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JHEP04(2018)136

Published for SISSA by Springer

Received: March 6, 2018

Revised: April 6, 2018

Accepted: April 7, 2018

Published: April 26, 2018

Light scalar dark matter at neutrino oscillation

experiments

Jiajun Liao,

Danny Marfatia

and Kerry Whisnant

Department of Physics and Astronomy, University of Hawaii-Manoa,

2505 Correa Rd., Honolulu, HI, 96822 U.S.A.

Department of Physics and Astronomy, Iowa State University,

2323 Osborn Drive, Ames, IA, 50011 U.S.A.

E-mail: liaoj@hawaii.edu, dmarf8@hawaii.edu, whisnant@iastate.edu

Abstract: Couplings between light scalar dark matter (DM) and neutrinos induce a per-

turbation to the neutrino mass matrix. If the DM oscillation period is smaller than ten

minutes (or equivalently, the DM particle is heavier than 0.69×10

−17

eV), the fast-averaging

over an oscillation cycle leads to a modiﬁcation of the measured oscillation parameters. We

present a speciﬁc µ − τ symmetric model in which the measured value of θ

is entirely

generated by the DM interaction, and which reproduces the other measured oscillation

parameters. For a scalar DM particle lighter than 10

−15

eV, adiabatic solar neutrino prop-

agation is maintained. A suppression of the sensitivity to CP violation at long baseline

neutrino experiments is predicted in this model. We ﬁnd that DUNE cannot exclude the

DM scenario at more than 3σ C.L. for bimaximal, tribimaximal and hexagonal mixing,

while JUNO can rule it out at more than 6σ C.L. by precisely measuring both θ

and θ

Keywords: Neutrino Physics, Beyond Standard Model, Solar and Atmospheric Neutrinos

ArXiv ePrint: 1803.01773

Open Access,

 The Authors.

Article funded by SCOAP

https://doi.org/10.1007/JHEP04(2018)136

JHEP04(2018)136

Contents

1 Introduction 1

2 The model 2

3 Eﬀects on neutrino oscillation parameters 4

3.1 Short-baseline reactor experiments 4

3.2 Long-baseline appearance experiments 4

3.3 Medium-baseline reactor experiments 5

3.4 Solar neutrinos 6

3.5 Atmospheric neutrinos 7

4 Tests of the model in future neutrino experiments 8

5 Summary 10

A Second-order corrections 11

B A general treatment of oscillation probabilities 13

1 Introduction

The existence of DM has been well established through various cosmological and astrophys-

ical observations. However, after decades of experimental searches for DM, the particle

nature of DM is still unknown, and viable DM particle candidates span an enormous mass

range from fuzzy DM [1] to primordial black holes [2]. Among the DM candidates, fuzzy

DM with a mass range 1–10 ×10

−22

eV has attracted much attention recently since it can

resolve the small scale crisis for standard cold DM due to its large de Broglie wavelength;

see ref. [3] and references therein. Constraints on fuzzy DM can be obtained from Lyman-α

forest data and a lower limit of 20×10

−22

eV at 2σ C.L. has been set from a combination of

XQ-100 and HIRES/MIKE data [4], although a proper handling of the eﬀect of quantum

pressure and systematic uncertainties may relax the limit [5]. Nevertheless, light scalar DM

candidate of mass below a few keV are generally expected in many extensions of the Stan-

dard Model (SM). Examples include a QCD axion [6–8], moduli [9–12], dilatons [13, 14],

and Higgs portal DM [15]. Constraints on hot DM require that light scalar DM cannot be

produced thermally in the early universe. A popular production mechanism for generating

light scalar DM is the misalignment mechanism, in which the ﬁelds take on some initial

nonzero value in the early universe, and as the Hubble expansion rate becomes comparable

to the light scalar mass, the DM ﬁeld starts to oscillate as a coherent state with a single

macroscopic wavefunction [16].

The properties of light scalar DM can be probed if they are coupled to SM fermions,

which induce a time variation to the masses of the SM fermions due to the oscillation of

– 1 –

JHEP04(2018)136

the DM ﬁeld. Here we consider the couplings between the light scalar DM and the SM

neutrinos, which were ﬁrst studied in ref. [17] by using the nonobservation of periodicities

in solar neutrino data. Constraints on light scalar DM couplings were also considered in

refs. [18, 19] by using the data from various atmospheric, reactor and accelerator neutrino

experiments. In general, the interactions between DM and neutrinos provide a small per-

turbation to the neutrino mass matrix; a generic treatment of small perturbations on the

neutrino mass matrix is provided in refs. [20, 21]. If the DM oscillation period is much

smaller than the periodicity to which an experiment is sensitive, the oscillation probabil-

ities get averaged, and a modiﬁcation of the oscillation parameters can be induced if the

data are interpreted in the standard three-neutrino framework.

