Enhanced neutrino polarizability S. Bansal1G. Paz2A.A. Petrov23M. Tammaro4J. Zupan1 1Department of Physics University of Cincinnati Cincinnati Ohio 45221USA

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Enhanced neutrino polarizability

S. Bansal,1G. Paz,2A.A. Petrov,2,3M. Tammaro,4J. Zupan,1

1Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221,USA

2Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA

3Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina

29205, USA

4Jozef Stefan Institute, Jamova 39, Ljubljana, Slovenia

E-mail: saurabhbansal20@gmail.com,gilpaz@wayne.edu,apetrov@sc.edu,

michele.tammaro@ijs.si,zupanje@ucmail.uc.edu

Abstract: We point out that neutrinos can have enhanced couplings to photons, if light

(pseudo)scalar mediators are present, resulting in a potentially measurable neutrino po-

larizability. We show that the expected suppression from small neutrino masses can be

compensated by the light mediator mass, generating dimension 7 Rayleigh operators at

low scales. We explore the rich phenomenology of such models, computing in details the

constraints on the viable parameter space, spanned by the couplings of the mediator to

neutrinos and photons. Finally, we build several explicit models that lead to an enhanced

neutrino polarizability by modifying the inverse see-saw majoron, i.e., the pseudo-Nambu-

Goldstone boson of the U(1)Lglobal lepton number responsible for generating small neu-

trino masses.

arXiv:2210.05706v2 [hep-ph] 9 Dec 2022

Contents

1 Introduction 2

2 Neutrino couplings to photons 4

2.1 Neutrino dipole moments 5

2.2 Neutrino anapole moments 6

2.3 Light scalar mediator model for enhanced neutrino polarizability 7

3 Cosmological constraints 9

3.1 Constraints from Planck 10

3.2 Constraints from BBN 15

3.3 Neutrino decay 16

4 Stellar cooling constraints 17

4.1 Horizontal branch stars 19

4.2 Supernova cooling 20

5 Bounds from terrestrial experiments 22

5.1 Bounds from Borexino 22

5.2 Bounds from dark matter detectors 24

5.3 Bounds from MiniBoone 25

5.4 Collider constraints 27

6 UV models of enhanced neutrino polarizability 30

6.1 Minimal singlet Majoron 30

6.2 Majoron as a QCD axion 31

6.3 Majoron from inverse see-saw with extra triplet fermions 32

6.3.1 The inverse see-saw sector 33

6.3.2 Couplings to photons via heavy electroweak triplets 34

6.4 Enhanced neutrino polarizability from U(1)L×U(1)035

7 Conclusions 37

A Notations and conventions 38

B Further details on stellar cooling rate calculations 39

B.1 Primakoﬀ conversion 39

B.2 Photon and neutrino coalescence 41

C Rare decays of heavy (pseudo)scalars 42

C.1 Constraints from invisible decay widths 43

C.2 Recasting the monophoton search 44

– 1 –

1 Introduction

Electromagnetic interactions of neutrinos serve as a primary venue for discovering new

physics interactions. It can be viewed as a qualitatively diﬀerent pathway to uncover

physics beyond the standard model compared to the observation of neutrino masses two

decades ago [1]. For instance, if neutrinos are of the Majorana type, their masses do point

to a new physical scale, Λ, since in this case the neutrino masses are generated through a

non-renormalizable dimension-5 Weinberg operator, L ⊃ y0

ij¯

iHc†H†Lj/Λ. However, it

is equally possible that neutrinos are of the Dirac type, in which case the neutrino masses

are due to the renormalizable Yukawa interactions, L ⊃ yij¯νRiH†Lj. To be certain that

the neutrino masses imply the existence of a new physics scale, ∆L= 2 neutrinoless double

βdecay needs to be discovered ﬁrst, see, e.g., [2–4].

