Dipole portal and neutrinophilic scalars at DUNE revisited The importance of the high-energy neutrino tail Maksym Ovchynnikov1 2Thomas Schwetz1yand Jing-Yu Zhu1 3z

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Dipole portal and neutrinophilic scalars at DUNE revisited:

The importance of the high-energy neutrino tail

Maksym Ovchynnikov,1, 2, ∗Thomas Schwetz,1, †and Jing-Yu Zhu1, 3, ‡

1Institut f¨ur Astroteilchen Physik, Karlsruher Institut f¨ur Technologie (KIT),

Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

2Instituut-Lorentz for Theoretical Physics, Universiteit Leiden,

Niels Bohrweg 2, 2333 CA Leiden, The Netherlands

3School of Physics and Astronomy and Tsung-Dao Lee Institute,

Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai 200240, China

We estimate the sensitivity of the DUNE experiment to new physics particles interacting with

neutrinos, considering the dipole portal to heavy neutral leptons and a neutrinophilic scalar with

lepton-number 2 as examples. We demonstrate that neutrinos from the high-energy tail of the

DUNE ﬂux, with energies Eν&5−10 GeV, may signiﬁcantly improve the sensitivity to these

models, allowing to search for particles as heavy as '10 GeV. We also study the impact of the

so-called tau-optimized neutrino beam conﬁguration, which slightly improves sensitivity to the new

physics models considered here. For both models, we consider new production channels (such as

deep-inelastic scattering) and provide a detailed comparison of diﬀerent signatures in the detector.

CONTENTS

I. Introduction 1

II. High-energy neutrinos at DUNE 2

A. The DUNE experiment 2

B. Neutrino ﬂux at DUNE 2

C. High-energy neutrinos and production of new

physics particles 4

III. Neutrino dipole portal 4

A. Phenomenology at DUNE 5

B. Discussion of results 6

IV. Neutrinophilic scalar portal 8

V. Conclusions 10

A. Flux of muon and electron neutrinos at DUNE 13

B. Dipole portal 14

1. Production 14

a. Decays of mesons 14

b. Neutrino up-scattering – inside 15

c. Neutrino up-scattering – outside 17

d. Comparison of diﬀerent production

channels 18

2. Number of events at DUNE 19

3. The shape of the sensitivity curves 20

C. Neutrinophilic scalar portal 21

1. Production 21

a. Quasi-elastic production 21

b. Deep inelastic scattering production 22

∗maksym.ovchynnikov@kit.edu

†schwetz@kit.edu

‡jing-yu.zhu@kit.edu

2. Number of events and discussion of

sensitivity 22

I. INTRODUCTION

In a broad class of Standard Model (SM) extensions,

an interaction of SM neutrinos with new particles in

the few GeV mass range is introduced. Such models

may be probed at neutrino experiments, where a high-

intensity neutrino beam is produced, see e.g. [1]. Ex-

amples of currently running and future neutrino beam

experiments are T2K [2,3], MiniBooNE [4], Micro-

BooNE [5] and DUNE [6]. Other promising facilities to

look for such new particles are LHC-based experiments

such as SND@LHC [7], FASERν[8], or beam-dump ex-

periments like SHADOWS [9] and SHiP [10].

The goal of this paper is to demonstrate the poten-

tial of the DUNE experiment to search for interactions

of new physics particles with neutrinos. We do this by

revising the sensitivity of DUNE to two example models

– a neutrinophilic scalar [11,12] and the dipole portal to

heavy neutral leptons (HNLs) [13,14]. We improve on

previous studies [11,12,15,16] in several aspects. First,

we include the high-energy neutrino tail in the calcula-

tion of the production rate, showing its importance to

extend the reach in the mass of new physics particles,

and we study the eﬀect of the so-called tau-optimized

beam conﬁguration. In particular, we demonstrate that,

depending on the model, DUNE may have sensitivity to

new physics particles with masses up to O(10 GeV) – a

few times larger than what it was obtained in the previ-

ous literature. Furthermore, for both models, we consider

new production channels for the new particles. For the

dipole portal, we discuss additional detection signatures;

the ratio of the diﬀerent signal types is a speciﬁc pre-

diction of the dipole portal, allowing us to identify this

model in case of detection.

arXiv:2210.13141v2 [hep-ph] 26 Mar 2023

Detector Stransverse Ldet Lto det nnucl

ND 2 ×6 m24 m 574 m 8.4×1029 m−3

FD 12 ×14 m258.2 m 1285 km 8.4×1029 m−3

Table I: Parameters of Near Detector and individual Far

Detector module at DUNE. The numbers are taken from [17,

18], where Stransverse,Ldet,Lto det, and nnucl stand for the

ﬁducial cross-sectional area of the detector, the ﬁducial length

of the detector, the distance to the proton collision point, and

the nucleon number density, respectively.

