandaroundmassivecelestialbodiesand gravitationalaccumulators, andis organized inhalos and clumps. Thedistributionofdarkmatterwithdensity

ρ

atagivensky loca-tion(r

,

θ,

φ

)isdescribedthroughthe J -factor

J

=

d

(θ, φ)

l.o.s.

ρ

2

(

s

(

r

, θ, φ))

ds

,

(1)

with

beingthesolid angleunderwhichthesourceisobserved, and

s the

radialcoordinateintegratedoverthelineofsight(l

.

o

.

s

.

) (see [2] for a detaileddiscussion).For neutrinotelescopes,which haveaverybroadﬁeldofview,valuesaslargeas10◦

−

30◦canbe consideredfortheopeninganglecharacterisingthesolidangle

. Preferred locationswheredarkmatter ispredictedtoaccumulate are:

1. theGalacticCentre,havingthelargest J -factor; 2. massive,non-luminousgalaxieslikedwarfspheroidals; 3. theSunorothernearbyverymassivecelestialbodies. DM messengers for indirect searches are neutrinos,

γ

rays or charged cosmic rays (e+, p),

¯

produced either as primary or as secondaryproductsofaWIMPpairannihilation,throughdifferent channels.TheGalacticCentreisnotonlyapromisingsourceforits large predictedDM density;it is alsoa target ofcomplementary searches for neutrinodetectors and

γ

-ray telescopes,due to the lowsourcecontaminationthatwouldgivewaytoanunambiguous signal identiﬁcation. Lastly,the GalacticCentre is ingood visibil-ityforneutrinotelescopeslocatedintheNorthernHemisphere(as will beclariﬁedinSection 2),orfor

γ

-raytelescopes installedin theSouthernHemisphere.TheﬂuxofneutrinosreachingtheEarth froma WIMPpairannihilation canbe expressedasafunction of

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thethermallyaveraged crosssection

σ

v

forWIMP pair annihi-lation,oftheenergydistributionofoutcomingparticlesperWIMP paircollision

dN

/

dEν , andoftheDMdistribution representedby the J -factor: d

(

Eν

)

dEν

=

1 4

π

M2_WIMP

σ

v

2 dN

(

Eν

)

dEν J

,

(2)

wherethefactor1/2,usedinthisanalysis,holdsforself-conjugate WIMPs,andistobe replacedbyafactor1/4otherwise.Similarly, theterm1

/

M2_WIMParisesfromthepresenceoftwoWIMPSinthe process,keepingintoaccountthatboththemassandthe volumet-ricdensityareexpressed inenergyunits.Through therelationin Equation (2), a measurement of the integratedneutrino and an-tineutrinoﬂuxfromtheregionoftheGalacticCentre

ν+¯ν

=

dEνd

ν dEν

+

dE_ν_¯d

ν¯ dE_ν_¯ (3)

is converted into limits on the thermally averaged cross section

σ

v

forWIMPpairannihilation.Alowerboundonthisquantityof 3

·

10−26 cm3s−1 canbemadebaseduponcosmologyarguments [3].

1.1. Directional and morphological information

Indirect searches for dark matter are unavoidably subject to largeuncertainties,mostlyarisingfromtheparameterisationofthe

unknown DM distribution. The spherically averaged DM density

proﬁle

ρ

containedinthe J -factor (Equation (1))ismodelled ac-cordingtodifferentassumptions,leadingto considerablydifferent results.Themainassumptionson

ρ

arebasedoncosmological N-bodysimulationresultsand/ordynamicalconstraintsontheMilky Way or spiral galaxies. Even if baryonic physics (star formation andfeedbacks)isnotfullyundercontrolinhydrodynamics simula-tions,thebaryonsmaysteepenorevenflattentheinnerbehaviour oftheDMprofile(see e.g.[4–7]).Alternatively,dynamicalstudies ofgalaxies show a large diversity inrotation curves [8] and can suggesta coredDMprofile [9,10].Apopular andsimple parame-terisationof the DMdensity obtained inpure (without baryons)

DM cosmological simulations is the Navarro-Frenk-White (NFW)

proﬁle[11]:

ρ

N F W

(

r

)

=

ρ

0 r rs

1

+

_rr s

γ (4)

with

γ

=

2. The NFW proﬁle is adopted in the presentanalysis with

ρ

0

=

1

.