In contrast, if neutrinos are found to couple directly to photons in the current or

immediately planned experiments, this would unambiguously point to the existence of a

new physical scale. The operators of the lowest dimension, invariant under SU(2)L×U(1)Y,

that couple neutrinos to photons Fµν are the dipole operators, which for Dirac neutrinos

are of dimension 6, ¯νRiσµν H†LjBµν /Λ2, and the dimension 8 Rayleigh operators such

as ¯νRiHLjBµν Bµν /Λ4(similar operators can be written for the weak isospin ﬁelds Wa

µν

by direct substitutions of the weak hypercharge ﬁelds Bµν ). After the Higgs obtains a

vev, H= (0, v)/√2, these operators lead to neutrino dipole moments, ¯νRiσµν νLj Fµν ,

and neutrino polarizability1, ¯νRiνLjFµν Fµν , respectively. The Dirac neutrino mass term,

mν¯νLνR, as well as the neutrino dipole moments and the neutrino polarizability operators,

are all chirality ﬂipping. The new physics that generates at some loop-level the neutrino

dipole moments and/or the neutrino polarizability is, therefore, expected to generate at

the same loop-level also the contributions to the neutrino masses. Unless there are large

cancellations between tree level and radiatively generated contributions to the neutrino

masses, the dipole moments and polarizability thus need to be tiny, eﬀectively proportional

to the tiny neutrino masses, mν, and out of reach of the experiments. In this manuscript,

we show that this is not necessarily the case for Rayleigh operators, for which the mν

suppression can be parametrically compensated if the couplings to photons arise from tree-

level exchanges of light new physics.

Similar naive dimensional analysis arguments apply to Majorana neutrinos, though

with several important diﬀerences. First, if neutrinos are Majorana, the same operators:

the neutrino mass term, the dipole, and the Rayleigh operators, require an extra Higgs

insertion compared to Dirac neutrinos. That is, for Majorana neutrinos the mass term

is of dimension 5, the dipole operators are of dimension 7, ¯

iHσµν H†LjBµν , while

Rayleigh operators are of dimension 9, ¯

iHc†H†LjBµν Bµν (and similarly for Wa

µν ). More

importantly, these operators violate the lepton number by ∆L= 2. This breaking is

1In the manuscript we use interchangeably neutrino polarizability and neutrino Rayleigh operators.

– 2 –

expected to be small, explaining why the neutrino masses are small and implying that the

neutrino magnetic moment and neutrino polarizability will be small.

There are, however, exceptions to this general rule. First of all, for Majorana neutrinos,

the tensor and scalar neutrino currents have deﬁnite symmetry under the interchange of

the neutrinos (unlike in the case of Dirac neutrinos). Since ¯νc

iLσµν νjL =−¯νc

jLσµν νiL is odd,

while ¯νc

iLνjL = ¯νc

jLνiL is even under the interchange of the two neutrinos, any new physics

that is odd under the same ﬂavor exchange will only contribute to the neutrino magnetic

moments and not to the neutrino masses [5]. This has been used in Refs. [6–9] to build

explicit models of enhanced neutrino magnetic moments.

No such symmetry distinguishes the neutrino mass operator from the Rayleigh opera-

tors since the neutrino currents in both are exactly the same. Neutrino polarizability is thus

inevitably suppressed by the same small ∆L= 2 breaking spurion as neutrino masses. That

is, neutrino polarizability is model-independently proportional to tiny neutrino masses.

However, it can still be parametrically enhanced if generated by a tree-level exchange

of a light scalar or pseudo-scalar mediator. A prototypical example is a pseudo-Nambu-

Goldstone boson (pNGB) due to spontaneous breaking of the lepton number – the majoron,

which couples derivatively to the ∆L= 2 current, i¯νc

LνL∂µφ/fφ→ −imννc

LνLφ/fφ. Gener-

ically, majoron also couples to photons through a higher dimension operator, φF F/Λγ.

For the minimal majoron, this operator is additionally suppressed by the majoron mass

squared, m2

φ, while this suppression is absent in non-minimal models. At energies below

mφthis then leads to the neutrino polarizability of the form ννF F ×(mν/fφ)×1/(m2

φΛγ).

The small majoron mass compensates for the mνsuppression, leading to parametrically

enhanced neutrino polarizability within reach of astrophysical and terrestrial experiments.

In this manuscript, we perform the ﬁrst phenomenological analysis of the existing con-

straints and possible future probes of neutrino polarizability over a wide range of mediator

masses, from eV, i.e., comparable to the neutrino masses, up to the GeV scale.