The paper is organized as follows. In Sec. II, we dis-

cuss the ﬂux of neutrinos at DUNE and stress the impor-

tance of its high-energy tail for the production of heavy

particles. In Sec. III, we consider the dipole portal to

HNLs, reestimate the DUNE sensitivity by considering

new production channels such as deep inelastic scatter-

ing and new search signatures. In Sec. IV, we discuss

the neutrinophilic scalar portal, revising the sensitivity

in a similar way. Finally, we conclude in Sec. V. Tech-

nical details, expressions for matrix elements and cross

sections, as well as further discussion can be found in

several appendices.

II. HIGH-ENERGY NEUTRINOS AT DUNE

A. The DUNE experiment

DUNE [6] is the next-generation long-baseline neu-

trino oscillation experiment, primarily aiming at pre-

cisely measuring neutrino oscillation parameters, such as

the unknown CP violation phase in the lepton sector. On

the other hand, it is also a powerful tool to search for a

variety of new physics beyond the SM. By using a 120

GeV proton beam onto a graphite target with a beam

power of 1.2 MW, this experiment can provide 1.1 ×1021

PoT/year, generating a large ﬂux of light mesons such as

π±, K±,0. A fraction of these mesons then would decay

inside a 194 meter long decay pipe, producing neutrinos.

As a result, DUNE provides the world’s most intense

neutrino beam with a wide range of neutrino energies

peaking at about 2.5 GeV. The interactions of neutri-

nos are supposed to be studied in two detectors – the

near detector (ND) and the far detector (FD). The for-

mer is designed to include a 67.2 ton Liquid Argon Time

Projection Chamber (LArTPC), a magnetized gaseous

argon time projection chamber, and a large, magnetized

monitor, which will be located 574 m downstream of the

neutrino target following the decay pipe. The FD will be

equipped with four 10-kton LArTPC modules at a dis-

tance of 1285 km from the target; one can refer to Fig 1.4

in Ref. [17] for the layout of the modules. The useful pa-

rameters of ND and FD are summarized in Table I.

In order to maximize the ﬂux of neutri-

nos/antineutrinos in the direction of the DUNE

detectors, the charged particles need to be collimated

with respect to the beam axis by a magnetic horn

νe, ND, CP-opt.

νμ, ND, CP-opt.

ντ+ντ, ND,×105

ντ, FD,×105, CP-opt.

νe, ND, τ-opt.

νμ, ND, τ-opt.

ντ, FD,×105,τ-opt.

0.5 1 5 10 50 100

10-12

10-10

10-8

10-6

10-4

Eν

[

GeV

]

Φν[GeV-1PoT-1m-2]

Figure 1: Neutrino ﬂuxes as deﬁned in Eq. (1) of νe,µ,τ at

the DUNE ND and the ﬂux of ντat the DUNE FD (due to

νµ→ντoscillations), assuming neutrino operating mode of

the focusing horns. ντﬂuxes are magniﬁed by a factor 105

for better visibility. The results for two beam conﬁgurations

are shown: the CP-optimized (solid), and the tau-optimized

(dashed). Note that the ντﬂux at the ND does not depend

on the horn conﬁguration, since it originates from decays of

promptly decaying Dsmesons and τleptons.

system. In dependence on the operating mode (the one

for neutrino or antineutrino), correspondingly positively

or negatively charged particles would be collimated. The

ﬂux in antineutrino mode is very similar to the one in

neutrino mode (see e.g., Fig. 5.4 in [6]), and we expect

similar sensitivities to the new physics models discussed

below for neutrino and antineutrino beam modes. To be

speciﬁc, in this work, we will only consider the neutrino

mode.

