Observation of an ultra-high-energy cosmic neutrino with KM3NeT

376 | Na u e | Vol 638 | 13 Feb ua y 2025
A icle
Obse a ion o an ul a-high-ene gy cosmic
neu ino wi h KM3NeT
The KM3NeT Collabo a ion* ✉
The de ec ion o cosmic neu inos wi h ene gies abo e a e aelec on ol (TeV) o e s
a unique explo a ion in o as ophysical phenomena1–3. Elec ically neu al and
in e ac ing only by means o he weak in e ac ion, neu inos a e no de lec ed by
magne ic ields and a e a ely abso bed by in e s ella ma e : hei di ec ion
indica es ha hei cosmic o igin migh be om he a hes eaches o he Uni e se.
High-ene gy neu inos can be p oduced when ul a- ela i is ic cosmic- ay p o ons o
nuclei in e ac wi h o he ma e o pho ons, and hei obse a ion could be a
signa u e o hese p ocesses. He e we epo an excep ionally high-ene gy e en
obse ed by KM3NeT, he deep-sea neu ino elescope in he Medi e anean Sea4,
which we associa e wi h a cosmic neu ino de ec ion. We de ec a muon wi h an
es ima ed ene gy o
120−60
+110
pe aelec on ol s (PeV). In ligh o i s eno mous ene gy
and nea -ho izon al di ec ion, he muon mos p obably o igina ed om he
in e ac ion o a neu ino o e en highe ene gy in he icini y o he de ec o . The
cosmic neu ino ene gy spec um measu ed up o now5–7 alls s eeply wi h ene gy.
Howe e , he ene gy o his e en is much la ge han ha o any neu ino de ec ed
so a . This sugges s ha he neu ino may ha e o igina ed in a di e en cosmic
accele a o han he lowe -ene gy neu inos, o his may be he i s de ec ion o a
cosmogenic neu ino8, esul ing om he in e ac ions o ul a-high-ene gy cosmic
ays wi h backg ound pho ons in he Uni e se.
Cosmic neu inos may be p oduced ei he in he icini y o he cosmic-
ay sou ce o along he cosmic- ay p opaga ion pa h, leading o he
p oduc ion o seconda y uns able pa icles, which subsequen ly decay
in o neu inos. Cosmic ays in e ac ing in he Ea h’s a mosphe e p o-
duce a mosphe ic neu inos, which o m an expe imen al backg ound
o cosmic neu inos. To de ec cosmic neu inos, e y-la ge- olume
neu ino obse a o ies moni o na u al bodies o wa e o ice o he
Che enko ligh induced by he passage o he cha ged pa icles ha
esul om neu ino in e ac ions in o nea he de ec o . The KM3NeT
esea ch in as uc u e comp ises wo de ec o a ays o op ical sen-
so s deep in he Medi e anean Sea
4
. The ARCA de ec o is loca ed
o sho e Po opalo di Capo Passe o, Sicily, I aly, a a dep h o abou
3,450 m and connec ed by means o an elec o-op ical cable o he
sho e s a ion o he INFN, Labo a o i Nazionali del Sud (LNS). The
geome y o ARCA is op imized o he s udy o high-ene gy cosmic
neu inos. The ORCA de ec o is loca ed a a dep h o abou 2,450 m,
o sho e Toulon, F ance, and is op imized o he s udy o neu ino
oscilla ions. Bo h de ec o s a e unde cons uc ion bu al eady ope a-
ional. Once comple ed, hey will comp ise 345 (230 o ARCA and 115
o ORCA) e ical de ec ion lines, each holding 18 op ical modules.
Each module hos s 31 3-inch pho omul iplie ubes (PMTs) poin ing
in all di ec ions and ensu ing 4π co e age
9
. Bo h de ec o s can iden-
i y all la ou s o neu ino in e ac ions: hose p oducing long-li ed
muons, denomina ed ‘ acks’, and hose p oducing elec omagne ic
and had onic cascades a he neu ino in e ac ion e ex, denomina ed
‘showe s’.
O in e es in his a icle a e neu ino in e ac ions ha p oduce
high-ene gy muons, which can a el se e al kilome es in seawa e
be o e being abso bed. These muons lose ene gy as hey p opaga e
mainly because o s ochas ic adia i e p ocesses such as b emss ahl-
ung, pai p oduc ion and pho onuclea eac ions. The a e age ene gy
loss pe uni pa h leng h is p opo ional o he muon ene gy. Elec-
omagne ic cascades a ise om hese s ochas ic ene gy losses; he
numbe o cha ged pa icles ha p oduce Che enko adia ion in he
cascades is p opo ional o he amoun o ene gy los by he muon in
he p ocess. The eco ded ime o a i al and ime-o e - h eshold o
he signals on he PMTs (deno ed as ‘hi s’) a e used o econs uc he
muon di ec ion and ene gy.
Al hough a mosphe ic neu inos a e mo e abundan a lowe ene -
gies (≈TeV), cosmic neu inos should become dominan a ene gies
abo e 100 TeV. The neu ino ene gy is hus a c ucial pa ame e o
es ablishing a cosmic o igin. The IceCube Collabo a ion announced he
disco e y o PeV cosmic neu inos in 2013 ( e . 10). The mos ene ge ic
neu inos epo ed so a a e a 6.05 ± 0.72 PeV elec on an ineu ino
obse ed a he ene gy o he Glashow esonance11 and a muon neu ino
abo e 10 PeV om he obse a ion o a 4.4-PeV muon5.
The neu ino e en KM3-230213A
An ex emely high-ene gy muon a e sing he ARCA de ec o was
obse ed on 13 Feb ua y 2023 a 01:16:47 UTC. This e en is e e ed o
he e as KM3-230213A. A ha ime, 21 de ec ion lines we e in ope a ion.
h ps://doi.o g/10.1038/s41586-024-08543-1
Recei ed: 19 Augus 2024
Accep ed: 18 Decembe 2024
Published online: 12 Feb ua y 2025
Open access
Check o upda es
*A lis o au ho s and hei a ilia ions appea s a he end o he pape . ✉e-mail: [email p o ec ed]
Na u e | Vol 638 | 13 Feb ua y 2025 | 377
The de ec o was in his con igu a ion om 23 Sep embe 2022 un il 11
Sep embe 2023, when se en u he lines we e ins alled. A e emo -
ing da a acqui ed in he de ec o commissioning phase and du ing
de ec o calib a ion pe iods, 287.4 days o da a aking we e selec ed o
analysis wi h his con igu a ion. Du ing his pe iod, abou 110 million
e en s we e igge ed and KM3-230213A is he highes -ene gy e en
obse ed. KM3-230213A is isualized in Fig.1. A o al o 28,086 hi s
we e egis e ed by he 21 de ec ion lines. Owing o he la ge amoun o
de ec ed ligh , he PMTs closes o he muon ajec o y a e sa u a ed.
As expec ed o e y-high-ene gy muons, a leas h ee la ge showe s,
p obably because o ene gy-loss p ocesses, a e obse ed along he
ack (mo e de ails a e p o ided in heSupplemen a y Ma e ials).