The paper is organized as follows. In Section 2, we introduce the neutrino dipole,

anapole, and polarizability operators within an EFT framework. The enhanced neutrino

polarizability via a light mediator exchange is detailed in Sec. 2.3. In Section 3, we explore

the consequences of this interaction for cosmological observables such as Cosmic Microwave

Background (CMB) and Big Bang Nucleosynthesis (BBN). In Section 4, we analyze bounds

from anomalous star cooling rates due to the production of light φparticles. At higher

energy scales, the Rayleigh operator can be probed with neutrino scatterings in terrestrial

experiments, including the production of φparticles in colliders; these are discussed in

Section 5. In Section 6, we discuss UV complete models that lead to enhanced neutrino

polarizability, focusing on spontaneously broken U(1)L. Our conclusions are summarized in

Section 7. Appendix Acontains our notation and conventions, while appendix Bcontains

further details on the calculation of production rates of light (pseudo)scalars in stellar

cores. Appendix Ccontains further details on constraints from invisible decays of heavy

(pseudo)scalars.

– 3 –

2 Neutrino couplings to photons

Neutrino couplings to photons arise from higher dimensional operators. Using the nota-

tion of Ref. [10] and restricting the discussion to low energies, well below the electroweak

symmetry breaking scale, the relevant operators are given by2(see also Appendix A),

LEFT ⊃X

i>j

C(5)

1,ij

8π2(¯νiσµν PLνj)Fµν +1

i,j C(7)

1,ij

Λ3

12π(¯νiPLνj)Fµν Fµν

+C(7)

2,ij

Λ3

8π(¯νiPLνj)Fµν ˜

Fµν + h.c.+··· ,

(2.1)

with ellipses denoting higher dimension terms. The indices i, j =e, µ, τ represent the

SM neutrino ﬂavors, while Fµν is the electromagnetic ﬁeld strength tensor, with ˜

Fµν =

2µνρσ Fρσ its dual. Here, and in the rest of the paper, the neutrinos, νi, are assumed to be

Majorana fermions. Throughout the manuscript, we also use the four-component notation

with the conventions from Ref. [11], so that ν=νc.

The dimension 5 operators in (2.1) encode the neutrino dipole moments. For Majorana

neutrinos the ﬂavor conserving dipole moments vanish because the dipole is antisymmetric

in ﬂavor indices, (¯νiσµν PLνj) = −(¯νjσµν PLνi). The dimension-7 Rayleigh operators, on

the other hand, are symmetric in ﬂavor indices, C(7)

1,ij =C(7)

1,ji, and thus mediate also ﬂavor

diagonal transitions. The deﬁnitions of the Wilson coeﬃcients in (2.1) include the loop

factor, anticipating that in many models the operators would be generated at one loop,

while Λ is the mass scale associated with the masses of particles running in the loop (see

also the discussion below and in Section 6).

Below we will also use a short hand notation, where Λ is absorbed in the deﬁnitions

of the Wilson coeﬃcients that now become dimensionful,

C(7)

1(2),ij ≡ C(7)

1(2),ij/Λ3.(2.2)

Quite often we will also assume that the neutrino polarizability is ﬂavor diagonal, so that

(no summation implied)

C(7)

1(2),ij =ˆ

C(7)

1(2),iδij ,(2.3)

and similarly for dimensionless Wilson coeﬃcients, C(7)

1(2),ij. For ﬂavor universal case we will

denote

C(7)

1(2),ij =ˆ

C(7)

1(2)δij ,(2.4)

Finally, we also deﬁne

CRe

1(2) =X

2 Re hˆ

C(7)

1(2),iji.(2.5)

In the remainder of this section we discuss in more detail the neutrino dipole moments

(Sec. 2.1), neutrino anapole moments (Sec. 2.2), and neutrino polarizability (Sec. 2.3),

including possible enhancements.

2The dimension six anapole moment operator induces a contact interaction and can be replaced through

the use of the equation of motion by the four fermion operators, a choice made in the construction of the

complete basis in Ref. [10]. See Section 2.2 for further details.

– 4 –

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EnhancedneutrinopolarizabilityS.Bansal,1G.Paz,2A.A.Petrov,2;3M.Tammaro,4J.Zupan,11DepartmentofPhysics,UniversityofCincinnati,Cincinnati,Ohio45221,USA2DepartmentofPhysicsandAstronomy,WayneStateUniversity,Detroit,Michigan48201,USA3DepartmentofPhysicsandAstronomy,UniversityofSouthCarolina,Columbia,Sout...

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Enhanced neutrino polarizability S. Bansal1G. Paz2A.A. Petrov23M. Tammaro4J. Zupan1 1Department of Physics University of Cincinnati Cincinnati Ohio 45221USA

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