In addition, there are two horn conﬁgurations consid-

ered by the DUNE collaboration: the CP-optimized con-

ﬁguration, which maximizes the ﬂux at Eντ<5 GeV im-

portant to study CP violations in neutrino oscillations,

and the tau-optimized conﬁguration, for which the ﬂux

of τneutrinos at the FD with Eν<5 GeV is some-

what lower, but the higher-energy ﬂux between 5 and

10 GeV gets signiﬁcantly increased, which would result

in an order of magnitude higher number of neutrino deep-

inelastic scattering (DIS) events [6].

B. Neutrino ﬂux at DUNE

We deﬁne the neutrino ﬂux at a given detector as

Φν≡1

NPoT ·Stransverse

dNν

dEν

,(1)

where NPoT is the number of protons on target, Stransverse

is the transverse area of the detector (Table I), dNν/dEν

is the diﬀerential distribution of neutrinos traveling in the

direction of the detector. The ﬂuxes at ND and FD for

various neutrino ﬂavors, assuming the neutrino operating

mode, are shown in Fig. 1. Below, we brieﬂy discuss their

main characteristics.

The electron and muon neutrinos at DUNE are pro-

duced mainly by decays of light long-lived mesons such

as π±, K±, K0

L, and muons. The low-energy part of the

spectra of νµ(Eνµ.6 GeV) and νe(Eνe.10 GeV)

originates from decays

π+→νµ+µ+, µ+→νe+ ¯νµ+e+(2)

correspondingly. The high-energy tail comes from decays

of kaons K+, K0

L. The relative suppression νe/νµcomes

from the fact that muons are long-lived, τµ/τπ/K ∝102,

and only a small fraction of them, '10−2, decays

inside the decay pipe before being scattered/absorbed

in the material after the decay pipe. To obtain the

ﬂuxes of these neutrinos, we use the publicly available

results of the detailed GEANT4 [19–21] based simula-

tion (G4LBNF) of the LBNF beamline developed by the

DUNE collaboration [6,22]. Technical details are given

in Appendix A.

When considering the DUNE sensitivity to new physics

interacting with νe,µ, we will only consider the ND. The

reason is that the ﬂuxes of νe/µ at the FD are much

smaller than at the ND due to the much smaller angular

coverage of the FD. To argue this point, let us compare

the products of the ﬂux times the detector volume Vdet,

Φ×Vdet, at the ND and FD. Using that VFD/VND ≈800

if assuming four FD module (Table I), and neglecting the

oscillations for the moment, one has

ΦFD

νe/µ VFD

ΦND

νe/µ VND ∼800 ×Lto ND

Lto FD 2

= 1.6·10−4,(3)

where (Lto ND/Lto FD)2≈2·10−7is the solid angle sup-

pression (see Table I). Thus, the FD is less relevant for

searching for hypothetical BSM particles interacting with

these ﬂavors.

Let us now discuss τneutrinos. At the DUNE ND,

their main production channels are the decays

D+

s→τ++ντ, τ+→¯ντ+X(4)

and their charge conjugated channels, where Xdenotes

lepton or hadron ﬁnal states. Since Dsand τdecay

promptly, their distribution (and hence the ﬂux of τneu-

trinos and antineutrinos at ND) is not aﬀected by the

horn conﬁguration. However, the ﬂux of these Ds/τ-

originated ντs or ¯ντs at the FD would be too small com-

pared to the ﬂux of ντoriginated from the oscillations

νµ→ντ, and therefore the former can be safely ignored.

Only the latter (ντfrom oscillations) would be present

at the FD when we calculate the sensitivities of neutrino

mode to new physics.

The DUNE simulations did not include Dsmesons and

τleptons. To generate the τneutrino ﬂux, we have used

the spectrum of Dsmesons from [23], then simulated the

decay chain (4) (see the Appendix A), and selected the

τneutrinos that point to the ND.

The relative ﬂux suppression ντ/νµat the ND para-

metrically behaves as

ΦND

ντ+¯ντ

ΦND

νµ'Ppp→Ds·Br(Ds→τ)

Ppp→π+

pEν'3·10−8×pEν.