40

·

107M

/

kpc3 and

r

s

=

16

.

1 kpc [12].Forthesake ofillustratingthoseDMdensityuncertainties,othertwocasesare considered:theproﬁlefromtherecentstudyofMcMillan[13] giv-ingan internal power lawr0.79±0.32, andtheBurkert proﬁle [14] forwhichtheinnerdensityisconstant.

1.2. Energy information

The energy distribution of a neutral massive particle pair-annihilatinginto Standard Model products can be effectively

de-scribed with a Monte Carlo generator such as PYTHIA or

HER-WIG[15,16]. The PPPC4 cookbook [17], used in this analysis, di-rectlyprovidesspectraforWIMPannihilationsintoStandardModel modeswhich arestraightforwardto adapttoanykindofindirect searches.

PPPC4 yields the energy distribution for an isotropic ﬂux of Standard Model particles originated in the WIMP pair annihila-tionatthesource.Severalﬁnal statesoftheannihilationprocess, resulting in different decay modes (

τ

+

τ

−, W+W−, bb, μ

¯

+

μ

−,

ν

¯

) have been simulated,evaluating the spectrum of the result-ingneutrinoﬂux,

dNν

/

dEν , foreach WIMPmass.Eachchannel is consideredwitha100%branchingratio(BR).Notethatthematter densityintheGalacticCentreisnotenoughtocausedistortionsor absorptioneffectsinoutcomingneutrinospectra.

Flavouroscillations occurbetweensource anddetectionpoint. ThethreeneutrinoﬂavoursareequallyproducedinWIMPpair an-nihilations,andthedata setconsidered hereonlycontains muon neutrinosrecordedatthedetector.Theoscillations

ν

e

,

ντ into νμ,

aswell asthe lossof

νμ into

the other two flavours,have been accounted for. The energy distribution of neutrino final states is therefore obtained from a modulated superposition of the three flavours, in the long-baseline approximation,1 _with _coefficients takenfrom[1].Neutrinosandantineutrinosaresymmetrically pro-ducedinWIMPannihilations,andaredetectedindistinctlyby cur-rentneutrinotelescopes. Thisanalysisisrestricted tomuon neu-trinoeventsatthedetector,aswillbedescribedinSection2.

2. Detectoranddataset

ANTARES isan underwater Cherenkovdetectorsituatedin the

Mediterranean Sea 40 km offshore from Toulon. It is composed

of12detectionlinesinstrumentedwithphotomultipliertubes en-closed inoptical modules [18]. ANTARES data analysisallows for energy and directional reconstruction of charged particle tracks originatedfromaneutrinointeractionoccurringaroundthe detec-tor.Theverylargebackgroundofmuonsproducedinatmospheric interactions of cosmic rays is suppressed by considering events witharrivaldirectionscrossingtheEarth.Underthiscondition,the GalacticCentre,locatedatadeclinationof

−

29

.

01◦,isvisiblefrom thedetectorlatitudeabout70% ofthetime[19].

Inthispaper,11yearsofdatacollectedwithANTARESbetween

May2007andDecember2017are analysed,updatingupon prior

searches [20]. Signatures of neutrinos from DM annihilation are

searched for in a data sample composed of reconstructed muon

tracks originatingfrom chargedcurrent (CC) interactions of neu-trinos around the detector. A set of pre-selection cuts has been applied to discriminate these

νμ CC-induced

events from

atmo-spheric muon background; this ﬁrst discrimination is based on

the zenith angle ofprovenience ofthe event andon the quality of thetrack reconstruction. Tracks are reconstructed inANTARES from the position andtimes of photomultiplier hits, recorded in generalfromdifferentdetectorlines. Thequality parameteris, in

thestandard approach,amaximumlikelihood

obtainedwitha

multi-line reconstruction ﬁt [21]. At low energies, however, it is possible to best reconstructthose tracks hitting only one line of thedetectorusingasingle-linereconstruction[22];thisﬁtisbased ona

χ

2_minimization_and_the

_χ

2_value_serves_as_a_quality

param-eter. The single-line reconstruction is more eﬃcient for energies

below

∼

100GeV.

