Supernova Neutrinos as a Precise Probe of Nuclear Neutron Skin Xu-Run Huang1and Lie-Wen Chen1 1School of Physics and Astronomy Shanghai Key Laboratory for Particle Physics and Cosmology

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Supernova Neutrinos as a Precise Probe of Nuclear Neutron Skin

Xu-Run Huang1and Lie-Wen Chen1, ∗

1School of Physics and Astronomy, Shanghai Key Laboratory for Particle Physics and Cosmology,

and Key Laboratory for Particle Astrophysics and Cosmology (MOE),

Shanghai Jiao Tong University, Shanghai 200240, China

(Dated: December 12, 2022)

A precise and model-independent determination of the neutron distribution radius Rnand thus the

neutron skin thickness Rskin of atomic nuclei is of fundamental importance in nuclear physics, particle

physics and astrophysics but remains a big challenge in terrestrial labs. We argue that the nearby

core-collapse supernova (CCSN) in our Galaxy may render a neutrino ﬂux with unprecedentedly

high luminosity, oﬀering perfect opportunity to determine the Rnand Rskin through the coherent

elastic neutrino-nucleus scattering (CEνNS). We evaluate the potential of determining the Rnof

lead (Pb) via CEνNS with the nearby CCSN neutrinos in the RES-NOVA project which is designed

to hunt CCSN neutrinos using an array of archaeological Pb based cryogenic detectors. We ﬁnd

that an ultimate precision of ∼0.1% for the Rn(∼0.006 fm for the Rskin) of Pb can be achieved

via RES-NOVA in the most optimistic case that the CCSN explosion were to occur at a distance of

∼1 kpc from the Earth.

I. INTRODUCTION

Neutrons are expected to be distributed more exten-

sively than protons in heavy neutron-rich nuclei, forming

a neutron skin which is featured quantitatively by the

skin thickness Rskin =Rn−Rpwhere Rnand Rpare the

(point) neutron and proton rms radii of the nucleus, re-

spectively. Theoretically, it has been established that the

Rskin provides an ideal probe for the density dependence

of the symmetry energy Esym(ρ) [1–15], which quanti-

ﬁes the isospin dependent part of the equation of state

(EOS) for isospin asymmetric nuclear matter and plays

a critical role in many issues of nuclear physics and as-

trophysics [16–27].

Experimentally, while the Rpcan be precisely inferred

from its corresponding charge rms radius Rch which

has been measured precisely via electromagnetic pro-

cesses [28,29], the Rnremains elusive since it is usually

determined from strong processes, generally involving in

model dependence (see, e.g., Ref. [30]). A clean approach

to determine the Rnis to measure the parity-violating

asymmetry APV in the elastic scattering of polarized elec-

trons from the nucleus since the APV is particularly sen-

sitive to the neutron distribution due to its large weak

charge compared to the tiny one of the proton [31,32].

Following this strategy, the 208Pb radius experiment

(PREX-2) [33] and 48Ca radius experiment (CREX) [34]

recently reported the determination of the Rnwith a pre-

cision of ∼1%, i.e., R208

skin = 0.283±0.071 fm for 208Pb [33]

and R48

skin = 0.121±0.026(exp)±0.024(model) fm for 48Ca

(1σuncertainty). Very remarkably, analyses within mod-

ern energy density functionals [35–37] conclude a tension

between the CREX and PREX-2 results, with the former

favoring a very soft Esym(ρ) while the latter a very stiﬀ

one, calling for further critical theoretical and experimen-

tal investigations. Especially, the Bayesian analysis [37]

∗Corresponding author; lwchen@sjtu.edu.cn

suggests that a higher precision for the Rnof 208Pb is of

particular importance to address this issue. The Mainz

Radius Experiment (MREX) [38] is expected to shrink

the uncertainty by a factor of two with a precision of

0.5% (or ±0.03 fm) for the Rnof 208Pb, but the experi-

ment’s start time is still largely uncertain [39].

Another clean and model-independent way to extract

the Rskin is through the coherent elastic neutrino-nucleus

scattering (CEνNS) [40,41], which was ﬁrstly observed

by the COHERENT Collaboration via a CsI detector

with the neutrino beam from the Spallation Neutron

Source at Oak Ridge National Laboratory [42]. Based

on the COHERENT data, the Rskin of CsI has been ex-

tracted [43,44] but the uncertainty is too large to claim a

determination, due to the low statistics of CEνNS events.

In nature, the nearby core-collapse supernova (CCSN)

may render a neutrino ﬂux with unprecedentedly high

luminosity, which provides an excellent chance to explore

CEνNS. Indeed, detecting the next galactic SN neutrinos

has received much attention both from large neutrino ob-

servatories and modern dark matter experiments [45–52].

One of the most powerful projects is the RES-NOVA ex-

periment which will hunt CCSN neutrinos via CEνNS

by adopting an archaeological Pb based cryogenic de-

tector [51,52]. One merit of RES-NOVA is that us-

ing CEνNS as its detection channel allows a ﬂavor-blind

neutrino measurement and thus avoids the uncertainties

from the neutrino oscillation. The other merit is that

archaeological Pb ensures the large CEνNS cross section

and the ultra-low levels of background, literally guaran-

teeing a high statistics.

In this work, we demonstrate that the very conﬁgura-

tion of the RES-NOVA experiment provides an ideal site

to determine the Rnof Pb, and an ultimate precision of

∼0.1% for the Rn(∼0.006 fm for the Rskin) of Pb can

be achieved in the most optimistic case that the galac-

tic CCSN would explode at a distance of ∼1 kpc from

the Earth. Even with a CCSN at 5 kpc, our present ap-

proach can still achieve a precision better than that from

arXiv:2210.04534v2 [nucl-th] 9 Dec 2022

PREX-2.