The muon ajec o y is econs uc ed om he measu ed imes and
posi ions o he i s hi s eco ded on he PMTs, using a maximum-
likelihood algo i hm, desc ibed in Me hods. KM3-230213A is he e en
wi h he bes ack log-likelihood among all hose collec ed in his de ec-
o con igu a ion, indica i e o a highly ela i is ic muon a elling
se e al hund eds o me es h ough he de ec o . The di ec ion o KM3-
230213A is econs uc ed as nea -ho izon al, o igina ing0.6° abo e
he ho izon a an azimu h o 259.8°(azimu h angles inc ease clock-
wise, wi h no h a 0°). The unce ain y on he di ec ion is es ima ed
o be 1.5° (68% con idence le el), domina ed by he p esen sys ema ic
unce ain y on he absolu e o ien a ion o he de ec o . The o igin o
his unce ain y is desc ibed in Me hods. A dedica ed sea campaign
N
100 m
N
100 m
1,800
1,600
1,400
1,200
1,000
800
600
400
200
0
Time (ns)
23
24 25
15
10 11
16
20
26 27
22
12
5
32
28
23
24
20
30
25
19
14
15
13
9
10
11
12
5
16
21
26
22
27 28
32
21
13
19
14
9
30
a
b
Fig. 1 | Views o he e en . a, Side and op iews o he e en . The econs uc ed
ajec o y o he muon is shown as a ed line, along wi h an a is ’s ep esen a ion
o he Che enko ligh cone. The hi s o indi idual PMTs a e ep esen ed by
sphe es s acked along he di ec ion o he PMT o ien a ions. Only he i s
i e hi s on each PMT a e shown. As indica ed in he legend, he sphe es a e
colou ed acco ding o he de ec ion ime ela i e o he i s igge ed hi . The
size o he sphe es is p opo ional o he numbe o pho ons de ec ed by he
co esponding PMT. The loca ions o he seconda y cascades, discussed in
heSupplemen a y Ma e ial, a e indica ed by he black sphe es along he muon
ajec o y. The no h di ec ion is indica ed by a ed a ow. A 100-m scale and
he Ei el Towe (330 m heigh , 125 m base wid h) a e shown o size compa ison.
b, Zoomed-in iew o he op ical modules ha a e close o he i s wo obse ed
seconda y showe s in he e en . He e ligh -blue sphe es ep esen hi s ha
a i e wi hin −5 o 25 ns o he expec ed Che enko a i al imes.
378 | Na u e | Vol 638 | 13 Feb ua y 2025
A icle
is planned in he u u e o imp o e he knowledge o he posi ions o
he de ec o elemen s on he sea loo ; a ecalib a ion o all da a will
hen be pe o med and will allow us o app oach he in insic s a is i-
cal unce ain y on he muon di ec ion o 0.12° (median, as desc ibed
in Me hods).
The muon ene gy a he de ec o is es ima ed by coun ing he num-
be o PMTs ha pa icipa e in he igge ing o he e en ,
ig
PMT
N. This
quan i y is obus agains limi a ions o he de ec o simula ions, as
desc ibed in Me hods, and agains con amina ion om he op ical
backg ounds in seawa e . The obse ed numbe o igge ed PMTs o
KM3-230213A is

N=3,6
72
ig
PMT
, co esponding o abou 35% o he ac i e
PMTs in he de ec o a he ime o he e en . This is much la ge han
o any o he neu ino-induced e en obse ed so a in he de ec o .
Dis ibu ions o
N
ig
PMT
as a unc ion o he muon ene gy, o modelled
muons a i ing om he same posi ion and di ec ion o KM3-230213A,
a e ob ained om Mon e Ca lo simula ions. These a e used o build
equen is con idence in e als12,13 on he ue muon ene gy, as
desc ibed in Me hods. Sys ema ic unce ain ies a e included in he
es ima ion by a ying he simula ed op ical module e iciencies, and
he sca e ing and abso p ion leng h o ligh , wi h espec o he nom-
inal alues. The
ig
PMT
N
dis ibu ions o simula ions o 10-PeV, 100-PeV
and 1,000-PeV muons a e shown in Fig.2. The es ima ed muon ene gy
is
120 PeV
−60
+110
, wi h a 90% con idence le el in e al o 35–380 PeV. Unce -
ain ies on he muon ene gy es ima e a e domina ed by he knowledge
o he abso p ion leng h o ligh in he seawa e .
The conside ed ange o a ia ions o pho on abso p ion (±10%) is
de i ed om he obse ed a ia ions o he wa e anspa ency in dedi-
ca ed measu emen s14. Se e al s udies in ecen da a ha e con i med
his. The numbe o i s hi s wi h small esiduals ( ha is, compa ible
wi h a di ec pho on pa h om he ack o he PMT) has been s udied
in KM3-230213A. A la ge dis ances, his numbe is sensi i e o he
abso p ion leng h. Da a we e ound o be in he ±10% ange ob ained
om simula ions wi h modi ied abso p ion. A simila s udy was ca ied
ou using downgoing a mosphe ic muons, which also con i med ha
de ia ions om nominal a e a mos on he o de o 10%. Finally, he
abso p ion can be de e mined om he obse ed a e o pho ons om
adioac i e 40K in he seawa e , which scales linea ly wi h he abso p ion
leng h. A i s -p inciples compu a ion
15
using he nominal abso p ion
model p edic s 5.1 ± 0.6 kHz, o which he unce ain y comes om
he PMT e iciency and he numbe o pho ons c ea ed in he decay.
The obse ed coun a e is 5.6 kHz a e accoun ing o da k noise and
a e pulses, which is wi hin he assigned 10% unce ain y ange.
Figu e3 is an illus a ion o he posi ion o KM3-230213A in he
(
N ig
PMT
, cos(zeni h angle)) phase space. Simula ed Mon e Ca lo e en s
a e shown in Fig.3a, wi h he expec ed annual a es o a mosphe ic
muons
16
and cosmic neu inos
5
in ARCA. The dis ibu ion o he ARCA
da a is shown in Fig.3b, also highligh ing KM3-230213A. E en s a e
selec ed choosing well- econs uc ed acks, as de ined on he basis
o he obse ed ack leng h in he de ec o ( ack leng h la ge han
250 m) and he ack econs uc ion likelihood: log-likelihood a io
la ge han 500, selec ing 0.02% o all econs uc ed a mosphe ic
muon and neu ino acks and 2% o he cosmic acks assuming he
lux om e . 5.
Gi en he econs uc ed ene gy and di ec ion, an uppe limi on
he backg ound o a mosphe ic muons is es ima ed using dedica ed
simula ions, as desc ibed in Me hods. A muon wi h he obse ed di ec-
ion would ha e a e sed abou 300 km wa e -equi alen o ma e ial,
which exceeds he maximal ange o any a mosphe ic muon (≤60 km
wa e -equi alen o 100-EeV muons). The uppe limi on he muon
con amina ion a 100 PeV, conside ing an e o on he zeni h angle
es ima e as la ge as 2°, is 10
−10
e en s pe yea . This numbe becomes on
he o de o 10
−9
e en s pe yea i he muon ene gy is ins ead 10 PeV. In
he e y unlikely scena io ha he de ec o is misaligned and he ue
zeni h angle would de ia e by 5σ om nominal ( ha is, a i al di ec ion
5.6° abo e he ho izon), muons would need o a el h ough 28 km
wa e -equi alen and he uppe limi on he a e becomes 10−4 muons
pe yea and 10
−3
o muon bundles in which se e al pa allel muons om
he same cosmic- ay ai showe could each he de ec o .
A mosphe ic neu inos could each he de ec o , bu hei numbe
dec eases subs an ially abo e PeV ene gies. The expec ed a e o a mos-
phe ic neu inos abo e 100 PeV is on he o de o (1–5) × 10
−5
e en s
pe yea , domina ed by he p omp a mosphe ic componen owing o
he decay o sho -li ed had ons om cosmic- ay in e ac ions in he
a mosphe e. The p obabili y ha KM3-230213A is o cosmic o igin is
much g ea e han any hypo hesis in ol ing an a mosphe ic o igin,
and a ious es ima ions a e p o ided in Me hods and Supplemen a y
Ma e ials. Beyond S anda d Model hypo heses on i s o igin ha e no
been in es iga ed he e.
The measu ed muon ene gy se es as a lowe limi on he incoming
neu ino ene gy. Gi en he es ima ed muon ene gy and i s unce ain y,
he median neu ino ene gy ha p oduces such muons in he simula-
ions o he ARCA de ec o is 220 PeV; 68% (90%) o simula ed e en s
om he whole sky all in he 110–790 PeV (72 PeV–2.6 EeV) ene gy
ange, unde he assump ion ha he incoming neu ino ene gy spec-
um is E
∝ν
−2
.
An iso opic lux o neu inos a ul a-high ene gies would gi e ise
o e en s de ec ed nea he ho izon: downgoing neu inos a e hidden
in an o e whelming backg ound o a mosphe ic muons, whe eas he
upgoing neu ino lux is se e ely supp essed, because neu inos o
such la ge ene gies would in e ac in he Ea h. The a i al di ec ion
o KM3-230213A ma ches his scena io.