The parameters

and

χ

2 _are _used _as _quality _indicator _for

multi-line andsingle-line tracks respectively. Additionally, an an-gular errorestimate

β

, provided by themulti-line reconstruction ﬁt, has been considered. Variable cuts have been applied as re-ported in Table 1, and the values yielding best sensitivity have beenchosentounblindthedata,asexplainedlaterinsection3.1.

This sample is composed of 8976 tracks reconstructed with

the multi-line algorithm and2522tracks withthe single-line al-gorithm recorded over 3170 days ofeffective livetime; note that in the text that follows the termneutrinos stands for

ν

+ ¯

ν

, as theevents generatedby their interactionsare seen indistinguish-ablyincurrentneutrinotelescopes.Tracks arereconstructedwith

1 _The_E_/_{L dependency}_of_the_oscillations_are_averaged_out_for_GeV–TeV_neutrino energiesoverthedistancebetweentheEarthandtheGalacticCentre.

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Table 1

Final selection criteria applied to the data set. The qualityof the multi-line reconstruction ﬁt is evalu-atedbyalikelihoodandangularerrorestimateβ;

χ2_{characterises}_the_single-line_ﬁt;_the_angle

θis com-plementarytothezenith,suchthatcosθ >0 identiﬁes anupgoing track,comingfromacrosstheEarth.

Fit Cut value

Multi-line >−5.2 Multi-line β <1◦ Single-line χ2_<₀_.₇

Both cosθ >0

an angular resolutionof theorder of 1◦ at theenergies relevant forthissearch[23].Givenitsgeometryandvolume,theANTARES telescopeisoptimisedforthedetectionofneutrinoswithenergies fromabout20GeVtoafewPeV.TheDManalysisis,therefore,in

themediumWIMPmassrange.TheamountofCherenkovphotons

induced along the paths of the propagating charged particles is proportionaltotheamountofdepositedenergyand,consequently, thenumber ofhit optical modules, NHITS,is a goodproxyofthe

neutrinoenergy

Eν .

A set of simulated data has been produced in

correspon-dencewiththeenvironmentalandtriggerconditionsofeachdata run [24],andhasbeenadaptedtothespeciﬁcDManalysisthrough theuseofweightsreproducingtheenergydistribution

dNν

/

dEν of eachWIMPannihilationchannel.Thesimulateddatausedforthis search contain

νμ CC

induced muons;thecontribution ofmuons from

ντ

→

τ

andsubsequent

τ

decayisnotconsideredinthe sim-ulatedsampleusedinthisanalysis.

Thesearchisoptimisedonshuﬄed(blind)right-ascensiondata, which are unblinded after having established the best selection criteria. A newly releasedversion ofthe ANTARES reconstruction software[21,22] wasrun onthefull dataset.Withthenew pro-cessing andreconstruction of the data a considerable amountof livetime could be recovered withrespect to the previous 9-year study[20].

The search method used forthis analysisis the same asthat used in the previous study [20], keeping into account the cor-rectionofacomputation problemwhichaffectedtheprevious re-sults [20].

3. Method

The signal from DM annihilation is expected to appear as a cluster of neutrino events scattered around the position of the Galactic Centre according to the J -factor proﬁle, whose energy distribution reproduces the WIMP annihilation spectra [17]. This spatial cluster ofsignal eventsis to be found overa background of atmospheric neutrinos [25]. Both background estimation and search optimisation useshuﬄed (blinded) realdata,by replacing

the right ascension value with a random value between0◦ and

360◦.Thisrandomshuﬄewashesoutanypossiblespatial cluster-ing in correspondenceto the source, permitting to use real data withfakecoordinatestoaccuratelydescribethebackground distri-butionofevents.