The paper is organized as follows. In Section II, we

give a brief description of the supernova neutrinos. In

Section III, we discuss the prospects of the neutrino de-

tection in RES-NOVA experiment. In Section IV, the

results on the neutron skin thickness sensitivity are pre-

sented and discussed. The conclusions are given in Sec-

tion V.

II. SUPERNOVA NEUTRINOS

The detailed knowledge of a SN neutrino ﬂux is still

missing in experiments since we have only observed two

dozen neutrino events from the SN 1987A [53,54]. How-

ever, after three decades, current neutrino experiments

have stepped into an era with unprecedented accuracy.

The robust reconstruction of SN neutrino spectra with

multiple detectors has been investigated [55–63] and an

accurate measurement is promising for a nearby SN (e.g.,

<5 kpc). Furthermore, modern SN simulations have

achieved a tremendous progress in unveiling the myster-

ies of SN phenomena [64–68]. Based on current under-

standing, the spectral shape of CCSN neutrino ﬂuxes for

each ﬂavor can be well approximated by a pinched ther-

mal distribution [69,70]

fν(Eν) = AEν

hEνiα

exp −(α+ 1) Eν

hEνi.(1)

Here, Eνand hEνiare the neutrino energy and the aver-

aged energy, αdescribes the amount of spectral pinching,

and A=(α+ 1)α+1

hEνiΓ(α+ 1) is the normalization constant,

where Γ is the gamma function. So the neutrino ﬂuence

per ﬂavor on the Earth from a CCSN at a distance dcan

be obtained as

Φ(Eν) = 1

4πd2

Etot

hEνifν(Eν),(2)

where Etot

νdenotes the total emitted energy per ﬂavor.

In a real CCSN explosion, both the amounts and spec-

tra of the emitted neutrinos change with time as the star

evolves into diﬀerent stages. However, to our goal, we

only need information of total neutrino emission. There-

fore, we adopt here the time-integrated neutrino emission

parameters from a typical long-term axisymmetric CCSN

simulation, which can be found in Table I of Ref. [58].

Note that although the neutrino emission of a CCSN

also depends on the details of the transient, e.g., the

progenitor mass, compactness, explosion dynamics, etc.,

it has a rough proﬁle of hEνi ∼ 10 MeV, 2 < α < 4

and Etot ∼1053 erg. Nevertheless, the accurate informa-

tion can be extracted from various detection data once a

nearby CCSN explosion occurs.

III. DETECTION PROSPECTS IN RES-NOVA

To explore the potential of determining the Rnof Pb

with RES-NOVA, we consider the RN-3 conﬁguration in

Table I of Ref. [51] which has a detector mass of 465 t

and an energy threshold of 1 keV. The absorber with

pure Pb is also adopted. For the detection channel, the

diﬀerential cross section in the standard model has the

form:

dσ

dT(Eν, T ) = G2

4πQ2

WF2

W(q)h1−T

Eν

−MT

2E2

νi,(3)

where GFis the Fermi coupling constant; Mdenotes

the mass of the target nucleus with N(Z) neutrons (pro-

tons); QWis the weak charge and FW(q) is the weak

form factor; Eνand Trepresent the neutrino energy and

the kinetic recoil energy of the nucleus, respectively; and

the momentum transfer qis given by q2'2MT . Note

Eq. (3) is for a nucleus with spin-0 and the result for a

spin-1/2 target (i.e., 207Pb in our case) will gain a tiny

correction [71] which is neglected in this work.

The weak charge QWcan be obtained as

QW=Zd3rρW(r) = Nqn+Zqp,(4)

where ρW(r) is the weak charge density. At tree level,

the nucleon weak charges are qn=q0

n= 2gn

Vand qp=

p= 2gp

V, where the neutron (proton) vector coupling is

deﬁned as gn

V=−1

2(gp

V=1

2−2 sin2θW) with the low-

energy weak mixing angle sin2θW= 0.23857(5) [72,73].

In the present work, we adopt the values qn=−0.9878

and qp= 0.0721 to include radiative corrections [74]. The

weak form factor FW(q) is expressed as

FW(q) = 1

QWZd3rsin qr

qr ρW(r).(5)

Here we use the Helm parametrization for the FW(q) [75,

76], which has been proven to be very successful for an-

alyzing electron scattering form factors [77,78]. The

FW(q) is then expressed as

FW(q)=3j1(qR0)

qR0

e−q2s2/2,(6)

where j1(x) = sin(x)/x2−cos(x)/x is the spherical Bessel

function of order one, R0is the diﬀraction radius and s

quantiﬁes the surface thickness. The rms radius RWof

weak charge density can then be obtained as

W=Zd3rr2ρW(r)

5R2

0+ 3s2.(7)

We use s= 1.02 fm following the discussion in Ref. [74].

The Rnand Rpare related to RWand Rch with the

following relations [74,79],

p=R2

ch − hr2

pi − N

Zhr2

ni(8)

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SupernovaNeutrinosasaPreciseProbeofNuclearNeutronSkinXu-RunHuang1andLie-WenChen1,1SchoolofPhysicsandAstronomy,ShanghaiKeyLaboratoryforParticlePhysicsandCosmology,andKeyLaboratoryforParticleAstrophysicsandCosmology(MOE),ShanghaiJiaoTongUniversity,Shanghai200240,China(Dated:December12,2022)Aprecisean...

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Supernova Neutrinos as a Precise Probe of Nuclear Neutron Skin Xu-Run Huang1and Lie-Wen Chen1 1School of Physics and Astronomy Shanghai Key Laboratory for Particle Physics and Cosmology

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