Celes ial o igin
The equa o ial coo dina es (J2000) and he de ec ion ime o KM3-
230213A a e: RA = 94.3°, dec. = −7.8°, MJD = 59988.0533299. The di e -
en con ainmen adii a e: R(50%) = 1.2°, R(68%) = 1.5°, R(90%) = 2.2° and
R(99%) = 3.0°, domina ed by he sys ema ic unce ain y on he absolu e
o ien a ion o he de ec o (see Me hods). The celes ial posi ion o
KM3-230213A is shown in Fig.4, oge he wi h he di e en e o egion
2,000 4,000 6,000
Numbe o igge ed PMTs
0
0.05
0.10
0.15
F ac ion o Mon e Ca lo e en s
Muon ene gy
10 PeV
100 PeV
1,000 PeV
KM3-230213A
Fig. 2 | Numbe o PMTs in he e en . The no malized dis ibu ions o he numbe
o PMTs pa icipa ing in he igge ing o he e en o simula ed muon ene gies
o 10, 100 and 1,000 PeV. The e ical dashed line indica es he obse ed alue
in KM3-230213A,
N
=3,6
72
ig
PMT
. The dashed his og ams ep esen he dis ibu ions
om he nominal simula ions, whe eas, in he illed his og ams, sys ema ic
unce ain ies a e included by weigh ing he simula ions acco ding o a no mal
dis ibu ion, cen ed a he nominal alue o he nuisance pa ame e and wi h a
±10% unce ain y. A he highes ene gy, he dis ibu ions seem o be unca ed
a ound N=6,
000
ig
PMT
because he ack c osses he de ec o in i s pe iphe y.
Na u e | Vol 638 | 13 Feb ua y 2025 | 379
con ou s. Sea ches we e pe o med o a po en ial sou ce coun e pa
wi hin a 3° adius a ound he e en coo dina es wi h publicly a ailable
mul iwa eleng h da a. Fou hypo heses we e es ed: galac ic, local
Uni e se, ansien and ex agalac ic o igin.
As he di ec ion o he e en is compa ible wi h he ex ension o he
galac ic in e s ella medium (abou 10° abo e and below he galac ic
plane), galac ic coun e pa was sea ched o in high-ene gy (4FGL-DR4
( e . 17)) and e y-high-ene gy (TeVCa
18
) gamma- ay ca alogues, as
well as in he 3HWC su ey da a
19
. Despi e he p esence o he O ion
molecula clouds in he e o egion, no ca alogued sou ce was ound
in he 99% e o egion. The di ec ion o he e en was c oss-ma ched
wi h he MANGROVE ca alogue20 o dis ances up o 100 Mpc o explo e
a local o igin: 40 galaxies we e ound. Fo each galaxy, op ical ansien
sou ces we e sea ched o in he ZTF public s eam in a ±6-mon h ime
window, using he FINK b oke 21. No ansien sou ce was iden i ied.
Also, no coinciden de ec ion o ansien objec s (such as gamma- ay
bu s s, idal-dis up ion e en s, supe no ae) was ound in he GCN
no ices and ci cula s (h ps://gcn.nasa.go /), in he As onome ’s Tel-
eg am (h ps://as onome s eleg am.o g/) and in he T ansien Name
Se e (h ps://www.wis- ns.o g/).
Ex agalac ic neu ino sou ces should be domina ed by ac i e
galac ic nuclei, and blaza s a e o pa icula in e es conside ing he
e y-high ene gy o KM3-230213A. To compile a census o po en ial
blaza coun e pa s wi hin he 99% con idence egion o KM3-230213A,
a chi al mul iwa eleng h da a we e also explo ed. The ollowing ca a-
logues we e c oss-ma ched o in es iga e a possible blaza coun e pa :
he 4FGL-DR4 Fe mi-LAT gamma- ay ca alogue17, he i s eROSITA
X- ay ca alogue22, he Wide- ield In a ed Su ey Explo e (WISE) op i-
cal ca alogue
23
, he RFC 2024b (h ps://as ogeo.o g/ c/) and NRAO
VLA Sky Su ey (NVSS)
24
adio ca alogues and Roma-BZCAT
25
. Fou
di e en s a egies we e pu sued, leading o a o al o 12 objec s. The
selec ion c i e ia a e desc ibed in Me hods, oge he wi h he p ope -
ies o hese sou ces. The celes ial posi ions o he selec ed sou ces a e
shown in Fig.4. Gi en he la ge numbe o blaza s in he sky, none o
hese associa ions can be conside ed compelling so a , and u he
in es iga ions will be needed.
Gi en ha a hypo he ical as ophysical sou ce associa ed wi h KM3-
230213A may ha e also p oduced lowe -ene gy neu inos, da a om
he ARCA and ORCA de ec o s, as well as public da a om he ANTARES
and IceCube de ec o s, we e checked o he p esence o a neu ino
signal compa ible wi h a poin -like sou ce hypo hesis in he icini y o
KM3-230213A. De ails on he da ase s, sea ch app oaches and esul s
a e gi en in Me hods. The la ges excess was ound in he IceCube da a
a a dis ance o 2.4° om KM3-230213A wi h a p e- ial P- alue o
1.6 × 10−4 and a pos - ial P- alue o 0.07. No signi ican excess was
1%
5%
KM3-230213A
100
101
102
103
Numbe o da a e en s
–1.00 –0.75 –0.50 –0.25 0 0.25 0.50 0.75 1.00
cos(zeni h angle)
–1.00 –0.75 –0.50 –0.25 0 0.25 0.50 0.75 1.00
cos(zeni h angle)
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
log10(numbe o igge ed PMTs)
1%
5%
1%
5%
KM3-230213A
0
0.002
0.004
0.006
0.008
0.010
0.012
Yea ly a e o cosmic neu inos
100
101
102
103
Yea ly a e o a mosphe ic muons
a
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
log10(numbe o igge ed PMTs)
b
Fig. 3 | Backg ound a es. a, Expec ed yea ly a e o a mosphe ic muons and
cosmic neu inos (acco ding o he bes - i lux o e . 5) in ARCA pe bin o
N ig
PMT
and cos(zeni h angle). The solid (dashed) lines ma k he bounda y o he
phase space ou side which 5% (1%) o he muon and neu ino dis ibu ions a e
con ained. KM3-230213A is shown by he c oss. b, Numbe o e en s collec ed
in he ARCA de ec o o e he 287 days o da a aking wi h 21 de ec ion lines,
wi h he same selec ion cu s. Two upgoing, lowe -ene gy e en s a e isible as
well as KM3-230213A, which a e candida e neu ino e en s, subjec o u u e
analysis.
9192939495969798
RA J2000 (°)
–11
–10
–9
–8
–7
–6
–5
–4
dec. J2000 (°)
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11 #12
KM3-230213A
R(68%) R(90%) R(99%)
5BZCAT X- ay + adio + in a ed
VLBI Gamma ay
Fig. 4 | Sky map in he di ec ion o KM3-230213A. KM3-230213A is indica ed
by he ed s a , wi h he e o egions wi hin R(68%), R(90%) and R(99%) shown
as do ed, dashed and solid con ou s, espec i ely. The di ec ions o he
selec ed sou ce candida es a e shown as colou ed ma ke s, whose colou s and
ma ke ype indica e he c i e ion acco ding o which he sou ce was selec ed.
The sou ces a e numbe ed acco ding o hei p oximi y o KM3-230213A, as
epo ed in Me hods.
380 | Na u e | Vol 638 | 13 Feb ua y 2025
A icle
obse ed a he coo dina es o KM3-230213A and 90% con idence le el
uppe limi s on he one- la ou neu ino lux no maliza ion a 1 GeV,
Φνν+
1GeV
, assuming a neu ino spec um o
ΦEΦ E()=((GeV))
νν νν++
1GeV −2
,
we e se and a e epo ed in Me hods. The mos s ingen limi on he
poin -sou ce o igin is 1.2 × 10
−9
GeV
−1
cm
−2
s
−1
. Al hough hese sea ches
a e also sensi i e o e y-high-ene gy e en s, he signal o an E−2 spec-
um is expec ed in he TeV–PeV ange and he epo ed limi s a e
he e o e applicable in his a ea.
Cosmic neu ino lux
To associa e a lux o he e en , he exposu e o he de ec o o e y-
high-quali y and high-ene gy acks is compu ed h ough simula ions.