(5)

Here, Ppp→Ds'4·10−6,Ppp→π+≈6.3 are multiplic-

ities (the number of decayed mesons per PoT), taken

from [24], Br(Ds→τ)≈0.055 [25], and pEνis a fac-

tor depending on the neutrino energy, varying from O(1)

at Eν.3 GeV to '103for Eν'50 GeV. The reason

of this behavior is that τleptons (and hence τneutrinos)

have much larger mean energy than pions and kaons (and

hence νe/µ) decaying inside the decay pipe.

Apart from the production in decays of mesons and τ

leptons, ντmay also be produced via oscillations νµ→

ντ. This channel is not relevant for the ND, since the

typical neutrino oscillation length is much larger than the

distance from the target to ND. However, it becomes the

main contribution to the ντﬂux at the FD (see Sec. II).

To obtain the oscillated ﬂux at the FD, we have ﬁrst

extracted the ﬂux of νµat the FD, and then convoluted

it with the oscillation probability

Pνµ→ντ≈0.943 ×sin2∆m2L

4Eν(6)

assuming ∆m2= 2.523 ×10−3eV2and L≈1300 km

for all neutrinos. The resulting ﬂux is

ΦFD

ντ= ΦFD

νµ×Posc 'ΦND

νµ×Lto ND

Lto FD 2

×Pνµ→ντ,(7)

where Pνµ→ντis O(1) at the FD. Since the oscillation

probabilities νµ→ντand ¯νµ→¯ντare the same up to

small CP-violating eﬀects, independently on the oscillat-

ing neutrino energy, the property of the relative suppres-

sion of the antineutrino to neutrino ﬂuxes in the neutrino

mode translates to the ﬂuxes of τneutrinos and antineu-

trinos at the FD.

Therefore, the ντﬂuxes at the ND and FD have a

diﬀerent origin. As a result, the conclusion that the FD

is not relevant for the DUNE sensitivities to new physics

becomes invalid in the case of interactions with τﬂavor.

To illustrate this, let us again compare the products of

the ﬂux times the detector volume. For the CP-optimized

horn conﬁguration, using Eqs. (5), (7), one has

ΦFD

ντ×VFD

ΦND

ντ×VND '1·103Posc(Eν)

pEν

.(8)

Considering the FD and Eν.5 GeV, both Posc and

pEνcan be of O(1), leading to the ratio in Eq. (8) being

very large. Hence, the FD may provide better sensitiv-

ities to new physics coupling to ντ[15]. However, since

Posc(Eν)∼E−2

νat energies Eν&10 GeV, together with

large pEνthey cause the suppression of this ratio at large

energies. As a result, with the increase of the neutrino

Detector Horn conf. NνeNνµNντ

ND CP-optimized 1.3·10−41.2·10−27.5·10−10

ND tau-optimized 1.0·10−41.4·10−27.5·10−10

FD CP-optimized 1.8·10−98.9·10−91.5·10−8

FD tau-optimized 1.05 ·10−91.4·10−81.1·10−8

Table II: Numbers of neutrinos per PoT within the angular

acceptance of the DUNE detectors (ND or FD), assuming the

parameters of the detectors given by Table I. Neutrino oscil-

lations are included. Two horn conﬁgurations are assumed:

CP-optimized and tau-optimized. For FD, we report numbers

corresponding to one module.

energy, the ratio (8), being 1 at Eν=O(1 GeV),

quickly drops and becomes O(1) at Eν'15 GeV.

The situation is somewhat diﬀerent for the tau-

optimized horn conﬁguration, for which tau neutrinos

at the FD are more energetic on average (see Fig. 1),

although qualitatively the conclusions do not change.

Therefore, both the ND and FD may be important for

searching for new particles coupling to ντ, depending on

their mass.

The total numbers of neutrinos traveling in the direc-

tion of the DUNE detectors (with the parameters given

in Table I) per PoT are given in Table II.

C. High-energy neutrinos and production of new

physics particles

In Refs. [12,15], which have studied the sensitivity

of DUNE to new physics particles produced in scatter-

ings of electron and muon neutrinos, artiﬁcial cuts on

the neutrino spectrum have been imposed: Eν<6 GeV

and Eν<10 GeV correspondingly. This is reasonable

if one studies the production of particles Ywith mass

mYEν,max. Indeed, ﬁrst, the production of such par-

ticles does not require large energies. Second, only a tiny

fraction of νe, νµhave energies Eν>5−10 GeV, see

Fig. 1.