Foridentifying the signal, discriminating variables are the di-rectionofthereconstructed neutrinotrackandthe energyproxy, NHITS, whose normalised distributions are used asan input in a

likelihoodfunctionasprobabilitydensityfunctions(PDFs).The sig-nal PDF,

S

, is built from simulated data weighted according to theWIMPannihilationspectra[17];thebackgroundPDF,

B

,is ob-tainedfromshuﬄeddata.Toassessthesignalsigniﬁcance,alarge numberofskymaps(pseudo-experiments)aregeneratedinjecting an variable number of signal events, ns, according to the signal PDF,overasetof

N

=

ns

+

nbgevents,with

n

bg backgroundevents.

Thetotalnumberofevents,N, isobtainedfromthetotalnumber oftracksinthe datasample.Thealgorithm usedtosearch foran excessofeventscomingfromtheregionofthe GalacticCentreis basedonanunbinnedlikelihoodfunction,

L

,associatedwitheach skymap(containing

N events)

log

L

(

ns

)

=

N

i=1 log

ns

S

(ψ

i

,

NiHITS

,

qi

)

+

nbg

B

(δi,

NHITSi

,

qi)

−

nbg

−

ns, (5)

where

ψ

i istheangulardistanceofthe

i-th

eventfromthe Galac-tic Centre;

δ

i,the Equatorial declinationof the i-th event; Ni_HITS, the numberoflight hitsrecordedby the detectorandassociated with the i-th reconstructed track, and qi, the quality of the re-construction. The likelihood maximisation returns thenumber of signal events, n∗s, found to belong to a cluster around the ﬁxed coordinatesoftheGalacticCentre(

α

,

δ

)=(266◦,

−

29

.

01◦).The sig-niﬁcanceofaclusterisestablishedbytheteststatistics,TS,which

is a function of the ratio between the maximum and the pure

backgroundlikelihood T S

= −

log

L

(

n ∗ s

)

L

(

ns

=

0

)

.

(6)

To determine the signiﬁcance of the observed TS, a series of

pseudo-experimentsisgenerated.Thisisperformedby creatinga largenumberofskymapswithavariablenumberofinjectedsignal events,

n

s,andrunningamaximumlikelihoodalgorithmoneach, returning the ﬁtted number of events n∗_s for each of them. The numberofeventsineach setofpseudo-experimentsissubjectto ﬂuctuationsfollowingaPoissondistribution.Toincludethiseffect, a transformationthroughaPoissonfunction,

P

,isperformed, re-turningtheTSasafunctionofthePoissonianmean

μ

:

P

(

T S

(

μ

))

=

N

n∗s=1

P

T S

(

n∗_s

)

P

(

n∗_s

,

μ

),

(7)

where P

(

T S

)

indicatestheTSdistribution.

The main source of systematic uncertainties comes from the determinationoftheneutrinotrackdirection.Thetrack reconstruc-tion relies on the time resolution of the detector,dependent on thephotomultipliertimespread,onthecalibrationandonpossible spacemisalignmentofthedetectorlines.Theeffectofsystematic uncertainties was estimatedin aprevious analysis [23] toa total of15%. AGaussiansmearing of15%is appliedtothesignal PDFs toaccountfordetectorsystematics.

3.1. Sensitivity of the search method

FollowingNeyman’sprescription [26],anaverageupperlimiton thenumberofsignal eventsiscomputedfromthemedianofthe background test statistics T S0, compared with each distribution

P

(

T S

)

foreach pseudo-experiment set.The sensitivity isdeﬁned asthe90% C.L.upperlimitforameasurementequaltothemedian ofthebackgroundTSdistribution.Theanalysiscutsareoptimised to yieldthebestsensitivity(see Section2andvaluesreportedin Table 1). If, afterunblinding, a value smallerthan the medianof thebackgroundTSisobservedinthedata,limitsare setequalto thesensitivity.

In case of a non-observation, a limit of the total number of signaleventsinthedata(

μ

90)isconvertedintoalimitonthe

in-tegratedﬂux,

ν+¯ν , throughtheacceptance,

A

,andthelivetime, t, as

(6)

Fig. 1. Upperlimitsat90% C.L.onthethermallyaveragedcrosssectionforWIMP pairannihilationasafunctionoftheWIMPcandidatemasssetwith11yearsof ANTARESdata,shownforﬁveindependentannihilationchannels(eachwith100% branchingratio)andNFWhalomodel[11].