The exposu e co esponds o selec ion c i e ia ha equi e a good
ack- econs uc ion likelihood (log-likelihood a io la ge han 500),
a long ack leng h wi hin he de ec o (la ge han 250 m) and
N>1
,500
ig
PMT
.
Conside ing he cen al (90%) 72 PeV–2.6 EeV ene gy ange, he
s eady iso opic lux ha would p oduce one e en is
EΦE()=5.8 ×10GeV cmss ,
2−3.7
+10.1−8−2−1−1
o which he con idence in e als a e compu ed acco ding o
e . 26. The 95% and 99.7% con idence le el in e als a e [0.30–29.8]
and [0.02–47.7] × 10−8 GeV cm−2 s−1 s −1, espec i ely. This ep esen s
he KM3NeT s andalone lux measu emen in he 335 days o li e ime
o ARCA wi h 19 and 21 de ec ion lines.
In Fig.5, he lux measu emen is compa ed wi h measu ed and
p edic ed neu ino luxes and limi s. The KM3NeT s andalone lux
measu emen exceeds p esen limi s om IceCube27 and Auge 28. A pos-
sible in e p e a ion is ha he KM3NeT e en is an upwa d luc ua ion.
In such a scena io, desc ibed in Me hods, one e en such as KM3-
230213A would be expec ed in 70 yea s o obse a ion wi h his de ec-
o con igu a ion, and he e en is an upwa d luc ua ion a he le el
o 2.2σ.
The expec ed e en a es in ARCA o a ious ex apola ions o he
lux measu ed by IceCube a e discussed in heSupplemen a y Ma e-
ial. Conside ing ex apola ions o he powe -law i o he IceCube
measu emen s, hese would yield a mos 0.12 e en s in he 335 days o
analysed KM3NeT da a wi h 19 and 21 de ec ion lines a e he selec ion
o ack e en s desc ibed abo e. The obse a ion o KM3-230213A,
ma ginally consis en wi h such expec a ion, may hin a he eme gence
o a new componen in he lux.
A iable al e na i e hypo hesis is cosmogenic neu ino p oduc-
ion8,29,30, in which neu inos a e gene a ed by he in e ac ion o cosmic
ays wi h ex agalac ic backg ound ligh o he cosmic mic owa e back-
g ound. The expec ed numbe o cosmogenic e en s in he selec ed
da a a ies be ween 1.5 × 10−3 ( e . 31) and 0.47 ( e . 32), depending on
he assumed injec ion spec um and cosmic- ay mass composi ion,
as well as he cosmological e olu ion o sou ces31–40. The en elope o
a selec ion o cosmogenic models is shown as a g ey-shaded band in
Fig.5. O he scena ios o di use emission om neu ino p oduc ion
in he sou ce en i onmen a e shown as he yellow-shaded band in
Fig.5. Among hese a e ansien emi e s such as gamma- ay-bu s s
and idal-dis up ion e en s34,39,41–44, low-luminosi y BL Lacs45 and
la -spec um adio quasa s46.
O e all, he de ec ion o a muon neu ino wi h an ene gy g ea e
han 100 PeV p o ides e idence o he exis ence o ul a-high-ene gy
neu inos in na u e. The new mul iPMT op ical module design and he
excellen op ical p ope ies o Medi e anean seawa e ha e allowed
he cha ac e iza ion o he neu ino in e ac ion and ha e acili a ed
his b eak h ough in neu ino as onomy.
1041051061071081091010 1011
Neu ino ene gy (GeV)
10–11
10–10
10–9
10–8
10–7
10
–6
ANTARES (2024)
Auge (2022)
Uppe limi s
KM3-230213A
IceCube i s
NST (2022)
HESE (2021)
Glashow (2021)
SPL 68% NST (2022)
SPL 68% HESE (2021)
Models
Cosmogenic band
Sou ces band
E2 + (GeV cm–2 s–1 s –1)
1
Φ
IceCube/EHE (2018)
Fig. 5 | Compa ison wi h models and ea lie measu emen s. Shown is he
ene gy-squa ed pe - la ou as ophysical lux de i ed om he obse a ion
o KM3-230213A wi h measu emen s and heo e ical p edic ions, assuming
equipa i ion (νe:νμ:ντ = 1:1:1). The blue c oss co esponds o he lux needed
o achie e one expec ed e en a e he ack selec ion desc ibed in he ex ,
in he cen al 90% neu ino ene gy ange associa ed wi h KM3-230213A,
illus a ed wi h he ho izon al span; he e ical ba s ep esen he 1σ,2σ and 3σ
Feldman–Cousins con idence in e als on his es ima e. The pu ple and pink
shaded egions ep esen he 68% con idence le el con ou s o he IceCube
single-powe -law (SPL) i s (No he n Sky T acks, NST5) and High-Ene gy
S a ing E en s (HESE)7, espec i ely: he da ke -shaded egions a e he
espec i e 90% cen al ene gy ange a he bes i (dashed line), whe eas he
ligh e -shaded egions a e ex apola ions o highe ene gies. The pu ple and
pink c osses a e he piece-wise i om he same analyses, whe eas he o ange
c oss co esponds o he IceCube Glashow esonance e en 11. The do ed lines
a e uppe limi s om ANTARES (95% con idence le el47), Pie e Auge (90%
con idence le el, o an E−2 neu ino spec um28, co ec ed o con e om
limi s in hal -decade o one-decade bins) and IceCube (90% con idence le el,
es ima ed assuming an E−1 neu ino spec um in sliding one-decade bins27). The
g ey-shaded band comp ises a a ie y o cosmogenic neu ino expec a ions
ollowing se e al models o cosmic- ay accele a ion and p opaga ion, whe eas
he yellow-shaded band comp ises se e al scena ios o di use ansien and
a iable ex agalac ic sou ces, bo h epo ed in heSupplemen a y Ma e ial.