However, as we show below, these cuts can signiﬁcantly

underestimate the maximal mass of new physics particles

that may be searched for at DUNE. Namely, the sensitiv-

ity of DUNE estimated in [12,15] rapidly drops at masses

mY= 2.5−3 GeV, which is directly related to the cuts.

To understand this, let us look closer at the relevant Y

production processes (here without specifying the model

details). Correspondingly, they are1

ν+p→Y+p, ν +p→Y+µ+n, (9)

1Apart from the scatterings oﬀ nucleons, [15] considered scatter-

ings oﬀ electrons and nuclei, but the former requires much larger

neutrino energies to produce a particle with the given mass, while

the latter is suppressed due to nuclear form factors for large

masses mr−1

nuclear.

ν+p→Y+p

ν+p→Y+n+μ,pT,Y>0.5 GeV

0.01 0.05 0.10 0.50 1 5 10

0.1

0.5

100

mY[GeV]

Eν,min [GeV]

Figure 2: Dependence of the minimal neutrino energies

E(1),(2)

ν,min , Eq. (11), required to produce a particle Yin the

scattering processes in Eq. (9), on the Ymass. The short-

and long-dashed black lines denote correspondingly the max-

imal energies of νe,µ and ντobtained in the simulation (see

Fig. 1).

where n, p are nucleons, and in the second process

a threshold for the invisible transverse momentum of

pT,Y > pT,min = 0.5 GeV is required to suppress back-

grounds (we will discuss this in more detail in Sec. IV).

The minimal energy Eν,min of the neutrino required to

produce the particle Yin these processes is, correspond-

ingly,

E(1)

ν,min =2mpmY+m2

2mp

,(10)

E(2)

ν,min '

hmn+mµ+qm2

Y+p2

T,min +p2

T,min

2(mn+mµ)i2

−m2

2mp

(11)

The behavior of E(1),(2)

ν,min as a function of mYis shown

in Fig. 2. We see from the ﬁgure that at DUNE it actu-

ally may be possible to produce much heavier particles

– up to mY'8 GeV (the production from νe/µ), or to

mY'10 GeV (from ντ) if neutrinos with energies up

to 100 GeV are taken into account, oﬀering a potential

trade-oﬀ to the reduced ﬂux at high energies.

In the next two sections, we will study how the DUNE

sensitivity to the mentioned models extends in detail.

We will consider both ND/FD CP-optimized and tau-

optimized horn conﬁgurations.

III. NEUTRINO DIPOLE PORTAL

The eﬀective Lagrangian of the neutrino dipole portal

below the electro-weak (EW) scale is [13]

Ldipole =dα¯

Nσµν PLναFµν + h.c.,(12)

where ναis the SM neutrino of ﬂavor α=e, µ, τ,σµν =

2[γµ, γν], PL= (1 −γ5)/2, Fµν =∂µAν−∂νAµis the

electromagnetic ﬁeld strength tensor, and Nis a Heavy

Neutral Lepton (HNL).

Note that this Lagrangian is not gauge-invariant and

therefore valid only at energies below the EW scale,

above which we need to consider UV-completions of the

operator in Eq. (12). Here we remain agnostic about

the UV origin of this new interaction and study its phe-

nomenological implications at energies below the EW

scale.

Motivated by the unsolved MiniBooNE [26],

ANITA [27,28], and muon g-2 anomalies [29,30],

the dipole portal provides another way to test the

existence of HNLs and has attracted a lot of attention

recently [15,16,31–48]. Bounds on dαcome from various

laboratory, astrophysical and cosmological observations.

Laboratory constraints come from neutrino oscillation

experiments, dark matter detectors, and the observa-

tion of high-energy neutrinos in neutrino telescope by

studying coherent elastic neutrino-nucleus scattering,

elastic neutrino-electron scattering, deep inelastic inter-

actions, etc. Astrophysical constraints on dαarise from

supernova bursts, Big Bang Nucleosynthesis, or Cosmic

Microwave Background. We refer to Refs. [13,14,46]

for a compilation of various constraints.