ν+¯ν

=

μ

90

A

·

t

.

(8)

Theacceptanceisdeﬁnedastheconvolutionoftheeffectivearea, Ae f f [23],witheachannihilationmodespectrum

dNν

/

dEν [17]:

A

(

M

)

=

M

E0 Aν_{e f f}

(

Eν

)

dNν

(

Eν

)

dEν dEν

+ [

ν

→ ¯

ν

],

(9)

where M is theconsidered WIMP mass, E0 theenergythreshold

ofthe detector,determined fromthe ﬁrst non-empty bin of the effectivearea,and

[

ν

→ ¯

ν

]

indicatesasymmetrictermfor antineu-trinos.Thedetectoreffectiveareaincreaseswithenergyduetothe raisewithenergyoftheCCcrosssection,combinedwiththebetter trackdeﬁnitionofhigh-energyevents,andwithanincreaseinthe muonrange,making suchthat partially containedtrackscanstill bemeasured.Theacceptancecalculationreliesonspectraprovided byPPPC4. The integratedﬂux ofEquation (8) isconverted intoa measurement (limit) on the thermallyaveraged cross section for WIMP annihilation

σ

v

using Equation (2), fora given J -factor assumingaspeciﬁcparameterisationoftheDMhalomodel.

4. Results

Upon unblinding, the TS computed for 11 years of ANTARES

data is compatible with background. We observed a TS smaller

thanthe backgroundmedianforall cases(massesandchannels),

hence we set all limit values equal to the corresponding

sen-sitivities. This measurement sets limits on the cross section for

WIMP-pairannihilation shownin Fig.1 andcomputed according

toEquation (2). Thisﬁgureshowslimitsfortheﬁvemost promi-nentWIMPpairannihilationchannels:

WIMP WIMP

→

bb

¯

,

τ

+

τ

−

,

W+W−

,

μ

+

μ

−

,

ν

¯

(10)

independentlycomputedwith100%BR. Thetotalamountofdark

matterwithina30◦anglearoundtheGalacticCentreistakeninto account,which correspondsto thesolid angle

inEquation (1). Bestlimitsareobtainedforthedirect

ν

¯

channel,asseeninFig.1, whichhasthehighestacceptanceandthebestsensitivityin

num-ber of events, due to the shape of the energy spectrum which

peaks around the WIMP candidate mass; channels with steeply

fallingspectrasuchas

b

b give

¯

theleaststringentlimits.Predictions onneutrinoﬂuxesderiving fromDMannihilationstronglyrelyon theparameterisationof the J -factor, asmentioned inSection 1.1. Fig.2showsthe90% C.L.limitson

σ

v

forthe

τ

+

τ

− channelfor

Fig. 2. Upperlimitsat90% C.L.onthethermallyaveragedcrosssectionforWIMP

pairannihilationasafunctionoftheWIMPcandidatemasssetwith11yearsof ANTARESdataforthreedifferenthalomodels [11,13,14].Here,onlythe

τ

+τ− chan-nelisshown.

Fig. 3. LimitsonthethermallyaveragedcrosssectionforWIMPpair-annihilation

setwith11yearsofANTARESdata,comparedwithcurrentsimilarsearchesfrom IceCube[27] andfrom

γ

-raytelescopesHESS[28],VERITAS[29] andFermi-LAT+ MAGIC[30].Allcurvesareforthe

τ

+τ−benchmarkchannel.

threedifferenthalomodels.TheNFWproﬁle [11] givespredictions overoneorderofmagnitudemorestringentthan

ﬂat proﬁles

such asBurkert [14].Anintermediateresultisachievedforthe McMil-lanproﬁle[13] whichhasanintermediateinnerslope.Theresults presentedinthisworkrepresentan improvementrangingfroma factor1.1to1.4withrespecttotheprevious9-yearstudy[20], ac-cordingtotheWIMPmassandchannelconsidered.