Na u e | Vol 638 | 13 Feb ua y 2025 | 381
Online con en
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© The Au ho (s) 2025, co ec ed publica ion 2025
The KM3NeT Collabo a ion
S. Aiello1, A. Albe 2,3, A. R. Alhebsi4, M. Alshamsi5, S. Al es Ga e6, A. Amb osone7,8,
F. Ameli9, M. And e10, M. Anghinol i11, L. Aphece che12, M. A did13, S. A did13, C. A güelles14,15,
H. A mani16, J. Aublin17, F. Bada acco11,18, L. Bailly-Salins19, Z. Ba dačo á20,21, B. Ba e 17,
A. Ba iego-Quin ana6, Y. Beche ini17, M. Bendahman7, F. Ben ena i Gualandi22,23,
M. Benhassi7,24, M. Bennani19, D. M. Benoi 25, E. Be bee26, V. Be in5, S. Biagi27, M. Boe che 28,
D. Bonanno27, A. B. Bouasla29, J. Boumaaza16, M. Bou a30, M. Bouwhuis26, C. Bozza7,31,
R. M. Bozza7,8, H. B ânzaş32, F. B e audeau12, M. B euhaus5, R. B uijn26,33, J. B unne 5,
R. B uno1, E. Buis26,34, R. Buompane7,24, S. Buson35,36, J. Bus o5, B. Cai i11, D. Cal o6,
A. Capone9,37, F. Ca enini22,23, V. Ca e e o26,33, T. Ca aud17, P. Cas aldi22,38, V. Cecchini6,
S. Celli9,37, L. Ce isy5, M. Chabab39, A. Chen40, S. Che ubini27,41, T. Chia usi22, M. Ci cella42,
R. Cocimano27, J. A. B. Coelho17, A. Colei o17, S. Colonges17, A. Condo elli7,8, R. Coniglione27,
P. Coyle5, A. C euso 17, G. Cu one27, A. D’Amico26, R. Dallie 12, A. De Benedi is7, B. De Ma ino5,
G. De Wasseige43, V. Decoene12, I. Del Rosso22,23, L. S. Di Mau o27, I. Di Palma9,37, A. F. Diaz44,
D. Diego-To osa27, C. Dis e ano27, A. Domi45, C. Donzaud17, D. Do nic5, E. D akopoulou46,
D. D ouhin2,3, J.-G. Ducoin5, R. D o nický21, T. Ebe l45, E. Ecke o á20,21, A. Eddymaoui16,
T. an Eeden26, M. E 17, D. an Eijk26, I. El Bojaddaini30, S. El Hed i17, V. Ellajosyula11,18,
A. Enzenhö e 5, G. Fe a a1,27, M. D. Filipo ić47, F. Filippini23, D. F ancio i27, L. A. Fusco7,31,
S. Gaglia dini9,37, T. Gal45, J. Ga cía Méndez13, A. Ga cia So o6, C. Ga ius Oli e 26,
N. Geißelb ech 45, E. Gen on43, H. Ghadda i30, L. Gialanella7,24, B. K. Gibson25, E. Gio gio27,
I. Goos17, P. Goswami17, S. R. Gozzini6, R. G acia45, K. G a 45, C. Guidi11,18, B. Guillon19,
M. Gu ié ez48, C. Haack45, H. an Ha en49, A. Heijboe 26, L. Hennig45, S. Hen y5,
J. J. He nández-Rey6, W. Id issi Ibnsalih7, A. Ilioni17, G. Illumina i23, D. Joly5, M. de Jong26,50,
P. de Jong26,33, B. J. Jung26, P. Kalaczyński51,52, O. Kalekin45, N. Kamp14,15, U. F. Ka z45,
G. Kis au i53,54, C. Koppe 45, A. Kouchne 17,55, Y. Y. Ko ale 56, V. Kue iakoe26, V. Kuliko skiy11,
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C. Las o ia19, J. Laza 43, A. Lazo6, S. Le S um5, G. Lehau 19, V. Lemai e43, E. Leono a1,
N. Lessing6, G. Le i22,23, M. Lince o36, M. Lindsey Cla k17, F. Longhi ano1, N. Lumb5,
F. Magnani5, J. Majumda 26, L. Male ba11,18, F. Mamedo 20, A. Man eda7, M. Ma coni11,18,
A. Ma gio a22,23, A. Ma inelli7,8, C. Ma kou46, L. Ma in12, F. Ma zaioli7,24, M. Mas odicasa9,37,
S. Mas oianni7, J. Mau o43, G. Miele7,8, P. Migliozzi7, E. Migneco27, M. L. Mi sou7,24,
C. M. Mollo7, M. Mongelli42, L. Mo ales-Gallegos7,24, A. Moussa30, I. Mozun Ma eo19,
R. Mulle 22, M. R. Musone7,24, M. Musumeci27, S. Na as48, A. Naye hoda42, C. A. Nicolau9,
382 | Na u e | Vol 638 | 13 Feb ua y 2025
A icle
B. Nkosi40, B. Ó Fea aigh11, V. Oli ie o7,8, A. O lando27, E. Oukacha17, D. Paesani27,
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D. Real6, G. Riccobene27, J. Robinson28, A. Romano 11,18,19, E. Ros56, A. Šaina6, F. Salesa G eus6,
D. F. E. Sam leben26,50, A. Sánchez Losa6, S. San ilippo27, M. Sanguine i11,18, D. San onoci o27,
P. Sapienza27, J. Schmelling26, J. Schnabel45, J. Schumann45, H. M. Schu e28, J. Seneca26,
N. Sennan30, P. Se le43, I. Sgu a42, R. Shanidze53, A. Sha ma17, Y. Shi o 20, F. Šimko ic21,
A. Simonelli7, A. Sinopoulou1, B. Spisso7, M. Spu io23,24, D. S a opoulos46, I. Š ekl20,
M. Taiu i11,18, Y. Tayala i16,59, H. Thie sen28, S. Thoudam4, I. Tos a e Melo1,41, B. T ocmé17,
V. Tsou apis46, A. Tudo ache9,37, E. Tzama iudaki46, A. Ukleja60, A. Vache e 19, V. Valsecchi27,
V. Van Elewyck17,55, G. Vannoye5, G. Vasileiadis61, F. Vazquez de Sola26, C. Ve ilhac17,
A. Veu o9,37, S. Viola27, D. Vi olo7,24, A. an Vlie 4, A. Y. Wen14,15, E. de Wol 26,33,
I. Lhen y-Y on17, S. Za a a elli11, A. Zega elli9,37, D. Zi o27, J. D. Zo noza6, J. Zúñiga6 &
N. Zywucka28
1INFN, Sezione di Ca ania (INFN-CT), Ca ania, I aly. 2Uni e si é de S asbou g, CNRS, IPHC
UMR 7178, S asbou g, F ance. 3Uni e si é de Hau e Alsace, Mulhouse, F ance. 4Depa men
o Physics, Khali a Uni e si y, Abu Dhabi, Uni ed A ab Emi a es. 5Aix Ma seille Uni e si é,
CNRS/IN2P3, CPPM, Ma seille, F ance. 6IFIC - Ins i u o de Física Co puscula (CSIC - Uni e si a
de València), Pa e na, Spain. 7INFN, Sezione di Napoli, Complesso Uni e si a io di Mon e S.
Angelo, Napoli, I aly. 8Uni e si à di Napoli “Fede ico II”, Dip. Scienze Fisiche “E. Pancini”,
Complesso Uni e si a io di Mon e S. Angelo, Napoli, I aly. 9INFN, Sezione di Roma, Roma,
I aly. 10Labo a o i d’Aplicacions Bioacús iques, Cen e Tecnològic de Vilano a i la Gel ú,
Uni e si a Poli ècnica de Ca alunya, Vilano a i la Gel ú, Spain. 11INFN, Sezione di Geno a,
Geno a, I aly. 12Suba ech, IMT A lan ique, IN2P3-CNRS, Nan es Uni e si é, Nan es, F ance.
13Ins i u o de In es igación pa a la Ges ión In eg ada delas Zonas Cos e as, Uni e si a
Poli ècnica de València, Gandia, Spain. 14Depa men o Physics, Ha a d Uni e si y, Camb idge,
MA, USA. 15Labo a o y o Pa icle Physics and Cosmology, Lyman Labo a o y, Ha a d Uni e si y,
Camb idge, MA, USA. 16Facul y o Sciences, Uni e si y Mohammed V in Raba , Raba , Mo occo.
17As opa icule e Cosmologie, Uni e si é Pa is Ci é, CNRS, Pa is, F ance. 18Uni e si à di
Geno a, Geno a, I aly. 19LPC CAEN, No mandie Uni e si é, ENSICAEN, UNICAEN, CNRS/IN2P3,
Caen, F ance. 20Ins i u e o Expe imen al and Applied Physics, Czech Technical Uni e si y in
P ague, P ague, Czech Republic. 21Depa men o Nuclea Physics and Biophysics, Comenius
Uni e si y, B a isla a, Slo ak Republic. 22INFN, Sezione di Bologna, Bologna, I aly.
23Dipa imen o di Fisica e As onomia, Uni e si à di Bologna, Bologna, I aly. 24Dipa imen o di
Ma ema ica e Fisica, Uni e si à degli S udi della Campania “Luigi Van i elli”, Case a, I aly.
25E. A. Milne Cen e o As ophysics, Uni e si y o Hull, Hull, Uni ed Kingdom. 26Nikhe ,
Na ional Ins i u e o Suba omic Physics, Ams e dam, The Ne he lands. 27INFN, Labo a o i
Nazionali del Sud (LNS), Ca ania, I aly. 28Cen e o Space Resea ch, No h-Wes Uni e si y,
Po che s oom, Sou h A ica. 29Dépa emen de Physique, Facul é des Sciences, Labo a oi e
de Physique des Rayonnemen s, Uni e si é Badji Mokh a -Annaba, Annaba, Alge ia. 30Facul y
o Sciences, Uni e si y Mohammed I, Oujda, Mo occo. 31Dipa imen o di Fisica, Uni e si à di
Sale no e INFN G uppo Collega o di Sale no, Fisciano, I aly. 32Ins i u e o Space Science (ISS),
Măgu ele, Romania. 33Ins i u e o Physics/IHEF, Uni e si y o Ams e dam, Ams e dam, The
Ne he lands. 34Technical Sciences, TNO, Del , The Ne he lands. 35Deu sches Elek onen-
Synch o on (DESY), Zeu hen, Ge many. 36Fakul ä ü Physik und As onomie, Ins i u ü
Theo e ische Physik und As ophysik, Leh s uhl ü As onomie, Julius-Maximilians-Uni e si ä
Wü zbu g, Wü zbu g, Ge many. 37Dipa imen o di Fisica, Uni e si à La Sapienza, Roma, I aly.
