PIUAN-2022-718FT Probing Freeze-in Dark Matter via Heavy Neutrino Portal Basabendu Barman1 2 P. S. Bhupal Dev3 4 and Anish Ghoshal2

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PI/UAN-2022-718FT

Probing Freeze-in Dark Matter via Heavy Neutrino Portal

Basabendu Barman,1, 2, ∗P. S. Bhupal Dev,3, 4, †and Anish Ghoshal2, ‡

1Centro de Investigaciones, Universidad Antonio Nari˜no

Carrera 3 este # 47A-15, Bogot´a, Colombia

2Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,

ul. Pasteura 5, 02-093 Warsaw, Poland

3Department of Physics and McDonnell Center for the Space Sciences,

Washington University, St. Louis, MO 63130, USA

4Theoretical Physics Department, Fermilab,

P.O. Box 500, Batavia, IL 60510, USA

arXiv:2210.07739v3 [hep-ph] 24 Aug 2023

Abstract

We explore the possibility of probing freeze-in dark matter (DM) produced via the right-handed

neutrino (RHN) portal using the RHN search experiments. We focus on a simpliﬁed framework of

minimally-extended type-I seesaw model consisting of only four free parameters, namely the RHN

mass, the fermionic DM mass, the Yukawa coupling between the DM and the RHN, and a real

singlet scalar mass. We consider two cases for the DM production either via decay of the thermal

RHN or via scattering of the bath particles mediated by the RHN. In both cases, we show that for

sub-TeV scale DM masses, the allowed model parameter space satisfying the observed DM relic

density for freeze-in scenario falls within the reach of current and future collider, beam dump and

forward physics facilities looking for feebly-coupled heavy neutrinos.

I. INTRODUCTION

The nature of dark matter (DM) remains mysterious and one of the most important

questions in fundamental physics today [1]. On one hand, we have overwhelming evidence

of DM as the dominant matter component of our Universe today from a plethora of cosmo-

logical and astrophysical observations [2]. On the other hand, there is no ﬁrm evidence for

DM coupling to the Standard Model (SM) sector except via gravity. No matter how non-

gravitational DM interactions may manifest, it would require some beyond the SM (BSM)

physics to provide a suitable particle DM candidate [3].

Among various possible DM candidates, the Weakly Interacting Massive Particle (WIMP) [4]

paradigm has gained a lot of attention so far, thanks to its miraculous property of being

able to reproduce the observed relic abundance via weak-scale interaction cross-sections for

a wide range of DM masses [5,6]. In spite of being so appealing, the strong experimental

constraints (from direct detection, indirect detection and colliders) on the typical WIMP

parameter space [7,8] have recently motivated quests for DM beyond the standard WIMP

paradigm [9].

Since DM is electrically neutral, a simple alternative to the WIMP paradigm (where the

DM is typically the neutral component of an electroweak multiplet; see e.g. Ref. [10]) is to

∗basabendu88barman@gmail.com

†bdev@wustl.edu

‡anish.ghoshal@fuw.edu.pl

have the DM as a pure singlet under the SM gauge group. In this case, the DM can interact

with the SM sector only via the so-called ‘portals’. There exist only three such portals in the

SM, depending on whether the mediator has spin-0 (Higgs portal) [11–23], spin-1 (vector

portal) [24–35], or spin-1/2 (neutrino portal) [26,36–64]. In this paper, we will focus on the

neutrino portal scenario which is particularly interesting because of its intimate connection

to neutrino mass – another outstanding puzzle that also calls for some BSM physics [65].

A simple realization of the neutrino portal relies on DM interactions being mediated

by SM gauge-singlet right-handed neutrinos (RHNs), also known as the sterile neutrinos

or heavy neutral leptons in the literature. The RHNs are well motivated from the type-I

seesaw mechanism for neutrino mass generation [66–71]. Depending on their mass and Dirac

Yukawa couplings, which together determine their mixing with the SM neutrinos, the RHNs

can be searched for in a wide range of experiments, such as beta decay, meson decay, beam

dump, and colliders; for a comprehensive summary of the existing constraints and future

prospects of RHN searches, see e.g. Refs. [72–74]. In this paper, we show that the same RHN

parameter space that can be probed in future experiments can also reproduce the observed

DM relic density, if the RHNs are the only mediators between the SM and the DM sectors.

In addition, we will assume that the portal couplings to the dark sector are suﬃciently

small so that the DM never reaches chemical equilibrium with the thermal bath. In this

case, the DM is slowly populated in the Universe by either decay or annihilation processes

involving the RHNs, until the production ceases due to Boltzmann suppression as the Hubble

temperature drops below the RHN mass. Therefore, this is a freeze-in, or feebly interacting

massive particles (FIMP) DM scenario [75,76], in contrast with the freeze-out scenario for

WIMPs. Due to their tiny interaction strength with the visible sector, FIMPs are inherently

very diﬃcult to search for directly in conventional DM direct detection, indirect detection,

or collider experiments1. However, unlike freeze-out, for freeze-in one typically looks for

signatures of the portal itself and its associated tiny couplings. For instance, the feeble

couplings associated with the portal could make either the heavier dark sector particles

or the mediator itself long-lived, leading to signatures in lifetime and intensity frontier

experiments [79]. Other examples involving properties of the individual BSM models like

kinetic mixing [77], temperature corrections [80,81] and scale-invariance [82,83] have been

proposed for freeze-in mechanism that can be searched for in direct detection experiments as

1Direct detection prospects of FIMP-like DM have been discussed in, for example, Refs. [77,78].

well. Similarly, a non-standard cosmological era can also make freeze-in sensitive to indirect

detection [56].