5. Discussionandconclusions

Limitsonthethermallyaveragedcrosssection

σ

v

forDM an-nihilation towardstheGalacticCentre wereplacedusing11years ofANTARESdata.Someofthechannelsconsideredforthissearch alsoyield

γ γ

pairsasaﬁnalproduct.Forthiscase,ANTARES lim-its are set in context withexisting limitsfrom

γ

-ray telescopes (Fig. 3) for the

τ

+

τ

− channel. In particular, the HESS Galactic Centresurvey[28] givesstrongconstraintsthankstothegood vis-ibility of this source from their location and to the prolongued

observation campaign performed on this target. Note that both

theMAGICandtheVERITASdetectorsarelocatedintheNorthern

Hemisphere and thereforethey obtain their limitson the WIMP

pairannihilationcross sectionfroma campaignofobservationof dwarf spheroidal Galaxies [29,30], not having the possibility to lookdirectly intothe GalacticCentre, ifnot withspecial settings for large zenith angle observations (e.g. [31]) with reduced sen-sitivity. Halo modeling in dwarf spheroidalGalaxies is subjectto

(7)

large uncertainties, andcomparison with the Galactic Centre re-sultsisthereforenotdirect.TheresultsshownforIceCube[27] are

obtained withDeep Core data, a conﬁguration where the whole

IceCube detector acts as a veto for atmospheric muons. Because of the GalacticCentre visibility,this analysis is limitedto WIMP masses up to 1 TeV/c2. All results shown in Fig. 3 are obtained withtheNFWproﬁle,withtheexceptionoftheHESSresultwhich referstotheEinastoDMhalomodel[32].

ThecurrentsearchesfordarkmatterperformedwithANTARES willbe continuedwithKM3NeT,which willinstrumentatotal of about1km3_of_deep-sea_water_[₃₃_]._KM3NeT_has_a_modular_layout

consistingofblocksof115detectionlineseach.Twomodulesare beingdeployedinalargevolume(36minter-optical-modulesand 90 minter-line spacing) to form the ARCA high-energy detector, andone inadensergeometryinstrumentingasmallervolume(9 mbetweenopticalmodules and20minter-linespacing)to form theORCAlow-energydetector.AstheprescriptionsfortheWIMP candidatemassvaryoverabroadrangeofvalues,bothARCAand ORCAwillcontributetoDMsearches.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting ﬁnan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

The authors acknowledge the ﬁnancial support of the

fund-ingagencies:CentreNationaldelaRechercheScientiﬁque(CNRS), Commissariat à l’Énergie Atomique et aux Énergies Alternatives

(CEA),CommissionEuropéenne(FEDERfundandMarieCurie

Pro-gram), Institut Universitaire de France (IUF), IdEx program and

UnivEarthS Labexprogram atSorbonne ParisCité

(ANR-10-LABX-0023 and ANR-11-IDEX-0005-02), Labex OCEVU

(ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02), Région

Île-de-France (DIM-ACAV), Région Alsace (contrat CPER), Région

Provence-Alpes-Côte d’Azur, Département du Var and Ville de

La Seyne-sur-Mer, France; Bundesministerium für Bildung und

Forschung (BMBF), Germany; Instituto Nazionale di Fisica Nucle-are (INFN), Italy; Nederlandse Organisatie voor Wetenschappelijk

Onderzoek (NWO), the Netherlands; Council of the President of

the Russian Federationforyoung scientists and leading scientiﬁc schools supporting grants, Russia; Executive Unit for Financing Higher Education, Research,Development and Innovation (UEFIS-CDI),Romania; Ministerio de Ciencia, Innovación yUniversidades

(MCIU): Programa Estatal de Generación de Conocimiento (refs.

PGC2018-096663-B-C41, -A-C42, -B-C43, -B-C44) (MCIU/FEDER),

Severo Ochoa Centre of Excellence and MultiDark Consolider

(MCIU), Junta de Andalucía(ref. SOMM17/6104/UGR), Generalitat Valenciana: Grisolía (ref. GRISOLIA/2018/119), Spain; Ministry of Higher Education, Scientiﬁc Research and Training, Morocco. We alsoacknowledgethetechnicalsupportofIfremer,AIMandFoselev MarinefortheseaoperationandtheCC-IN2P3 forthecomputing facilities.

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