38Dipa imen o di Ingegne ia dell’Ene gia Ele ica e dell’In o mazione “Guglielmo Ma coni”,
Uni e si à di Bologna, Cesena, I aly. 39Physics Depa men , Facul y o Science Semlalia, Cadi
Ayyad Uni e si y, Ma akech, Mo occo. 40School o Physics, Uni e si y o he Wi wa e s and,
Johannesbu g, Sou h A ica. 41Dipa imen o di Fisica e As onomia “E o e Majo ana”,
Uni e si à di Ca ania (INFN-CT), Ca ania, I aly. 42INFN, Sezione di Ba i, Ba i, I aly. 43Cen e o
Cosmology, Pa icle Physics and Phenomenology, UCLou ain, Lou ain-la-Neu e, Belgium.
44Depa men o Compu e Enginee ing, Au oma ion, and Robo ics, CITIC, Uni e si y o
G anada, G anada, Spain. 45E langen Cen e o As opa icle Physics, F ied ich-Alexande -
Uni e si ä E langen-Nü nbe g (FAU), E langen, Ge many. 46Ins i u e o Nuclea and
Pa icle Physics, NCSR Demok i os, A hens, G eece. 47School o Compu ing, Enginee ing
and Ma hema ics, Wes e n Sydney Uni e si y, Pen i h, New Sou h Wales, Aus alia.
48Depa amen o de Física Teó ica y del Cosmos and CAFPE, Uni e si y o G anada, G anada,
Spain. 49Royal Ne he lands Ins i u e o Sea Resea ch (NIOZ Texel), Den Bu g, The Ne he lands.
50Leiden Ins i u e o Physics, Leiden Uni e si y, Leiden, The Ne he lands. 51As oCeNT, Nicolaus
Cope nicus As onomical Cen e , Polish Academy o Sciences, Wa saw, Poland. 52Cen e o
Excellence in A i icial In elligence, AGH Uni e si y o K akow, K akow, Poland. 53Depa men
o Physics, Tbilisi S a e Uni e si y, Tbilisi, Geo gia. 54Ins i u e o Physics, Uni e si y o Geo gia,
Tbilisi, Geo gia. 55Ins i u Uni e si ai e de F ance, Pa is, F ance. 56Max-Planck-Ins i u ü
Radioas onomie, Bonn, Ge many. 57Black Hole Ini ia i e, Ha a d Uni e si y, Camb idge,
MA, USA. 58Depa men Physics, Uni e si y o Johannesbu g, Auckland Pa k, Sou h A ica.
59Ins i u e o Applied Physics, Mohammed VI Poly echnic Uni e si y, Ben Gue i , Mo occo.
60Na ional Cen e o Nuclea Resea ch, Wa saw, Poland. 61Labo a oi e Uni e s e Pa icules
de Mon pellie , Mon pellie , F ance. 62Deceased: V. Popa.
Me hods
The de ec o
The KM3NeT de ec o s
4
a e h ee-dimensional a ays o pho osen-
so s ins alled a g ea dep hs in he Medi e anean Sea. The senso s
de ec he Che enko adia ion induced in seawa e by ela i is ic
cha ged pa icles. They a e housed in op ical modules9, which a e
44-cm-diame e p essu e- esis an glass sphe es, each wi h 31 3-inch
PMTs. Each op ical module con ains da a-acquisi ion elec onics
and calib a ion ins umen a ion. The modules o he ARCA de ec o ,
loca ed a a dep h o 3,450 m o sho e Po opalo di Capo Passe o, Sicily,
in he Medi e anean Sea, a e chained oge he in g oups o 18, spaced
by 36 m, along 700-m-long e ical de ec ion lines ancho ed o he
seabed and kep au by he buoyancy o he op ical modules and op
buoys. An elec o-op ical cable uns along he de ec ion lines, powe -
ing he op ical modules and anspo ing da a h ough op ical ib es.
De ec ion lines a e placed on he sea loo wi h an a e age ho izon al
spacing o 95 m. A he ime o he e en , he ARCA de ec o consis ed
o 21 de ec ion lines. The ins umen ed olume, ha is, he smalles
cylinde con aining all op ical modules, was abou 0.15 km3. In i s inal
con igu a ion, he a ay will comp ise 230 de ec ion lines.
The da a-acquisi ion sys em is based on he ‘all-da a- o-sho e’ con-
cep : all analogue signals om he PMTs abo e a ce ain unable h esh-
old a e digi ized o sho e and all digi al da a a e sen o sho e, whe e
hey a e p ocessed in eal ime. The da a con ain he ime s amp o he
leading edge and he pulse leng h o he ime-o e - h eshold signal
om a disc imina o , join ly e e ed o as ‘hi ’. The ime-o e - h eshold
is p opo ional o he numbe o con e ed pho oelec ons on he PMT.
Al hough he linea beha iou holds ela i ely well o pulses up o a
ew ens o pho oelec ons, abo e 30 pho oelec ons, a sa u a ion
e ec is obse ed, p oducing a la ening o he ime-o e - h eshold
measu emen s wi h inc easing cha ge9.
T igge algo i hms sea ch o clus e s o hi s co ela ed in space and
ime. Local coincidences o hi s a e iden i ied on each op ical module
wi hin a 25-ns ime window. Then, h ee di e en clus e ing algo i hms
a e applied, assuming ha hi s come om ligh p opaga ing acco ding
o a possible ack o showe o igin. A space- ime coincidence be ween
a leas i e hi s on i e modules wi hin 250 m, unde he assump ion
ha ligh expands om a poin -like sou ce, cons i u e a clus e o he
nominal showe igge , allowing o a 25-ns delay o ligh p opaga ion
in wa e . A simila condi ion is applied o he ack igge , bu his
ime conside ing ha he ligh sou ce is a ack ha mo es in he de ec-
o a he speed o ligh in acuum, and sea ching o hi s in a cylinde
o adius 120 m. A low- h eshold showe igge is also applied, equi -
ing coincidences o eigh hi s on h ee modules wi hin 110 m. When
one o mo e clus e s a e ound, all da a om an
Oμ(10)-s
ime window
a e eco ded as an e en o o line calib a ion and p ocessing. T ig
-
ge ing c i e ia a e designed o de ec e en s a he lowe -ene gy h esh-
old. In he case o KM3-230213A, 3,659 indi idual (o e lapping) igge
clus e s we e ound in he ime window and

N=3,6
72
ig
PMT
PMTs pa -
icipa ed o o m a leas one o hose igge clus e s. PMTs ha ha e
eco ded hi s bu ha do no pa icipa e in any igge clus e a e p e-
dominan ly caused by op ical backg ounds ha a e e y a away and/
o no ime-co ela ed wi h he physical e en . I is o his eason ha

N ig
PMT
is used as obse able o he ene gy es ima e.
Da a-quali y c i e ia a e applied o ejec pe iods wi h de ec o ins a-
bili ies om he analysis sample.
De ec o simula ion
High-ene gy neu ino e en s (100 GeV < Eν < 100 EeV) we e simu-
la ed wi h gSeaGen 7.4.3 ( e s. 48,49), using GENIE
50
o simula e he
neu ino in e ac ion by means o he HEDIS package
51,52
. The deep-
inelas ic sca e ing model CSMS11 ( e . 53) was used. PROPOSAL
54
and TAUSIC
55
we e used by gSeaGen o p opaga e muons and aus
up o he de ec o .