Evidence of time varying signals has been searched for in many neutrino oscillation

experiments. Super-Kamiokande ﬁnds no evidence for a seasonal variation in the atmo-

spheric neutrino ﬂux [22], and the annual modulation of the atmospheric neutrino ﬂux

observed at IceCube is correlated with the upper atmospheric temperature [23]. Monthly-

binned data from KamLAND indicate time variations in reactor powers [24]. Tests of

Lorentz symmetry via searches for sidereal variation in LSND [25], MINOS [26–28], Ice-

Cube [29], MiniBooNE [30], Double Chooz [31], and T2K [32] data, are negative. Also,

Super-Kamiokande [34] and SNO [35, 36] ﬁnd no signiﬁcant temporal variation in the solar

neutrino ﬂux with periods ranging from ten minutes to ten years. We therefore take the

DM oscillation period to be smaller than ten minutes.

In this work, we study the modiﬁcation of neutrino oscillation parameters due to

light scalar DM-neutrino interactions. Since the predictions are ﬂavor structure-dependent,

we present a speciﬁc µ − τ symmetric model in which the symmetry is broken by light

scalar DM interactions thus generating a nonzero mixing angle θ

. We ﬁrst examine

the eﬀects of this model on data from various neutrino experiments. We then study the

potential to distinguish this model from the standard three-neutrino oscillation scenario at

the future long-baseline accelerator experiment, DUNE, and the medium-baseline reactor

experiment, JUNO.

The paper is organized as follows. In section 2, we present a model in which µ − τ

symmetry is broken by the DM interactions. In section 3, we examine the implications

of this model for the measured neutrino oscillation parameters. In section 4, we simulate

future neutrino oscillation experiments to study the potential to distinguish this model

from the standard scenario. We summarize our results in section 5. In appendix A we

calculate how the scalar DM interactions with neutrinos aﬀect neutrino mass and mixing

parameters, and in appendix B we determine how the DM oscillations cause a shift in the

eﬀective neutrino oscillation parameters measured in experiments.

2 The model

The Lagrangian describing the interactions between light scalar DM and neutrinos can be

written in the ﬂavor basis as [18, 19]

L = ¯ν

Lα

∂ν

Lα

−

αβ

Lα

Lβ

−

αβ

φν

Lα

Lβ

+ h.c. , (2.1)

– 2 –

JHEP04(2018)136

where α, β = e, µ, τ, m

is the initial neutrino mass matrix, and λ is the coupling constant

matrix. Since the light scalar DM can be treated as a classical ﬁeld, the nonrelativistic

solution to the classical equation of motion can be approximated as [17]

φ(x) '

2ρ

(x)

cos(m

t −~v·~x) , (2.2)

where m

is the mass of the scalar DM particle, ρ

∼ 0.3 GeV/cm

is the local DM density,

and v ∼ 10

−3

is the virialized DM velocity. Since v  1, we neglect the spatial variation

in φ for neutrino oscillation experiments. In the presence of scalar DM interactions, the

eﬀective Hamiltonian for neutrino oscillations can be written as

H =

†

M +

√







1 0 0

0 0 0







, (2.3)

where N

is the number density of electrons. The eﬀective mass matrix can be treated as

the sum of an initial mass matrix and a small perturbation [21], i.e.,

M = U

∗







0 0

0 m

0 0 m







†

+ E cos(m

t) , (2.4)

where U

is the initial mixing matrix, m

’s are the initial neutrino eigenmasses, and the

elements of the perturbation matrix are

αβ

= λ

αβ

2ρ

= 0.0021 eV ×

αβ

−22

2ρ

0.3 GeV/cm

. (2.5)

Note that the bounds in ﬁgure 1 of ref. [17] only apply to a speciﬁc combination of λ

αβ

and m

. Planck measurements yield

< 0.23 eV at the 95% C.L. [33], which is much

larger than the size of perturbation considered here.

We consider a model in which the initial mixing angle θ

= 0 and the measured

value is generated by the DM interactions. In order to simplify our calculations, we

specialize to models in which the DM interactions only aﬀect the masses at higher orders

in the perturbation, leaving them eﬀectively unchanged. From the generalized perturba-

tion results of ref. [21], we ﬁnd that the most general perturbation satisfying the latter

requirement is of the form,

E =







√

2s

√

2c

√

2s



sin 2θ



cos 2θ

√

2c



cos 2θ

−

sin 2θ







. (2.6)

As a further simpliﬁcation, we assume the model is µ −τ symmetric, i.e., θ

= π/4. Then

the perturbation becomes

E =







0  

 

 0 −







. (2.7)

– 3 –

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