In this paper, we show that the RHN portal eﬀectively provides a complementary labo-

ratory probe of the FIMP DM scenario. Although we study the minimal type-I seesaw for

concreteness, our prescription for RHN-portal searches is generic and can also be applied

to other neutrino mass models, such as inverse seesaw [84] and radiative models [85,86],

as well as to other dark singlet fermion portal models (see e.g. Refs. [87–89], and references

therein). The main novelty of our analysis is the projection of FIMP DM-allowed param-

eter space onto the RHN mass-mixing plane, which makes it straightforward to correlate

the RHN-portal freeze-in parameter space with the experimental detection prospects at the

RHN-frontier.

The rest of the paper is organized as follows. In Sec. II we have introduced the details

of the RHN portal freeze-in DM model under consideration. We then discuss the DM

phenomenology in Sec. III, where we elucidate the sensitivity reach of present and future

experiments in probing the relic density allowed parameter space, possible collider search

prospects for this model is discussed in Sec. V, and ﬁnally we conclude in Sec. VI. Freeze-in

reaction densities are presented in Appendix A, relevant RHN decay widths, together with

DM production cross-sections are listed in Appendix Band Appendix Crespectively, ﬁnally,

production cross-sections for φare reported in Appendix D.

II. THE MODEL

We extend the SM particle content with the addition of the following:

•SM gauge-singlet RHNs Ni. We need at least two RHNs (i.e., i= 1,2) in order to

reproduce two nonzero mass-squared diﬀerences, as observed in neutrino oscillation

data, using the seesaw mechanism. For our current interest, a hierarchical spectrum

can be assumed, so that only the lightest RHN N1will be relevant for us.2

•A gauge-singlet Majorana fermion χwhich serves as the DM candidate. Note that a

Dirac fermion would also serve the purpose, but at the expense of doubling the degrees

2If the RHN mass is the keV range and its Yukawa couplings are suﬃciently small, then it could be a

DM candidate itself [90–92], but here we are interested in the Yukawa couplings relevant for seesaw and

potentially accessible in laboratory experiments.

of freedom.

•A real singlet scalar φwhich is needed to connect the DM to the RHN portal.

We will assume that both χand φare charged under a Z2symmetry and that χis lighter

than φto ensure the stability of the DM. The SM particles and the RHNs are assumed to be

even under this Z2symmetry, which forbids couplings between SM and dark sector particles

(χ,φ). The relevant piece of the Lagrangian giving rise to neutrino mass is given by

−Lν= (YD)αj LαH Nj+1

2(MN)ij Nc

iNj+ H.c. ,(1)

where Land Hare the SU(2)Llepton and Higgs doublets respectively, and α=e, µ, τ is the

ﬂavor index. The interaction Lagrangian for the dark sector containing the singlet Majorana

DM χand the real singlet scalar φreads

−Ldark =yχNcφ χ +mχχcχ+V(H, φ) + H.c. ,(2)

where V(H, φ) is the scalar potential (see below) and we have assumed a universal coupling

of DM to the RHNs. The RHNs serve as the portal to mediate the interactions between

the dark and visible sectors, owing to the couplings YDand yχ. Note that the same YDis

also involved in active-sterile neutrino mixing, leading to light neutrino mass generation via

type-I seesaw mechanism.

Once the SM Higgs doublet gets a nonzero vacuum expectation value (VEV)

H=1

√2

0

h+v

(3)

with v≃246 GeV, we obtain the Dirac mass matrix MD=YD⟨H⟩. The singlet scalar φ,

on the other hand, does not acquire a VEV, and therefore, there is no mixing between the

DM and the RHNs. The Lagrangian in Eq. (1) in the ﬂavor basis then reads

−Lν=1

2(νL)cNM

νL

Nc

+ H.c. ,(4)

where the mass matrix can be realized as

M=

0MD

DMN

,(5)

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PI/UAN-2022-718FTProbingFreeze-inDarkMatterviaHeavyNeutrinoPortalBasabenduBarman,1,2,∗P.S.BhupalDev,3,4,†andAnishGhoshal2,‡1CentrodeInvestigaciones,UniversidadAntonioNari˜noCarrera3este#47A-15,Bogot´a,Colombia2InstituteofTheoreticalPhysics,FacultyofPhysics,UniversityofWarsaw,ul.Pasteura5,02-093Warsa...

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