The accu a e simula ion o he ligh p oduced by a muon o a gi en
ene gy is c ucial o he muon ene gy es ima e. KM3NeT uses p op ie-
a y code, which simula es he con inuous and s ochas ic ene gy losses
owing o b emss ahlung, pai p oduc ion, pho onuclea in e ac ions,
del a ays and ioniza ion, as well as he mul iple Coulomb sca e ing
and deep-inelas ic sca e ing. Di e en ial c oss-sec ions o he main
p ocesses a e ex ac ed om e s. 56,57. The ligh p oduced by he
muon and he seconda y pa icles is simula ed by sampling pho on
ables ha con ain he p obabili y densi y unc ions o he a i al ime
o Che enko ligh on a PMT as a unc ion o he dis ance om he emis-
sion poin and he PMT o ien a ion wi h espec o he pa icle
58
. Fo
seconda y pa icles, equi alen abula ed alues o elec omagne ic
showe ligh a e used. The amoun o pho ons gene a ed depends on
he ype and ene gy o he pa icle and has been adjus ed acco ding
o Gean 4 simula ions59.
The pho on ables accoun o ligh abso p ion, sca e ing and ch o-
ma ic dispe sion. Abso p ion is modelled on he basis o insi u meas-
u emen s
14
; he sca e ing model o seawa e accoun s o pu e-wa e
sca e ing, ollowing he Eins ein and Smoluchowski desc ip ion60,61,
and pa icle sca e ing, accoun ing o he wa eleng h dependence
using he Kopele ich pa ame e iza ion62 and conside ing he Pe zold
da a
63
o he angula dependence. The angula accep ance and a e age
quan um e iciency o he PMTs a e also accoun ed o in he ables, as
de i ed om de ailed simula ions o he PMT and he s uc u e o he
op ical module64, and om labo a o y measu emen s65.
The simula ion o he s ochas ic ene gy losses has been c oss-checked
by compa ing he o al simula ed amoun o ene gy los by he muon
o e a gi en dis ance wi h he same quan i y compu ed using he PRO-
POSAL so wa e
54
. Ag eemen a be e han he 10% le el was ound
o e he whole ene gy ange o in e es . Mo eo e , PROPOSAL has
also been used o check ha a ying he heo e ical models used o
desc ibe ene gy losses
66–69
yields di e ences ha a e wi hin he s o-
chas ic luc ua ions o he ene gy-loss p ocesses.
Because no ex e nal da a a e a ailable in his ene gy ange o alida e
he simula ion p ocedu e, he pa icle-p opaga ion and ligh -simula ion
code has also been compa ed wi h s a e-o - he-a Gean 4-based59 simu-
la ion and wi h a cus om GPU-based pho on- acking code (h ps://
gi hub.com/PLEnuM-g oup/Pho onP opaga ion.jl) in which he same
wa e model and de ec o esponse ha e been implemen ed in an inde-
penden way. The ou pu o hese simula ions a e in good ag eemen ;
when using he al e na i e simula ions o he ene gy measu emen ,
he esul is wi hin 10% o he nominal alue.
A e ligh simula ion, he eadou is simula ed. The con e sion om
pho oelec ons on he ca hode o he PMT o a ime-o e - h eshold
measu emen and he ansi - ime dis ibu ions o he PMTs ep o-
duce labo a o y measu emen s65. The gain, gain sp ead and ela i e
PMT e iciencies come om insi u measu emen s70. A e pulses in
he PMTs a e a p esen no simula ed. Op ical backg ound a es and
he s a us o each PMT in he de ec o a e simula ed using he a es
measu ed in he de ec o , ollowing he un-by- un app oach pionee ed
by he ANTARES Collabo a ion71,72. Subsequen ly, he simula ed da a
a e subjec ed o he same igge and econs uc ion algo i hms ha
a e applied o he da a. Compa isons be ween da a and Mon e Ca lo
simula ions a e p o ided in Ex ended Da a Fig.1 o a loose e en selec-
ion in which he sample is domina ed by a mosphe ic muons. W ongly
econs uc ed a mosphe ic muons ha appea as upgoing e en s in
he zeni h dis ibu ion a e comple ely emo ed once he selec ion on
he econs uc ion log-likelihood is applied.
E en econs uc ion
The di ec ional econs uc ion o he muon ack is pe o med wi h
he s anda d algo i hm, which is based on he a i al ime o he Che -
enko pho ons a he PMTs
73
. Unde he hypo hesis ha a muon a el-
ling in di ec ion
→
d
is a posi ion
→
p
0
a ime
0
, he a i al ime o he
Che enko ligh a posi ion
→
q
is
A icle
zc
D
θ =+/+
sin( ),(1
)
0
C
g
−1
in which D is he dis ance o closes app oach o he muon o
→
q
and z
is he dis ance he muon a els be o e emi ing a pho on unde angle
θC,
→→
zd qp=⋅(−
→
)− D
θ0 an
C
; g is he g oup eloci y o ligh a a e e ence
wa eleng h o 460 nm.
The econs uc ion algo i hm maximizes he likelihood o he a i al
ime esiduals
L
∏
p dϕθ=(,,,),(2
)
i
iiii
in which p deno es he p obabili y densi y unc ion o he a i al ime
esidual i, ob ained om in e pola ed pho on ables, a a dis ance di
om he emission poin . The angles ϕi and θi desc ibe he o ien a ion
o he PMT wi h espec o he ack di ec ion. The pho on ables a e
he same as hose ha ha e been desc ibed abo e o he simula ion
o ligh om he muon ajec o y. They include he con ibu ion o
op ical backg ound.
The algo i hm uses only he i s hi on each PMT, as hey ca y mos
o he in o ma ion on he muon di ec ion. As a esul o his choice,
he econs uc ion is obus agains PMT a e pulses and o he de ails
o modelling o la e hi s. Fo he likelihood maximiza ion, only he
i s hi s in a cylinde o adius 175 m and axis de ined by he p e i
di ec ion a e used. This is he s anda d se ing, which was chosen as
i op imizes he speed o he algo i hm. In he case o KM3-230213A,
he e a e hi s ou side his cylinde , bu i was es ed ha including hem
al e s he econs uc ed ack by less han he s a is ical unce ain y
on he di ec ion.
To mi iga e he e ec o local minima on he likelihood unc ion, he
maximiza ion is p eceded by a p e i , scanning in 4π s o e assumed
ack di ec ions. This p ocedu e gene a es a se o s a ing poin s o
he likelihood maximiza ion. The ack wi h he la ges likelihood is
e ained.
Fo asce aining he quali y o he e en s, he log-likelihood a io,
LLlog(/ )
b
is used, wi h
b
L
he likelihood compu ed o he case o only
op ical backg ound hi s. This quan i y e ec i ely quan i ies he num-
be o hi s whose a i al ime ma ches he expec a ion om he ack
hypo hesis. Typical well- econs uc ed muons ha e a alue ≳50, wi h
a ail o la ge alues esul ing om well- econs uc ed e en s wi h
many hi s. KM3-230213A has a log-likelihood a io o 1,415.2, which is
he highes alue obse ed in he 21-line ARCA da a.
To illus a e he quali y o he econs uc ion, Ex ended Da a Fig.2
p esen s he pho on a i al ime esiduals, which ep esen he di -
e ence be ween he measu ed ime and he expec ed ime om he
econs uc ed muon ajec o y hypo hesis, shown he e o he i s
hi s on he PMTs. Many hi s a e compa ible wi h he muon hypo h-
esis wi h nanosecond accu acy, e en o PMTs loca ed a om he
ack. Hi s a i ing a e he main peak a e because o pho ons ha
ha e sca e ed in he wa e and/o ha we e emi ed unde some
angle o he han θC om he muon ack. These con ibu ions a e
accoun ed o in he econs uc ion and he la ge log-likelihood
a io alue e lec s he ag eemen o hese esiduals wi h he de ailed
expec a ion.
Poin ing o he elescope
The di ec ional unce ain y on he e en is domina ed by unce ain y
on he absolu e o ien a ion o he de ec o on Ea h.
Compasses and accele ome e s in he op ical modules allow o an
es ima ion o hei o ien a ion. The de ec ion lines mo e wi h he sea
cu en , which can displace he op modules by
O(10)m
. The con inu-
ous moni o ing o he op ical module posi ions is he e o e manda o y.
