Uncovering the neutrino mass ordering with the next galactic core-collapse supernova neutrino burst using water Cherenkov detectors C esar Jes us-Valls1

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Uncovering the neutrino mass ordering with the next galactic core-collapse supernova

neutrino burst using water Cherenkov detectors

C´esar Jes´us-Valls1, ∗

1Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan

A major challenge of particle physics is determining the neutrino mass ordering (MO). Due to

matter eﬀects, the ﬂavor content of the neutrino ﬂux from a Core-Collapse Supernova (CCSN)

depends on the true neutrino MO resulting in markedly diﬀerent energy and angle distributions

for the measured lepton in water Cherenkov neutrino detectors. In this article, those distributions

are compared for eight diﬀerent CCSN models and used to study how their diﬀerences aﬀect the

determination of the neutrino mass ordering. In all cases, the inferred neutrino mass ordering is

found to be either correct or inconclusive, with no signiﬁcant false positives. However, the substantial

variation observed among model predictions emphasizes the criticality of ongoing research in CCSN

modeling.

I. INTRODUCTION

Neutrinos are essential ingredients of particle physics,

astrophysics and cosmology, and yet, some of their fun-

damental properties remain unknown. In the three-ﬂavor

picture describing experimentally observed neutrino mix-

ing, there are seven parameters divided into three neu-

trino masses (m1,m2and m3) and four mixing param-

eters (θ12,θ23,θ13 and δCP ). Currently, θ12,θ23,θ13,

δm2

21(≡m2

2−m2

1) and |∆m2

32|(≡ |m2

3−m2

2|) are known

with good precision [1, 2] so that only three quantities

remain elusive: a) the absolute neutrino mass scale, for

a review see Ref. [3], b) the value of δCP [2, 4] and c)

the sign of ∆m2

32, namely, the so-called neutrino mass

ordering (MO) that can be normal m2< m3(NMO) or

inverted m3< m2(IMO).

Regarding the MO, current data shows a statistical pref-

erence for the NMO of about 3σ[2]. Future experi-

ments Hyper-Kamiokande [5], JUNO [6] and DUNE [7]

will characterize the MO in detail via the study of at-

mospheric, reactor and accelerator neutrino oscillations.

The complementarity of the above experiments is an at-

tractive advantage: if all the MO results are consistent

the existing view of neutrino phenomenology will be re-

inforced, however, the appearance of tensions in the data

could give us hints of new physics [8–10], requiring the-

oretical extensions. In the second scenario, the presence

of additional data would be particularly helpful in dis-

entangling the true MO of new physical eﬀects. In this

regard, a unique opportunity would arise in the event of

a galactic supernova (SN) neutrino burst [11–13].

A. Supernova neutrino bursts

Core collapse Supernovae (CCSNe) emit O(1053) erg

as neutrinos, O(1058) neutrinos of ⟨Eν⟩ ∼ 10 MeV,

in a ten-second burst [14, 15]. A low galactic rate

∗E-mail: cesar.jesus-valls@ipmu.jp

of 1.63 ±0.46 CCSNe per century is expected [16].

Consequently, so far only a couple dozen neutrinos

have been detected from a single supernova, SN-1987a

[17–20]. Nonetheless, the detection of SN-1987a con-

ﬁrmed our basic understanding of CCSNe explosions and

signiﬁed the start of experimental neutrino astrophysics.

Furthermore, since the predicted neutrino ﬂux is greatly

inﬂuenced by a plethora of eﬀects, the SN-1987a data

was used to establish signiﬁcant limits on several exotic

processes [21–25] and neutrino properties, including

their mass [26, 27], magnetic moment [28] and ﬂavor

mixing [29]. These achievements, however, are just a

tantalizing hint of what might be possible with the

next generation of neutrino detectors. The increase

of available data would be spectacular, e.g., O(104−6)

detected neutrinos at Hyper-Kamiokande for a burst at

a distance of 10-1 kpc [5]. Such drastic improvement

would certainly pose new challenges, speciﬁcally, the

decrease in statistical error would force a shift of the

analysis focus towards the treatment and evaluation of

systematic uncertainties and potential model biases, so

far mostly overlooked, in order to get the most out of

the precious supernova data.

B. Experimental prospects: DUNE,

Super-Kamiokande and Hyper-Kamiokande

Among future experiments, DUNE is mainly sensitive

to the νeﬂavor, such that the (non-)observation of the so-

called neutronization peak in the ﬁrst milliseconds of the

explosion would naturally constitute strong evidence of

the IMO (NMO) [12]. Notably, the emission in this initial

stage of the explosion is also the better understood from a

phenomenological standpoint and therefore this analysis

strategy can be considered robust [12, 30]. In contrast,

water Cherenkov detectors are mainly sensitive to the ¯νe

ﬂavor and, consequently, the positive identiﬁcation of the

neutronization peak would need to be accompanied of a

more intricate analysis of the measured lepton kinematic

distributions, as highlighted in the Hyper-Kamiokande

arXiv:2210.11676v4 [hep-ex] 6 Jul 2023

design report [31]. In this article, the physics potential

of such an analysis is discussed.