A. Phenomenology at DUNE

The DUNE sensitivity to HNLs with a dipole por-

tal interaction has been studied previously in Refs. [15,

16]. The HNL production mechanism studied there was

mainly quasi-elastic (QE) neutrino up-scattering [13],

να+T→N+T, (13)

where T=e, n/p, Ar or atomic nuclei in the crust along

the trajectory of the neutrino beam.

Here, we will include also the deep-inelastic (DIS) con-

tribution, να+p/n →N+X, where Xis an arbitrary

hadronic state, see Fig. 3(a). Furthermore, in addition to

the neutrino up-scattering, we consider the production of

HNLs by decays of short-lived and long-lived mesons [13],

π±,0, K±,0, η, ρ0, see Fig. 3(b), (c) for two example dia-

grams. A detailed discussion of the relevant cross sections

and production rates is given in Appendix B 1. The HNL

production may occur either inside the detector (neutrino

up-scattering) or outside it (both neutrino up-scattering

and meson decays). In the latter case, HNLs need to

reach the detector in order to decay inside it and hence

be detected. As discussed in detail in Appendix B1d, in

most cases the production from meson decays plays only

a sub-leading role and the main production channel is ei-

ther inside or outside up-scattering. The only exception

is HNL production via dτat the ND.

The main HNL decay channels are

N→γ+να, N →l++l−+να,(14)

with l=e, µ. The dominant channel is the mono-photon

channel, with the decay width being

ΓN→ναγ=|dα|2m3

4π(15)

for Dirac neutrinos.

Above the di-electron and di-muon mass threshold,

the leptonic channel becomes available. This channel

has been considered in ref. [35] in the context of test-

ing the dipole portal at FASER and in ref. [40] in the

context of the T2K near detector. These processes are

sub-dominant. However, they have the advantage that it

is possible to reconstruct the decay vertex since we have

two charged particles. In the limit mN2ml, the decay

width behaves as

ΓN→ναl+l−≈αEM|dα|2m3

12π2log m2

l−3(16)

The branching ratios of the leptonic decay modes are

shown in Fig. 4. At large masses mNml, the

suppression of the leptonic decay width with a factor

αEM/3π'10−3compared to the photon channel (15)

gets partially compensated by the logarithm.

The two decay modes lead to diﬀerent experimental

signatures and imply diﬀerent requirements for back-

ground rejection. Furthermore, if both decay channels

can be observed, their ratio is a speciﬁc prediction of the

model, serving as a smoking-gun signature.

The combination of the diﬀerent production and decay

processes leads to diﬀerent signatures of the dipole portal

at DUNE:

1. Monophoton – an event consisting of a single iso-

lated photon appearing inside the detector. This

type of events occur when the HNL is produced

outside of the detector (via e.g. decays of mesons

or by neutrino up-scatterings), then enters the de-

tector, and decays through N→ν+γ.

2. Double-bang – an event inside the detector con-

sisting of two vertices: the one with recoil matter

particles (electrons, nucleons, nuclei) and the one

with a displaced monophoton or a pair of charged

leptons [16,32]. This type of signature appears if

a HNL is produced inside the detector via neutrino

up-scattering, and then travels a distance larger

than the DUNE spatial resolution, which is of order

∆lDUNE '1 cm [17].2

2Whether the recoil particle (and hence the HNL production

point) would be detected depends on the recoil energy of the

target particles. If it is below the DUNE energy detection thresh-

old, it will be not visible. In this case, instead of the double-bang

event, one would see a monophoton from the decaying HNL. In

our current estimates, we assume ideal recoil energy reconstruc-

tion eﬃciency.

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DipoleportalandneutrinophilicscalarsatDUNErevisited:Theimportanceofthehigh-energyneutrinotailMaksymOvchynnikov,1,2,ThomasSchwetz,1,yandJing-YuZhu1,3,z1InstitutfurAstroteilchenPhysik,KarlsruherInstitutfurTechnologie(KIT),Hermann-von-Helmholtz-Platz1,76344Eggenstein-Leopoldshafen,Germany2Instituut-...

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Dipole portal and neutrinophilic scalars at DUNE revisited The importance of the high-energy neutrino tail Maksym Ovchynnikov1 2Thomas Schwetz1yand Jing-Yu Zhu1 3z

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