Fo his pu pose, a sys em o au onomous acous ic emi e s is used,
loca ed in and up o 1 km ou side he de ec o on he seabed74. The
acous ic signals a e eco ded by piezoelec ic senso s in he op ical
modules. A χ2 i o he a i al imes o he sound is used o de e mine
he o ien a ion and shape o he de ec ion line as pa ame e ized by a
mechanical model. In his way, he ela i e posi ions o he op ical
modules can be de e mined o wi hin 0.15 m. Acous ic signals a e p o-
cessed a 10-min in e als; he esul s o he i a e in e pola ed o
p o ide he ela i e posi ions o he op ical modules o e ime
75
. A
he ime o he e en , he s ing il s changed s eadily by abou 2° o e
a ime span o 2 h, co esponding o less han 0.1° in 10 min. The unce -
ain y on he posi ion o he de ec o elemen s owing o he in e pola-
ion o he acous ic da a is hus negligible.
The acous ic sys em measu es dis ances be ween he op ical mod-
ules and acous ic emi e s bu his does no cons ain he absolu e
o ien a ion o he elescope on Ea h. Du ing sea campaigns, he posi-
ions o he de ec ion lines and acous ic emi e s a e measu ed. The
emi e posi ions a e used o de e mine he nominal absolu e o ien a-
ion. These da a a e a a p esen accu a e o app oxima ely 10 m. This
is suppo ed by compa isons wi h wo ba hyme y da ase s ( o he
e ical posi ions) and in e nal c oss-checks wi h he acous ic sys em
( o he ho izon al posi ions). The posi ion unce ain y ansla es, a e
conse a i ely ounding he esul , o an unce ain y o 1° on o a ions
o he de ec o a ound each o he h ee axes.
An independen c oss-check o he poin ing was pe o med by means
o a measu emen o he di ec ional de ici o a mosphe ic muons
owing o he abso p ion o cosmic ays in he Moon, simila o e . 76.
This an i-signal o he Moon was s udied in 335 days o da a when he
de ec o consis ed o 19 and 21 de ec ion lines. The Moon shadow signal
was ound a a signi icance o 3.2σ. In e alua ing he Moon shadow o
di e en assumed o a ions a ound he e ical axis, in he ange ±3°
in s eps o 0.25°, he la ges signi icance was ound o he nominal
o ien a ion. The co esponding unce ain y is e alua ed by means o
simula ions o 0.24°.
A compa ison o de ec o -line dep hs de e mined wi h he acous ic
sys em and he wo ba hyme y da ase s yields u he e idence ha
he sys em is aligned o wi hin 1°.
P opaga ing he 1° unce ain y o he celes ial coo dina es o he
e en yields a ci cula 68% con idence egion on he sky wi h a adius o
1.5°. This unce ain y is he dominan sou ce o (sys ema ic) unce ain y
in he de e mina ion o he celes ial coo dina es o KM3-230213A.
Simula ions o muons in he same loca ion as KM3-230213A we e
pe o med a ene gies om 1 o 1,000 PeV o e alua e he s a is ical
unce ain y on he di ec ion es ima ion. A 100 PeV, 50% (90%) o he
muons a e econs uc ed wi hin 0.12° (0.28°) om he nominal di ec-
ion. The azimu hal unce ain y inc eases wi h ene gy, so ha , o an
ene gy o 500 PeV, 50% (90%) o he muons we e econs uc ed wi hin
0.17° (0.38°). These unce ain ies a e negligible wi h espec o he
1.5° 68% con idence egion and a e men ioned he e only o indica e
he u u e po en ial o a ully aligned de ec o .
We o esee upg ading he de ec o in he nex sea campaign by using
new acous ic emi e s whose absolu e posi ion will be measu ed wi h
<1-m accu acy in each di ec ion. This, as well as he ex a collec ed
da a o he Moon shadow analysis, will allow o a ecalib a ion o
he da a and a mo e p ecise de e mina ion o he celes ial o igin o
KM3-230213A.
Ene gy es ima e
The ene gy o a muon abo e a ew TeV can be es ima ed by measu ing
i s ene gy loss. Radia i e ene gy losses p oduce showe s o cha ged
pa icles along he muon ajec o y ha induce excess Che enko
pho ons along he ack. The pho ons a i e on he PMTs e y close in
ime, p oducing a la ge numbe o pho oelec ons ha ansla e in o
hi s wi h a la ge ime-o e - h eshold. In he case o KM3-230213A, he
la ge numbe o pho ons induced by he muon sa u a es mos o he
PMTs wi hin abou 100 m om he ack, and hi s a e eco ded e en
up o a dis ance o 300 m. This sa u a ion e ec is isible in mo e han
25% o he PMTs ha pa icipa ed in he igge ing o KM3-230213A
Ex ended Da a Fig. 4 | Illus a ion o he opog aphy. Using ba hyme ic
da a om EMODne 90, a sec ional iew along he incoming di ec ion and
posi ion o he e en is shown, wi h he sea shown in blue and he seabed and
he ock benea h in b own. The x axis indica es he o al dis ance om he
ARCA si e and he y axis and g ey lines ep esen he dep h wi h espec o
he sea le el. The shaded a ea shows he e ec o a a ia ion o ±1.5° in he
di ec ion econs uc ion, co esponding o he 68% e o egion om he
e alua ion o sys ema ic unce ain ies.

A icle
Ex ended Da a Fig. 5 | All- la ou sky-a e aged e ec i e a ea o KM3NeT/ARCA. The a ea in he 21 de ec ion line con igu a ion is shown as a unc ion o
neu ino ene gy. This e ec i e a ea is compu ed a e applying he e en selec ion desc ibed in he ex and is a e aged be ween neu inos and an ineu inos.
Ex ended Da a Table 1 | Da ase s and me hods used in he sea ches o a cosmic poin -like neu ino sou ce in he di ec ion o
KM3-230213A. Re s. 91–93
Fo each in es iga ed da ase , he co esponding de ec o , co e ed pe iod, li e ime, ype o da a, analysis me hod and adius o he ci cula inspec ed egion cen ed a he loca ion o
KM3-230213A a e epo ed. The ‘Type o da a’ column e e s o ully calib a ed da a (o line) o using p elimina y calib a ions (online). KM3-230213A was emo ed om he ARCA6-21 da ase .
The ANTARES da ase is aken om h ps://an a es.in2p3. /da a/da a-se - o - he-2007-2017-an a es-sea ch- o -cosmic-neu ino-poin -sou ces/; i is analysed wi h a me hod om e . 94,
wi h he di e ence ha no ene gy in o ma ion is conside ed in he likelihood and ha a wo-dimensional Gaussian is used o desc ibe he signal spa ial dis ibu ion. Fo he IceCube da a,
he IceCubePy amewo k95 is used, wi hou including he ene gy in o ma ion in he likelihood.
A icle
Ex ended Da a Table 2 | Resul s o he sea ches o a cosmic poin -like neu ino sou ce in he di ec ion o KM3-230213A
Fo each in es iga ed da ase , he co esponding esul s a e shown in e ms o he numbe o signal e en s (ei he obse ed in he ON egion o i ed by he likelihood maximiza ion), p e- ial
P- alue and 90% con idence le el uppe limi on he one- la ou neu ino lux no maliza ion a 1 GeV,
+
Φνν
1GeV
, assuming a neu ino spec um o =
++ −
ΦEΦE() ((GeV))
νν νν
1GeV 2
. In he case o
likelihood scan (ARCA6-21, ANTARES, IceCube), esul s a e gi en bo h o he loca ion o KM3-230213A (RA = 94.3°, dec. = −7.8°) and o he mos signi ican di ec ion in he inspec ed egion,
oge he wi h equa o ial coo dina es and dis ance om he e en . Fo he mos signi ican di ec ion, he pos - ial P- alue (P- alue) is also p o ided. The i h ow epo s he combined limi o
he wo ORCA analyses ob ained wi h he dedica ed amewo k MOMENTA96.
Ex ended Da a Table 3 | Po en ial blaza s pinpoin ed using he s a egies desc ibed in Me hods, loca ed wi hin 68%, 90%
and 99% e o egions a ound KM3-230213A
Thei posi ions a e gi en in equa o ial (J2000) coo dina es. Sou ces a e numbe ed acco ding o hei dis ance om KM3-230213A, co esponding o he sou ce lis ed in he ‘Name’ column. The
‘Associa ion’ column includes ca alogued objec s a o he wa eleng hs ha a e associa ed wi h his sou ce. The las column indica es he me hod ha led o he iden i ica ion o he sou ce.