C. Neutrino ﬂux predictions

The explosion mechanism of CCSN is still poorly un-

derstood [32]. However, the gradual increase in available

computational power has allowed the set of simplifying

assumptions about said mechanism to be reduced over

time, and in recent years CCSN models have begun to

achieve realistic self-triggered explosions [32]. Further-

more, a general concordance has emerged among the neu-

trino ﬂux predictions from diﬀerent research teams [33–

37]. New data from a future CCSN would be game-

changing to better understand the dynamics of the ex-

plosion. Hyper-Kamiokande will have great sensitivity to

discriminate between diﬀerent explosion models [5, 38]

and might be complemented by studies from JUNO [39]

and DUNE [30].

D. Flavor transformations

During the neutronization burst or shock period, i.e.

the ﬁrst ≲50 ms [12], the matter potential is anticipated

to be dominant over the neutrino-neutrino potential.

Consequently, ﬂavor transformations can be described by

the standard Mikheyev-Smirnov-Wolfenstein (MSW) ef-

fect [5, 12, 30, 40, 41]. Since sin2θ13 >10−3[42], a non-

oscillatory adiabatic ﬂavor conversion is expected [43],

sensitive to the neutrino MO. At later times, 50 ≲t≲

200 ms [12], during the so-called accretion phase and

along the cooling phases, that describe the remainder of

the burst, non-trivial eﬀects such as SASI (standing ac-

cretion shock instability), turbulence, and neutrino self-

interactions might change signiﬁcantly the ﬂavor compo-

sition of the ﬂux [32, 44–47].

E. Relevant interaction cross-sections

Supernova neutrino energies are typically of the order

of a few tens of MeV [20]. At such energies, the main in-

teractions with detector targets consist of neutrino- and

antineutrino-electron elastic scattering (eES) [48], elec-

tron antineutrino inverse beta decay (IBD) [49] with un-

bound protons such as Hydrogen in water, and neutrino-

nucleon charged- and neutral-current interactions with

bound nucleons (e.g. νe-CC 16O [50, 51]). Due to nu-

clear eﬀects, neutrino interactions with bound nucleons

are poorly understood [52, 53], instead, eES and IBD

predictions are well known.

II. METHODOLOGY

A. Flux models

To study diﬀerent ﬂux models, the open-sourced

software package SNEWPY [54, 55] is used. The

models under consideration are, following SNEWPY’s

nomenclature, Bollig 2016 (27 M⊙) [56], Fornax

2021 (20 M⊙) [32], Kuroda 2020 (9.6M⊙) [57],

Nakazato 2013 (20 M⊙) [58], OConnor

2015 (40 M⊙) [59], Sukhbold 2015 (9.6M⊙) [60],

Warren 2020 (13 M⊙) [61] and Zha 2021 (16 M⊙) [62].

This set of models aims to reﬂect the variability in the

existing neutrino predictions among diﬀerent models,

computational approaches and progenitor masses. To

account for ﬂavor transformations, the neutrino ﬂux

predictions are modiﬁed according to AdiabaticMSW

transformationsiusing SNEWPY. These transformations

depend on θ13 and θ23 [11], with values chosen from

the Particle Data Group [63]. Since the uncertainty

on these parameters is small the variations inﬂicted to

the expected ﬂavor predictions are minor, especially

when compared to CCSN model-to-model variations.

Henceforth, the uncertainty on these parameters is

neglected, such as in Ref. [5].

Neutrino ﬂux models, as seen in Fig. 1, have the neutrino

luminosity divided into four ﬂavor categories: Lνe,L¯νe,

Lνxand L¯νx, where x≡µ+τ. The time evolution of

the supernova explosion is markedly diﬀerent between

models such that L(t) is not a model-robust observable.

This is also true for the total neutrino luminosity

integrated over time (RLν(t)dt) due to, among other

eﬀects, scale diﬀerences, such as the progenitor mass.

However, as presented in Fig. 1, the time-integrated

fraction for each ﬂavor is consistently diﬀerent as a

function of the true neutrino MO across ﬂux models.

Since each model uses a diﬀerent time reference deﬁni-

tion, small time oﬀsets are applied by setting the t0of

each model as the time at which the neutrino luminosity

reaches its maximum. Notably, this time frame could

also be set for data by analyzing the time spectrum of

the events. Although this calculation would contribute

to the detector systematic uncertainty its role is later

neglected as it is arguably a sub-leading correctionii.

B. Observable deﬁnition

To be sensitive to the MO, it is necessary to deﬁne an

observable that changes with the ﬂux ﬂavor content such

iImplementation details are available in Appendix A of Ref. [54].

ii If a low number of interactions is recorded, statistical errors dom-

inate. Else, σt0could be determined precisely, and a small time

oﬀset would translate into a minor variation of the integrated

ﬂavor composition, due to the small ﬂavor gradients in the cu-

mulative distributions observed at around 50 ms in Fig. 1.

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Uncoveringtheneutrinomassorderingwiththenextgalacticcore-collapsesupernovaneutrinoburstusingwaterCherenkovdetectorsC´esarJes´us-Valls1,∗1KavliIPMU(WPI),UTIAS,TheUniversityofTokyo,Kashiwa,Chiba277-8583,JapanAmajorchallengeofparticlephysicsisdeterminingtheneutrinomassordering(MO).Duetomattereffects,th...

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Uncovering the neutrino mass ordering with the next galactic core-collapse supernova neutrino burst using water Cherenkov detectors C esar Jes us-Valls1

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